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
[ 34, 44, 93, 24 ]
95
[ "44+24=68", "68/34=2", "93+2=95" ]
Current State: 95:[34, 44, 93, 24], Operations: [] Exploring Operation: 44+24=68, Resulting Numbers: [34, 93, 68] Generated Node #2: [34, 93, 68] from Operation: 44+24=68 Current State: 95:[34, 93, 68], Operations: ['44+24=68'] Exploring Operation: 68/34=2, Resulting Numbers: [93, 2] Generated Node #3: [93, 2] from Operation: 68/34=2 Current State: 95:[93, 2], Operations: ['44+24=68', '68/34=2'] Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[34, 44, 93, 24], Operations: [] Exploring Operation: 34+44=78, Resulting Numbers: [93, 24, 78] Generated Node #0,0: 95:[93, 24, 78] Operation: 34+44=78 Exploring Operation: 44-24=20, Resulting Numbers: [34, 93, 20] Generated Node #0,1: 95:[34, 93, 20] Operation: 44-24=20 Exploring Operation: 44-34=10, Resulting Numbers: [93, 24, 10] Generated Node #0,2: 95:[93, 24, 10] Operation: 44-34=10 Moving to Node #0,2 Current State: 95:[93, 24, 10], Operations: ['44-34=10'] Exploring Operation: 24-10=14, Resulting Numbers: [93, 14] Generated Node #0,2,0: 95:[93, 14] Operation: 24-10=14 Exploring Operation: 93-10=83, Resulting Numbers: [24, 83] Generated Node #0,2,1: 95:[24, 83] Operation: 93-10=83 Exploring Operation: 93+10=103, Resulting Numbers: [24, 103] Generated Node #0,2,2: 95:[24, 103] Operation: 93+10=103 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 95:[93, 14], Operations: ['44-34=10', '24-10=14'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 93*14=1302, Resulting Numbers: [1302] 1302,95 unequal: No Solution Exploring Operation: 93+14=107, Resulting Numbers: [107] 107,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 95:[24, 103], Operations: ['44-34=10', '93+10=103'] Exploring Operation: 103-24=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 24*103=2472, Resulting Numbers: [2472] 2472,95 unequal: No Solution Exploring Operation: 24+103=127, Resulting Numbers: [127] 127,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 95:[24, 83], Operations: ['44-34=10', '93-10=83'] Exploring Operation: 24*83=1992, Resulting Numbers: [1992] 1992,95 unequal: No Solution Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,95 unequal: No Solution Exploring Operation: 24+83=107, Resulting Numbers: [107] 107,95 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: 95:[34, 93, 20], Operations: ['44-24=20'] Exploring Operation: 34-20=14, Resulting Numbers: [93, 14] Generated Node #0,1,0: 95:[93, 14] Operation: 34-20=14 Exploring Operation: 93+20=113, Resulting Numbers: [34, 113] Generated Node #0,1,1: 95:[34, 113] Operation: 93+20=113 Exploring Operation: 34+93=127, Resulting Numbers: [20, 127] Generated Node #0,1,2: 95:[20, 127] Operation: 34+93=127 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[93, 14], Operations: ['44-24=20', '34-20=14'] Exploring Operation: 93+14=107, Resulting Numbers: [107] 107,95 unequal: No Solution Exploring Operation: 93*14=1302, Resulting Numbers: [1302] 1302,95 unequal: No Solution Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[34, 113], Operations: ['44-24=20', '93+20=113'] Exploring Operation: 34+113=147, Resulting Numbers: [147] 147,95 unequal: No Solution Exploring Operation: 113-34=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 34*113=3842, Resulting Numbers: [3842] 3842,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 95:[20, 127], Operations: ['44-24=20', '34+93=127'] Exploring Operation: 20+127=147, Resulting Numbers: [147] 147,95 unequal: No Solution Exploring Operation: 127-20=107, Resulting Numbers: [107] 107,95 unequal: No Solution Exploring Operation: 20*127=2540, Resulting Numbers: [2540] 2540,95 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: 95:[93, 24, 78], Operations: ['34+44=78'] Exploring Operation: 24+78=102, Resulting Numbers: [93, 102] Generated Node #0,0,0: 95:[93, 102] Operation: 24+78=102 Exploring Operation: 93-78=15, Resulting Numbers: [24, 15] Generated Node #0,0,1: 95:[24, 15] Operation: 93-78=15 Exploring Operation: 78-24=54, Resulting Numbers: [93, 54] Generated Node #0,0,2: 95:[93, 54] Operation: 78-24=54 Moving to Node #0,0,0 Current State: 95:[93, 102], Operations: ['34+44=78', '24+78=102'] Exploring Operation: 93*102=9486, Resulting Numbers: [9486] 9486,95 unequal: No Solution Exploring Operation: 102-93=9, Resulting Numbers: [9] 9,95 unequal: No Solution Exploring Operation: 93+102=195, Resulting Numbers: [195] 195,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[24, 15], Operations: ['34+44=78', '93-78=15'] Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,95 unequal: No Solution Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,95 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[93, 54], Operations: ['34+44=78', '78-24=54'] Exploring Operation: 93+54=147, Resulting Numbers: [147] 147,95 unequal: No Solution Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,95 unequal: No Solution Exploring Operation: 93*54=5022, Resulting Numbers: [5022] 5022,95 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 83, 80, 27, 82 ]
73
[ "83-80=3", "27/3=9", "82-9=73" ]
Current State: 73:[83, 80, 27, 82], Operations: [] Exploring Operation: 83-80=3, Resulting Numbers: [27, 82, 3] Generated Node #2: [27, 82, 3] from Operation: 83-80=3 Current State: 73:[27, 82, 3], Operations: ['83-80=3'] Exploring Operation: 27/3=9, Resulting Numbers: [82, 9] Generated Node #3: [82, 9] from Operation: 27/3=9 Current State: 73:[82, 9], Operations: ['83-80=3', '27/3=9'] Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[83, 80, 27, 82], Operations: [] Exploring Operation: 83-27=56, Resulting Numbers: [80, 82, 56] Generated Node #0,0: 73:[80, 82, 56] Operation: 83-27=56 Exploring Operation: 80-27=53, Resulting Numbers: [83, 82, 53] Generated Node #0,1: 73:[83, 82, 53] Operation: 80-27=53 Exploring Operation: 82-27=55, Resulting Numbers: [83, 80, 55] Generated Node #0,2: 73:[83, 80, 55] Operation: 82-27=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[80, 82, 56], Operations: ['83-27=56'] Exploring Operation: 82-56=26, Resulting Numbers: [80, 26] Generated Node #0,0,0: 73:[80, 26] Operation: 82-56=26 Exploring Operation: 80-56=24, Resulting Numbers: [82, 24] Generated Node #0,0,1: 73:[82, 24] Operation: 80-56=24 Exploring Operation: 80+56=136, Resulting Numbers: [82, 136] Generated Node #0,0,2: 73:[82, 136] Operation: 80+56=136 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[80, 26], Operations: ['83-27=56', '82-56=26'] Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 80*26=2080, Resulting Numbers: [2080] 2080,73 unequal: No Solution Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,73 unequal: No Solution No 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: 73:[82, 24], Operations: ['83-27=56', '80-56=24'] Exploring Operation: 82+24=106, Resulting Numbers: [106] 106,73 unequal: No Solution Exploring Operation: 82*24=1968, Resulting Numbers: [1968] 1968,73 unequal: No Solution Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,73 unequal: No Solution No 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: 73:[82, 136], Operations: ['83-27=56', '80+56=136'] Exploring Operation: 82*136=11152, Resulting Numbers: [11152] 11152,73 unequal: No Solution Exploring Operation: 136-82=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 82+136=218, Resulting Numbers: [218] 218,73 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: 73:[83, 80, 55], Operations: ['82-27=55'] Exploring Operation: 80-55=25, Resulting Numbers: [83, 25] Generated Node #0,2,0: 73:[83, 25] Operation: 80-55=25 Exploring Operation: 83-55=28, Resulting Numbers: [80, 28] Generated Node #0,2,1: 73:[80, 28] Operation: 83-55=28 Exploring Operation: 83+55=138, Resulting Numbers: [80, 138] Generated Node #0,2,2: 73:[80, 138] Operation: 83+55=138 Moving to Node #0,2,1 Current State: 73:[80, 28], Operations: ['82-27=55', '83-55=28'] Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,73 unequal: No Solution Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[83, 25], Operations: ['82-27=55', '80-55=25'] Exploring Operation: 83*25=2075, Resulting Numbers: [2075] 2075,73 unequal: No Solution Exploring Operation: 83+25=108, Resulting Numbers: [108] 108,73 unequal: No Solution Exploring Operation: 83-25=58, Resulting Numbers: [58] 58,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[80, 138], Operations: ['82-27=55', '83+55=138'] Exploring Operation: 80+138=218, Resulting Numbers: [218] 218,73 unequal: No Solution Exploring Operation: 80*138=11040, Resulting Numbers: [11040] 11040,73 unequal: No Solution Exploring Operation: 138-80=58, Resulting Numbers: [58] 58,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[83, 82, 53], Operations: ['80-27=53'] Exploring Operation: 82-53=29, Resulting Numbers: [83, 29] Generated Node #0,1,0: 73:[83, 29] Operation: 82-53=29 Exploring Operation: 83-53=30, Resulting Numbers: [82, 30] Generated Node #0,1,1: 73:[82, 30] Operation: 83-53=30 Exploring Operation: 83+53=136, Resulting Numbers: [82, 136] Generated Node #0,1,2: 73:[82, 136] Operation: 83+53=136 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[82, 30], Operations: ['80-27=53', '83-53=30'] Exploring Operation: 82*30=2460, Resulting Numbers: [2460] 2460,73 unequal: No Solution Exploring Operation: 82+30=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 82-30=52, Resulting Numbers: [52] 52,73 unequal: No Solution No 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: 73:[83, 29], Operations: ['80-27=53', '82-53=29'] Exploring Operation: 83*29=2407, Resulting Numbers: [2407] 2407,73 unequal: No Solution Exploring Operation: 83+29=112, Resulting Numbers: [112] 112,73 unequal: No Solution Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,73 unequal: No Solution No 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: 73:[82, 136], Operations: ['80-27=53', '83+53=136'] Exploring Operation: 82*136=11152, Resulting Numbers: [11152] 11152,73 unequal: No Solution Exploring Operation: 136-82=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 82+136=218, Resulting Numbers: [218] 218,73 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
[ 98, 16, 77, 10 ]
47
[ "98+16=114", "77-10=67", "114-67=47" ]
Current State: 47:[98, 16, 77, 10], Operations: [] Exploring Operation: 98+16=114, Resulting Numbers: [77, 10, 114] Generated Node #2: [77, 10, 114] from Operation: 98+16=114 Current State: 47:[77, 10, 114], Operations: ['98+16=114'] Exploring Operation: 77-10=67, Resulting Numbers: [114, 67] Generated Node #3: [114, 67] from Operation: 77-10=67 Current State: 47:[114, 67], Operations: ['98+16=114', '77-10=67'] Exploring Operation: 114-67=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[98, 16, 77, 10], Operations: [] Exploring Operation: 77-16=61, Resulting Numbers: [98, 10, 61] Generated Node #0,0: 47:[98, 10, 61] Operation: 77-16=61 Exploring Operation: 98-77=21, Resulting Numbers: [16, 10, 21] Generated Node #0,1: 47:[16, 10, 21] Operation: 98-77=21 Exploring Operation: 98-16=82, Resulting Numbers: [77, 10, 82] Generated Node #0,2: 47:[77, 10, 82] Operation: 98-16=82 Exploring Operation: 98-10=88, Resulting Numbers: [16, 77, 88] Generated Node #0,3: 47:[16, 77, 88] Operation: 98-10=88 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[16, 10, 21], Operations: ['98-77=21'] Exploring Operation: 10+21=31, Resulting Numbers: [16, 31] Generated Node #0,1,0: 47:[16, 31] Operation: 10+21=31 Exploring Operation: 16-10=6, Resulting Numbers: [21, 6] Generated Node #0,1,1: 47:[21, 6] Operation: 16-10=6 Exploring Operation: 16+10=26, Resulting Numbers: [21, 26] Generated Node #0,1,2: 47:[21, 26] Operation: 16+10=26 Exploring Operation: 16+21=37, Resulting Numbers: [10, 37] Generated Node #0,1,3: 47:[10, 37] Operation: 16+21=37 Moving to Node #0,1,0 Current State: 47:[16, 31], Operations: ['98-77=21', '10+21=31'] Exploring Operation: 16*31=496, Resulting Numbers: [496] 496,47 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[98, 16, 77, 10], Operations: [] Exploring Operation: 98-77=21, Resulting Numbers: [16, 10, 21] Generated Node #0,1: 47:[16, 10, 21] Operation: 98-77=21 Moving to Node #0,1 Current State: 47:[16, 10, 21], Operations: ['98-77=21'] Exploring Operation: 10+21=31, Resulting Numbers: [16, 31] Generated Node #0,1,0: 47:[16, 31] Operation: 10+21=31 Moving to Node #0,1,0 Current State: 47:[16, 31], Operations: ['98-77=21', '10+21=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 7, 69, 37, 71 ]
88
[ "7+37=44", "71-69=2", "44*2=88" ]
Current State: 88:[7, 69, 37, 71], Operations: [] Exploring Operation: 7+37=44, Resulting Numbers: [69, 71, 44] Generated Node #2: [69, 71, 44] from Operation: 7+37=44 Current State: 88:[69, 71, 44], Operations: ['7+37=44'] Exploring Operation: 71-69=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 71-69=2 Current State: 88:[44, 2], Operations: ['7+37=44', '71-69=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[7, 69, 37, 71], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [7, 37, 2] Generated Node #0,0: 88:[7, 37, 2] Operation: 71-69=2 Exploring Operation: 69-37=32, Resulting Numbers: [7, 71, 32] Generated Node #0,1: 88:[7, 71, 32] Operation: 69-37=32 Exploring Operation: 71-37=34, Resulting Numbers: [7, 69, 34] Generated Node #0,2: 88:[7, 69, 34] Operation: 71-37=34 Moving to Node #0,0 Current State: 88:[7, 37, 2], Operations: ['71-69=2'] Exploring Operation: 7+37=44, Resulting Numbers: [2, 44] Generated Node #0,0,0: 88:[2, 44] Operation: 7+37=44 Exploring Operation: 37-7=30, Resulting Numbers: [2, 30] Generated Node #0,0,1: 88:[2, 30] Operation: 37-7=30 Exploring Operation: 37+2=39, Resulting Numbers: [7, 39] Generated Node #0,0,2: 88:[7, 39] Operation: 37+2=39 Moving to Node #0,1 Current State: 88:[7, 71, 32], Operations: ['69-37=32'] Exploring Operation: 71-32=39, Resulting Numbers: [7, 39] Generated Node #0,1,0: 88:[7, 39] Operation: 71-32=39 Exploring Operation: 7+71=78, Resulting Numbers: [32, 78] Generated Node #0,1,1: 88:[32, 78] Operation: 7+71=78 Exploring Operation: 71+32=103, Resulting Numbers: [7, 103] Generated Node #0,1,2: 88:[7, 103] Operation: 71+32=103 Moving to Node #0,2 Current State: 88:[7, 69, 34], Operations: ['71-37=34'] Exploring Operation: 69-34=35, Resulting Numbers: [7, 35] Generated Node #0,2,0: 88:[7, 35] Operation: 69-34=35 Exploring Operation: 69+34=103, Resulting Numbers: [7, 103] Generated Node #0,2,1: 88:[7, 103] Operation: 69+34=103 Exploring Operation: 7+69=76, Resulting Numbers: [34, 76] Generated Node #0,2,2: 88:[34, 76] Operation: 7+69=76 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 88:[7, 35], Operations: ['71-37=34', '69-34=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 88:[7, 103], Operations: ['71-37=34', '69+34=103'] Exploring Operation: 7+103=110, Resulting Numbers: [110] 110,88 unequal: No Solution Exploring Operation: 103-7=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 7*103=721, Resulting Numbers: [721] 721,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[34, 76], Operations: ['71-37=34', '7+69=76'] Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,88 unequal: No Solution Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,88 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: 88:[2, 44], Operations: ['71-69=2', '7+37=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[7, 69, 37, 71], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [7, 37, 2] Generated Node #0,0: 88:[7, 37, 2] Operation: 71-69=2 Moving to Node #0,0 Current State: 88:[7, 37, 2], Operations: ['71-69=2'] Exploring Operation: 7+37=44, Resulting Numbers: [2, 44] Generated Node #0,0,0: 88:[2, 44] Operation: 7+37=44 Moving to Node #0,0,0 Current State: 88:[2, 44], Operations: ['71-69=2', '7+37=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.977431
hs_3
sum_heuristic
[ 61, 68, 28, 22 ]
57
[ "68-61=7", "28+22=50", "7+50=57" ]
Current State: 57:[61, 68, 28, 22], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [28, 22, 7] Generated Node #2: [28, 22, 7] from Operation: 68-61=7 Current State: 57:[28, 22, 7], Operations: ['68-61=7'] Exploring Operation: 28+22=50, Resulting Numbers: [7, 50] Generated Node #3: [7, 50] from Operation: 28+22=50 Current State: 57:[7, 50], Operations: ['68-61=7', '28+22=50'] Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[61, 68, 28, 22], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [61, 68, 6] Generated Node #0,0: 57:[61, 68, 6] Operation: 28-22=6 Exploring Operation: 28+22=50, Resulting Numbers: [61, 68, 50] Generated Node #0,1: 57:[61, 68, 50] Operation: 28+22=50 Exploring Operation: 68-61=7, Resulting Numbers: [28, 22, 7] Generated Node #0,2: 57:[28, 22, 7] Operation: 68-61=7 Moving to Node #0,2 Current State: 57:[28, 22, 7], Operations: ['68-61=7'] Exploring Operation: 28-7=21, Resulting Numbers: [22, 21] Generated Node #0,2,0: 57:[22, 21] Operation: 28-7=21 Exploring Operation: 28-22=6, Resulting Numbers: [7, 6] Generated Node #0,2,1: 57:[7, 6] Operation: 28-22=6 Exploring Operation: 28/7=4, Resulting Numbers: [22, 4] Generated Node #0,2,2: 57:[22, 4] Operation: 28/7=4 Moving to Node #0,0 Current State: 57:[61, 68, 6], Operations: ['28-22=6'] Exploring Operation: 68-6=62, Resulting Numbers: [61, 62] Generated Node #0,0,0: 57:[61, 62] Operation: 68-6=62 Exploring Operation: 68-61=7, Resulting Numbers: [6, 7] Generated Node #0,0,1: 57:[6, 7] Operation: 68-61=7 Exploring Operation: 61-6=55, Resulting Numbers: [68, 55] Generated Node #0,0,2: 57:[68, 55] Operation: 61-6=55 Moving to Node #0,1 Current State: 57:[61, 68, 50], Operations: ['28+22=50'] Exploring Operation: 68-50=18, Resulting Numbers: [61, 18] Generated Node #0,1,0: 57:[61, 18] Operation: 68-50=18 Exploring Operation: 61-50=11, Resulting Numbers: [68, 11] Generated Node #0,1,1: 57:[68, 11] Operation: 61-50=11 Exploring Operation: 68-61=7, Resulting Numbers: [50, 7] Generated Node #0,1,2: 57:[50, 7] Operation: 68-61=7 Moving to Node #0,2,2 Current State: 57:[22, 4], Operations: ['68-61=7', '28/7=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,57 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,57 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[61, 18], Operations: ['28+22=50', '68-50=18'] Exploring Operation: 61+18=79, Resulting Numbers: [79] 79,57 unequal: No Solution Exploring Operation: 61*18=1098, Resulting Numbers: [1098] 1098,57 unequal: No Solution Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[22, 21], Operations: ['68-61=7', '28-7=21'] Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,57 unequal: No Solution Exploring Operation: 22*21=462, Resulting Numbers: [462] 462,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[7, 6], Operations: ['68-61=7', '28-22=6'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[6, 7], Operations: ['28-22=6', '68-61=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,57 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[61, 62], Operations: ['28-22=6', '68-6=62'] Exploring Operation: 62-61=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 61*62=3782, Resulting Numbers: [3782] 3782,57 unequal: No Solution Exploring Operation: 61+62=123, Resulting Numbers: [123] 123,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[50, 7], Operations: ['28+22=50', '68-61=7'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,57 unequal: No Solution Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[61, 68, 28, 22], Operations: [] Exploring Operation: 28+22=50, Resulting Numbers: [61, 68, 50] Generated Node #0,1: 57:[61, 68, 50] Operation: 28+22=50 Moving to Node #0,1 Current State: 57:[61, 68, 50], Operations: ['28+22=50'] Exploring Operation: 68-61=7, Resulting Numbers: [50, 7] Generated Node #0,1,2: 57:[50, 7] Operation: 68-61=7 Moving to Node #0,1,2 Current State: 57:[50, 7], Operations: ['28+22=50', '68-61=7'] Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.96875
hs_3
sum_heuristic
[ 5, 35, 18, 8 ]
63
[ "5*18=90", "35-8=27", "90-27=63" ]
Current State: 63:[5, 35, 18, 8], Operations: [] Exploring Operation: 5*18=90, Resulting Numbers: [35, 8, 90] Generated Node #2: [35, 8, 90] from Operation: 5*18=90 Current State: 63:[35, 8, 90], Operations: ['5*18=90'] Exploring Operation: 35-8=27, Resulting Numbers: [90, 27] Generated Node #3: [90, 27] from Operation: 35-8=27 Current State: 63:[90, 27], Operations: ['5*18=90', '35-8=27'] Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[5, 35, 18, 8], Operations: [] Exploring Operation: 35-18=17, Resulting Numbers: [5, 8, 17] Generated Node #0,0: 63:[5, 8, 17] Operation: 35-18=17 Exploring Operation: 35-8=27, Resulting Numbers: [5, 18, 27] Generated Node #0,1: 63:[5, 18, 27] Operation: 35-8=27 Exploring Operation: 35/5=7, Resulting Numbers: [18, 8, 7] Generated Node #0,2: 63:[18, 8, 7] Operation: 35/5=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[18, 8, 7], Operations: ['35/5=7'] Exploring Operation: 18+8=26, Resulting Numbers: [7, 26] Generated Node #0,2,0: 63:[7, 26] Operation: 18+8=26 Exploring Operation: 18-8=10, Resulting Numbers: [7, 10] Generated Node #0,2,1: 63:[7, 10] Operation: 18-8=10 Exploring Operation: 18-7=11, Resulting Numbers: [8, 11] Generated Node #0,2,2: 63:[8, 11] Operation: 18-7=11 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 63:[7, 10], Operations: ['35/5=7', '18-8=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 63:[8, 11], Operations: ['35/5=7', '18-7=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,63 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 63:[7, 26], Operations: ['35/5=7', '18+8=26'] Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,63 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,63 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,63 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: 63:[5, 8, 17], Operations: ['35-18=17'] Exploring Operation: 17-8=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 63:[5, 9] Operation: 17-8=9 Exploring Operation: 8-5=3, Resulting Numbers: [17, 3] Generated Node #0,0,1: 63:[17, 3] Operation: 8-5=3 Exploring Operation: 5+17=22, Resulting Numbers: [8, 22] Generated Node #0,0,2: 63:[8, 22] Operation: 5+17=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[5, 9], Operations: ['35-18=17', '17-8=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,63 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,63 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 63:[8, 22], Operations: ['35-18=17', '5+17=22'] Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,63 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[17, 3], Operations: ['35-18=17', '8-5=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,63 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,63 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,63 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: 63:[5, 18, 27], Operations: ['35-8=27'] Exploring Operation: 27-5=22, Resulting Numbers: [18, 22] Generated Node #0,1,0: 63:[18, 22] Operation: 27-5=22 Exploring Operation: 27-18=9, Resulting Numbers: [5, 9] Generated Node #0,1,1: 63:[5, 9] Operation: 27-18=9 Exploring Operation: 5+18=23, Resulting Numbers: [27, 23] Generated Node #0,1,2: 63:[27, 23] Operation: 5+18=23 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[5, 9], Operations: ['35-8=27', '27-18=9'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,63 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[18, 22], Operations: ['35-8=27', '27-5=22'] Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,63 unequal: No Solution Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 63:[27, 23], Operations: ['35-8=27', '5+18=23'] Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,63 unequal: No Solution Exploring Operation: 27*23=621, Resulting Numbers: [621] 621,63 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
[ 38, 8, 46, 11 ]
92
[ "38*46=1748", "8+11=19", "1748/19=92" ]
Current State: 92:[38, 8, 46, 11], Operations: [] Exploring Operation: 38*46=1748, Resulting Numbers: [8, 11, 1748] Generated Node #2: [8, 11, 1748] from Operation: 38*46=1748 Current State: 92:[8, 11, 1748], Operations: ['38*46=1748'] Exploring Operation: 8+11=19, Resulting Numbers: [1748, 19] Generated Node #3: [1748, 19] from Operation: 8+11=19 Current State: 92:[1748, 19], Operations: ['38*46=1748', '8+11=19'] Exploring Operation: 1748/19=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[38, 8, 46, 11], Operations: [] Exploring Operation: 38+11=49, Resulting Numbers: [8, 46, 49] Generated Node #0,0: 92:[8, 46, 49] Operation: 38+11=49 Exploring Operation: 38+8=46, Resulting Numbers: [46, 11, 46] Generated Node #0,1: 92:[46, 11, 46] Operation: 38+8=46 Exploring Operation: 8+11=19, Resulting Numbers: [38, 46, 19] Generated Node #0,2: 92:[38, 46, 19] Operation: 8+11=19 Exploring Operation: 38-11=27, Resulting Numbers: [8, 46, 27] Generated Node #0,3: 92:[8, 46, 27] Operation: 38-11=27 Exploring Operation: 11-8=3, Resulting Numbers: [38, 46, 3] Generated Node #0,4: 92:[38, 46, 3] Operation: 11-8=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[8, 46, 49], Operations: ['38+11=49'] Exploring Operation: 46-8=38, Resulting Numbers: [49, 38] Generated Node #0,0,0: 92:[49, 38] Operation: 46-8=38 Exploring Operation: 8+46=54, Resulting Numbers: [49, 54] Generated Node #0,0,1: 92:[49, 54] Operation: 8+46=54 Exploring Operation: 49-8=41, Resulting Numbers: [46, 41] Generated Node #0,0,2: 92:[46, 41] Operation: 49-8=41 Exploring Operation: 49-46=3, Resulting Numbers: [8, 3] Generated Node #0,0,3: 92:[8, 3] Operation: 49-46=3 Exploring Operation: 46+49=95, Resulting Numbers: [8, 95] Generated Node #0,0,4: 92:[8, 95] Operation: 46+49=95 Moving to Node #0,0,2 Current State: 92:[46, 41], Operations: ['38+11=49', '49-8=41'] Exploring Operation: 46*41=1886, Resulting Numbers: [1886] 1886,92 unequal: No Solution Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 46+41=87, Resulting Numbers: [87] 87,92 unequal: No Solution Moving to Node #0,0,3 Current State: 92:[8, 3], Operations: ['38+11=49', '49-46=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,92 unequal: No Solution Moving to Node #0,0,4 Current State: 92:[8, 95], Operations: ['38+11=49', '46+49=95'] Exploring Operation: 8*95=760, Resulting Numbers: [760] 760,92 unequal: No Solution Exploring Operation: 95-8=87, Resulting Numbers: [87] 87,92 unequal: No Solution Exploring Operation: 8+95=103, Resulting Numbers: [103] 103,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[49, 38], Operations: ['38+11=49', '46-8=38'] Exploring Operation: 49-38=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 49*38=1862, Resulting Numbers: [1862] 1862,92 unequal: No Solution Exploring Operation: 49+38=87, Resulting Numbers: [87] 87,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[49, 54], Operations: ['38+11=49', '8+46=54'] Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 49*54=2646, Resulting Numbers: [2646] 2646,92 unequal: No Solution Exploring Operation: 49+54=103, Resulting Numbers: [103] 103,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[46, 11, 46], Operations: ['38+8=46'] Exploring Operation: 46+11=57, Resulting Numbers: [46, 57] Generated Node #0,1,0: 92:[46, 57] Operation: 46+11=57 Exploring Operation: 46-46=0, Resulting Numbers: [11, 0] Generated Node #0,1,1: 92:[11, 0] Operation: 46-46=0 Exploring Operation: 46/46=1, Resulting Numbers: [11, 1] Generated Node #0,1,2: 92:[11, 1] Operation: 46/46=1 Exploring Operation: 46+46=92, Resulting Numbers: [11, 92] Generated Node #0,1,3: 92:[11, 92] Operation: 46+46=92 Exploring Operation: 46-11=35, Resulting Numbers: [46, 35] Generated Node #0,1,4: 92:[46, 35] Operation: 46-11=35 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 92:[11, 92], Operations: ['38+8=46', '46+46=92'] Exploring Operation: 92-11=81, Resulting Numbers: [81] 81,92 unequal: No Solution Exploring Operation: 11*92=1012, Resulting Numbers: [1012] 1012,92 unequal: No Solution Exploring Operation: 11+92=103, Resulting Numbers: [103] 103,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 92:[11, 1], Operations: ['38+8=46', '46/46=1'] Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 92:[11, 0], Operations: ['38+8=46', '46-46=0'] Exploring Operation: 11+0=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 11-0=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 11*0=0, Resulting Numbers: [0] 0,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 92:[46, 57], Operations: ['38+8=46', '46+11=57'] Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 46*57=2622, Resulting Numbers: [2622] 2622,92 unequal: No Solution Exploring Operation: 46+57=103, Resulting Numbers: [103] 103,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 92:[46, 35], Operations: ['38+8=46', '46-11=35'] Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,92 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 92:[8, 46, 27], Operations: ['38-11=27'] Exploring Operation: 27-8=19, Resulting Numbers: [46, 19] Generated Node #0,3,0: 92:[46, 19] Operation: 27-8=19 Exploring Operation: 46-27=19, Resulting Numbers: [8, 19] Generated Node #0,3,1: 92:[8, 19] Operation: 46-27=19 Exploring Operation: 46-8=38, Resulting Numbers: [27, 38] Generated Node #0,3,2: 92:[27, 38] Operation: 46-8=38 Exploring Operation: 8+27=35, Resulting Numbers: [46, 35] Generated Node #0,3,3: 92:[46, 35] Operation: 8+27=35 Exploring Operation: 8+46=54, Resulting Numbers: [27, 54] Generated Node #0,3,4: 92:[27, 54] Operation: 8+46=54 Moving to Node #0,3,0 Current State: 92:[46, 19], Operations: ['38-11=27', '27-8=19'] Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,92 unequal: No Solution Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,92 unequal: No Solution Moving to Node #0,3,1 Current State: 92:[8, 19], Operations: ['38-11=27', '46-27=19'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 8*19=152, Resulting Numbers: [152] 152,92 unequal: No Solution Exploring Operation: 8+19=27, Resulting Numbers: [27] 27,92 unequal: No Solution Moving to Node #0,3,3 Current State: 92:[46, 35], Operations: ['38-11=27', '8+27=35'] Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,92 unequal: No Solution Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,92 unequal: No Solution Moving to Node #0,3,2 Current State: 92:[27, 38], Operations: ['38-11=27', '46-8=38'] Exploring Operation: 27*38=1026, Resulting Numbers: [1026] 1026,92 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 27+38=65, Resulting Numbers: [65] 65,92 unequal: No Solution Moving to Node #0,3,4 Current State: 92:[27, 54], Operations: ['38-11=27', '8+46=54'] Exploring Operation: 54/27=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 27+54=81, Resulting Numbers: [81] 81,92 unequal: No Solution Exploring Operation: 27*54=1458, Resulting Numbers: [1458] 1458,92 unequal: No Solution Exploring Operation: 54-27=27, Resulting Numbers: [27] 27,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 92:[38, 46, 3], Operations: ['11-8=3'] Exploring Operation: 38-3=35, Resulting Numbers: [46, 35] Generated Node #0,4,0: 92:[46, 35] Operation: 38-3=35 Exploring Operation: 38+46=84, Resulting Numbers: [3, 84] Generated Node #0,4,1: 92:[3, 84] Operation: 38+46=84 Exploring Operation: 46-38=8, Resulting Numbers: [3, 8] Generated Node #0,4,2: 92:[3, 8] Operation: 46-38=8 Exploring Operation: 46+3=49, Resulting Numbers: [38, 49] Generated Node #0,4,3: 92:[38, 49] Operation: 46+3=49 Exploring Operation: 38+3=41, Resulting Numbers: [46, 41] Generated Node #0,4,4: 92:[46, 41] Operation: 38+3=41 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 92:[3, 8], Operations: ['11-8=3', '46-38=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,92 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 92:[46, 41], Operations: ['11-8=3', '38+3=41'] Exploring Operation: 46*41=1886, Resulting Numbers: [1886] 1886,92 unequal: No Solution Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 46+41=87, Resulting Numbers: [87] 87,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 92:[3, 84], Operations: ['11-8=3', '38+46=84'] Exploring Operation: 3+84=87, Resulting Numbers: [87] 87,92 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,92 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,92 unequal: No Solution Exploring Operation: 3*84=252, Resulting Numbers: [252] 252,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 92:[46, 35], Operations: ['11-8=3', '38-3=35'] Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,92 unequal: No Solution Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,92 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 92:[38, 49], Operations: ['11-8=3', '46+3=49'] Exploring Operation: 38+49=87, Resulting Numbers: [87] 87,92 unequal: No Solution Exploring Operation: 49-38=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 38*49=1862, Resulting Numbers: [1862] 1862,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[38, 46, 19], Operations: ['8+11=19'] Exploring Operation: 38/19=2, Resulting Numbers: [46, 2] Generated Node #0,2,0: 92:[46, 2] Operation: 38/19=2 Exploring Operation: 38+19=57, Resulting Numbers: [46, 57] Generated Node #0,2,1: 92:[46, 57] Operation: 38+19=57 Exploring Operation: 38-19=19, Resulting Numbers: [46, 19] Generated Node #0,2,2: 92:[46, 19] Operation: 38-19=19 Exploring Operation: 46-38=8, Resulting Numbers: [19, 8] Generated Node #0,2,3: 92:[19, 8] Operation: 46-38=8 Exploring Operation: 38+46=84, Resulting Numbers: [19, 84] Generated Node #0,2,4: 92:[19, 84] Operation: 38+46=84 Moving to Node #0,2,0 Current State: 92:[46, 2], Operations: ['8+11=19', '38/19=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,92 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,92 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,92 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[38, 8, 46, 11], Operations: [] Exploring Operation: 8+11=19, Resulting Numbers: [38, 46, 19] Generated Node #0,2: 92:[38, 46, 19] Operation: 8+11=19 Moving to Node #0,2 Current State: 92:[38, 46, 19], Operations: ['8+11=19'] Exploring Operation: 38/19=2, Resulting Numbers: [46, 2] Generated Node #0,2,0: 92:[46, 2] Operation: 38/19=2 Moving to Node #0,2,0 Current State: 92:[46, 2], Operations: ['8+11=19', '38/19=2'] Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.912326
hs_5
sum_heuristic
[ 37, 58, 17, 30 ]
48
[ "37+58=95", "17+30=47", "95-47=48" ]
Current State: 48:[37, 58, 17, 30], Operations: [] Exploring Operation: 37+58=95, Resulting Numbers: [17, 30, 95] Generated Node #2: [17, 30, 95] from Operation: 37+58=95 Current State: 48:[17, 30, 95], Operations: ['37+58=95'] Exploring Operation: 17+30=47, Resulting Numbers: [95, 47] Generated Node #3: [95, 47] from Operation: 17+30=47 Current State: 48:[95, 47], Operations: ['37+58=95', '17+30=47'] Exploring Operation: 95-47=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[37, 58, 17, 30], Operations: [] Exploring Operation: 58-30=28, Resulting Numbers: [37, 17, 28] Generated Node #0,0: 48:[37, 17, 28] Operation: 58-30=28 Exploring Operation: 37-30=7, Resulting Numbers: [58, 17, 7] Generated Node #0,1: 48:[58, 17, 7] Operation: 37-30=7 Exploring Operation: 37-17=20, Resulting Numbers: [58, 30, 20] Generated Node #0,2: 48:[58, 30, 20] Operation: 37-17=20 Exploring Operation: 58-37=21, Resulting Numbers: [17, 30, 21] Generated Node #0,3: 48:[17, 30, 21] Operation: 58-37=21 Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[17, 30, 21], Operations: ['58-37=21'] Exploring Operation: 30+21=51, Resulting Numbers: [17, 51] Generated Node #0,3,0: 48:[17, 51] Operation: 30+21=51 Exploring Operation: 17+30=47, Resulting Numbers: [21, 47] Generated Node #0,3,1: 48:[21, 47] Operation: 17+30=47 Exploring Operation: 30-17=13, Resulting Numbers: [21, 13] Generated Node #0,3,2: 48:[21, 13] Operation: 30-17=13 Exploring Operation: 30-21=9, Resulting Numbers: [17, 9] Generated Node #0,3,3: 48:[17, 9] Operation: 30-21=9 Moving to Node #0,3,3 Current State: 48:[17, 9], Operations: ['58-37=21', '30-21=9'] Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,48 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[21, 47], Operations: ['58-37=21', '17+30=47'] Exploring Operation: 21+47=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 21*47=987, Resulting Numbers: [987] 987,48 unequal: No Solution Moving to Node #0,3,0 Current State: 48:[17, 51], Operations: ['58-37=21', '30+21=51'] Exploring Operation: 17*51=867, Resulting Numbers: [867] 867,48 unequal: No Solution Exploring Operation: 17+51=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[21, 13], Operations: ['58-37=21', '30-17=13'] Exploring Operation: 21+13=34, Resulting Numbers: [34] 34,48 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 21*13=273, Resulting Numbers: [273] 273,48 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 #0,1 Current State: 48:[58, 17, 7], Operations: ['37-30=7'] Exploring Operation: 17-7=10, Resulting Numbers: [58, 10] Generated Node #0,1,0: 48:[58, 10] Operation: 17-7=10 Exploring Operation: 17+7=24, Resulting Numbers: [58, 24] Generated Node #0,1,1: 48:[58, 24] Operation: 17+7=24 Exploring Operation: 58-7=51, Resulting Numbers: [17, 51] Generated Node #0,1,2: 48:[17, 51] Operation: 58-7=51 Exploring Operation: 58-17=41, Resulting Numbers: [7, 41] Generated Node #0,1,3: 48:[7, 41] Operation: 58-17=41 Moving to Node #0,1,2 Current State: 48:[17, 51], Operations: ['37-30=7', '58-7=51'] Exploring Operation: 17*51=867, Resulting Numbers: [867] 867,48 unequal: No Solution Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,48 unequal: No Solution Exploring Operation: 17+51=68, Resulting Numbers: [68] 68,48 unequal: No Solution Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,48 unequal: No Solution Moving to Node #0,1,3 Current State: 48:[7, 41], Operations: ['37-30=7', '58-17=41'] Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[37, 58, 17, 30], Operations: [] Exploring Operation: 37-30=7, Resulting Numbers: [58, 17, 7] Generated Node #0,1: 48:[58, 17, 7] Operation: 37-30=7 Moving to Node #0,1 Current State: 48:[58, 17, 7], Operations: ['37-30=7'] Exploring Operation: 58-17=41, Resulting Numbers: [7, 41] Generated Node #0,1,3: 48:[7, 41] Operation: 58-17=41 Moving to Node #0,1,3 Current State: 48:[7, 41], Operations: ['37-30=7', '58-17=41'] Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 9, 54, 96, 70 ]
89
[ "9+54=63", "96-70=26", "63+26=89" ]
Current State: 89:[9, 54, 96, 70], Operations: [] Exploring Operation: 9+54=63, Resulting Numbers: [96, 70, 63] Generated Node #2: [96, 70, 63] from Operation: 9+54=63 Current State: 89:[96, 70, 63], Operations: ['9+54=63'] Exploring Operation: 96-70=26, Resulting Numbers: [63, 26] Generated Node #3: [63, 26] from Operation: 96-70=26 Current State: 89:[63, 26], Operations: ['9+54=63', '96-70=26'] Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[9, 54, 96, 70], Operations: [] Exploring Operation: 96-9=87, Resulting Numbers: [54, 70, 87] Generated Node #0,0: 89:[54, 70, 87] Operation: 96-9=87 Exploring Operation: 9+70=79, Resulting Numbers: [54, 96, 79] Generated Node #0,1: 89:[54, 96, 79] Operation: 9+70=79 Exploring Operation: 9+54=63, Resulting Numbers: [96, 70, 63] Generated Node #0,2: 89:[96, 70, 63] Operation: 9+54=63 Exploring Operation: 54-9=45, Resulting Numbers: [96, 70, 45] Generated Node #0,3: 89:[96, 70, 45] Operation: 54-9=45 Exploring Operation: 9+96=105, Resulting Numbers: [54, 70, 105] Generated Node #0,4: 89:[54, 70, 105] Operation: 9+96=105 Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[54, 96, 79], Operations: ['9+70=79'] Exploring Operation: 54+96=150, Resulting Numbers: [79, 150] Generated Node #0,1,0: 89:[79, 150] Operation: 54+96=150 Exploring Operation: 96-79=17, Resulting Numbers: [54, 17] Generated Node #0,1,1: 89:[54, 17] Operation: 96-79=17 Exploring Operation: 96-54=42, Resulting Numbers: [79, 42] Generated Node #0,1,2: 89:[79, 42] Operation: 96-54=42 Exploring Operation: 79-54=25, Resulting Numbers: [96, 25] Generated Node #0,1,3: 89:[96, 25] Operation: 79-54=25 Exploring Operation: 54+79=133, Resulting Numbers: [96, 133] Generated Node #0,1,4: 89:[96, 133] Operation: 54+79=133 Moving to Node #0,1,4 Current State: 89:[96, 133], Operations: ['9+70=79', '54+79=133'] Exploring Operation: 96*133=12768, Resulting Numbers: [12768] 12768,89 unequal: No Solution Exploring Operation: 96+133=229, Resulting Numbers: [229] 229,89 unequal: No Solution Exploring Operation: 133-96=37, Resulting Numbers: [37] 37,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[79, 42], Operations: ['9+70=79', '96-54=42'] Exploring Operation: 79+42=121, Resulting Numbers: [121] 121,89 unequal: No Solution Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 79*42=3318, Resulting Numbers: [3318] 3318,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[79, 150], Operations: ['9+70=79', '54+96=150'] Exploring Operation: 79+150=229, Resulting Numbers: [229] 229,89 unequal: No Solution Exploring Operation: 79*150=11850, Resulting Numbers: [11850] 11850,89 unequal: No Solution Exploring Operation: 150-79=71, Resulting Numbers: [71] 71,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[96, 25], Operations: ['9+70=79', '79-54=25'] Exploring Operation: 96+25=121, Resulting Numbers: [121] 121,89 unequal: No Solution Exploring Operation: 96-25=71, Resulting Numbers: [71] 71,89 unequal: No Solution Exploring Operation: 96*25=2400, Resulting Numbers: [2400] 2400,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[54, 17], Operations: ['9+70=79', '96-79=17'] Exploring Operation: 54+17=71, Resulting Numbers: [71] 71,89 unequal: No Solution Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 54*17=918, Resulting Numbers: [918] 918,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[96, 70, 63], Operations: ['9+54=63'] Exploring Operation: 96+63=159, Resulting Numbers: [70, 159] Generated Node #0,2,0: 89:[70, 159] Operation: 96+63=159 Exploring Operation: 96-63=33, Resulting Numbers: [70, 33] Generated Node #0,2,1: 89:[70, 33] Operation: 96-63=33 Exploring Operation: 96-70=26, Resulting Numbers: [63, 26] Generated Node #0,2,2: 89:[63, 26] Operation: 96-70=26 Exploring Operation: 70-63=7, Resulting Numbers: [96, 7] Generated Node #0,2,3: 89:[96, 7] Operation: 70-63=7 Exploring Operation: 70+63=133, Resulting Numbers: [96, 133] Generated Node #0,2,4: 89:[96, 133] Operation: 70+63=133 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 89:[96, 133], Operations: ['9+54=63', '70+63=133'] Exploring Operation: 96*133=12768, Resulting Numbers: [12768] 12768,89 unequal: No Solution Exploring Operation: 96+133=229, Resulting Numbers: [229] 229,89 unequal: No Solution Exploring Operation: 133-96=37, Resulting Numbers: [37] 37,89 unequal: No Solution No 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: 89:[70, 33], Operations: ['9+54=63', '96-63=33'] Exploring Operation: 70-33=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 70+33=103, Resulting Numbers: [103] 103,89 unequal: No Solution Exploring Operation: 70*33=2310, Resulting Numbers: [2310] 2310,89 unequal: No Solution No 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: 89:[70, 159], Operations: ['9+54=63', '96+63=159'] Exploring Operation: 159-70=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[9, 54, 96, 70], Operations: [] Exploring Operation: 9+54=63, Resulting Numbers: [96, 70, 63] Generated Node #0,2: 89:[96, 70, 63] Operation: 9+54=63 Moving to Node #0,2 Current State: 89:[96, 70, 63], Operations: ['9+54=63'] Exploring Operation: 96+63=159, Resulting Numbers: [70, 159] Generated Node #0,2,0: 89:[70, 159] Operation: 96+63=159 Moving to Node #0,2,0 Current State: 89:[70, 159], Operations: ['9+54=63', '96+63=159'] Exploring Operation: 159-70=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 56, 65, 14, 67 ]
44
[ "65-56=9", "67-14=53", "53-9=44" ]
Current State: 44:[56, 65, 14, 67], Operations: [] Exploring Operation: 65-56=9, Resulting Numbers: [14, 67, 9] Generated Node #2: [14, 67, 9] from Operation: 65-56=9 Current State: 44:[14, 67, 9], Operations: ['65-56=9'] Exploring Operation: 67-14=53, Resulting Numbers: [9, 53] Generated Node #3: [9, 53] from Operation: 67-14=53 Current State: 44:[9, 53], Operations: ['65-56=9', '67-14=53'] Exploring Operation: 53-9=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[56, 65, 14, 67], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [56, 14, 2] Generated Node #0,0: 44:[56, 14, 2] Operation: 67-65=2 Exploring Operation: 67-56=11, Resulting Numbers: [65, 14, 11] Generated Node #0,1: 44:[65, 14, 11] Operation: 67-56=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[56, 14, 2], Operations: ['67-65=2'] Exploring Operation: 56-14=42, Resulting Numbers: [2, 42] Generated Node #0,0,0: 44:[2, 42] Operation: 56-14=42 Exploring Operation: 56/14=4, Resulting Numbers: [2, 4] Generated Node #0,0,1: 44:[2, 4] Operation: 56/14=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[2, 4], Operations: ['67-65=2', '56/14=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[2, 42], Operations: ['67-65=2', '56-14=42'] Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[56, 65, 14, 67], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [56, 14, 2] Generated Node #0,0: 44:[56, 14, 2] Operation: 67-65=2 Moving to Node #0,0 Current State: 44:[56, 14, 2], Operations: ['67-65=2'] Exploring Operation: 56-14=42, Resulting Numbers: [2, 42] Generated Node #0,0,0: 44:[2, 42] Operation: 56-14=42 Moving to Node #0,0,0 Current State: 44:[2, 42], Operations: ['67-65=2', '56-14=42'] Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 36, 52, 84, 60 ]
26
[ "36+84=120", "52*60=3120", "3120/120=26" ]
Current State: 26:[36, 52, 84, 60], Operations: [] Exploring Operation: 36+84=120, Resulting Numbers: [52, 60, 120] Generated Node #2: [52, 60, 120] from Operation: 36+84=120 Current State: 26:[52, 60, 120], Operations: ['36+84=120'] Exploring Operation: 52*60=3120, Resulting Numbers: [120, 3120] Generated Node #3: [120, 3120] from Operation: 52*60=3120 Current State: 26:[120, 3120], Operations: ['36+84=120', '52*60=3120'] Exploring Operation: 3120/120=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[36, 52, 84, 60], Operations: [] Exploring Operation: 84-36=48, Resulting Numbers: [52, 60, 48] Generated Node #0,0: 26:[52, 60, 48] Operation: 84-36=48 Exploring Operation: 84-52=32, Resulting Numbers: [36, 60, 32] Generated Node #0,1: 26:[36, 60, 32] Operation: 84-52=32 Exploring Operation: 60-52=8, Resulting Numbers: [36, 84, 8] Generated Node #0,2: 26:[36, 84, 8] Operation: 60-52=8 Exploring Operation: 84-60=24, Resulting Numbers: [36, 52, 24] Generated Node #0,3: 26:[36, 52, 24] Operation: 84-60=24 Exploring Operation: 60-36=24, Resulting Numbers: [52, 84, 24] Generated Node #0,4: 26:[52, 84, 24] Operation: 60-36=24 Moving to Node #0,3 Current State: 26:[36, 52, 24], Operations: ['84-60=24'] Exploring Operation: 36+24=60, Resulting Numbers: [52, 60] Generated Node #0,3,0: 26:[52, 60] Operation: 36+24=60 Exploring Operation: 52-36=16, Resulting Numbers: [24, 16] Generated Node #0,3,1: 26:[24, 16] Operation: 52-36=16 Exploring Operation: 36-24=12, Resulting Numbers: [52, 12] Generated Node #0,3,2: 26:[52, 12] Operation: 36-24=12 Exploring Operation: 52-24=28, Resulting Numbers: [36, 28] Generated Node #0,3,3: 26:[36, 28] Operation: 52-24=28 Exploring Operation: 52+24=76, Resulting Numbers: [36, 76] Generated Node #0,3,4: 26:[36, 76] Operation: 52+24=76 Moving to Node #0,1 Current State: 26:[36, 60, 32], Operations: ['84-52=32'] Exploring Operation: 36-32=4, Resulting Numbers: [60, 4] Generated Node #0,1,0: 26:[60, 4] Operation: 36-32=4 Exploring Operation: 60-32=28, Resulting Numbers: [36, 28] Generated Node #0,1,1: 26:[36, 28] Operation: 60-32=28 Exploring Operation: 60-36=24, Resulting Numbers: [32, 24] Generated Node #0,1,2: 26:[32, 24] Operation: 60-36=24 Exploring Operation: 36+60=96, Resulting Numbers: [32, 96] Generated Node #0,1,3: 26:[32, 96] Operation: 36+60=96 Exploring Operation: 36+32=68, Resulting Numbers: [60, 68] Generated Node #0,1,4: 26:[60, 68] Operation: 36+32=68 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[32, 24], Operations: ['84-52=32', '60-36=24'] Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,26 unequal: No Solution Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[36, 28], Operations: ['84-52=32', '60-32=28'] Exploring Operation: 36+28=64, Resulting Numbers: [64] 64,26 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 36*28=1008, Resulting Numbers: [1008] 1008,26 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:[60, 4], Operations: ['84-52=32', '36-32=4'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,26 unequal: No Solution Exploring Operation: 60*4=240, Resulting Numbers: [240] 240,26 unequal: No Solution Exploring Operation: 60+4=64, Resulting Numbers: [64] 64,26 unequal: No Solution Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 26:[32, 96], Operations: ['84-52=32', '36+60=96'] Exploring Operation: 96/32=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 32+96=128, Resulting Numbers: [128] 128,26 unequal: No Solution Exploring Operation: 32*96=3072, Resulting Numbers: [3072] 3072,26 unequal: No Solution Exploring Operation: 96-32=64, Resulting Numbers: [64] 64,26 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 #0,1,4 Current State: 26:[60, 68], Operations: ['84-52=32', '36+32=68'] Exploring Operation: 60+68=128, Resulting Numbers: [128] 128,26 unequal: No Solution Exploring Operation: 60*68=4080, Resulting Numbers: [4080] 4080,26 unequal: No Solution Exploring Operation: 68-60=8, Resulting Numbers: [8] 8,26 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:[36, 84, 8], Operations: ['60-52=8'] Exploring Operation: 84-36=48, Resulting Numbers: [8, 48] Generated Node #0,2,0: 26:[8, 48] Operation: 84-36=48 Exploring Operation: 84+8=92, Resulting Numbers: [36, 92] Generated Node #0,2,1: 26:[36, 92] Operation: 84+8=92 Exploring Operation: 36-8=28, Resulting Numbers: [84, 28] Generated Node #0,2,2: 26:[84, 28] Operation: 36-8=28 Exploring Operation: 36+8=44, Resulting Numbers: [84, 44] Generated Node #0,2,3: 26:[84, 44] Operation: 36+8=44 Exploring Operation: 84-8=76, Resulting Numbers: [36, 76] Generated Node #0,2,4: 26:[36, 76] Operation: 84-8=76 Moving to Node #0,0 Current State: 26:[52, 60, 48], Operations: ['84-36=48'] Exploring Operation: 52+60=112, Resulting Numbers: [48, 112] Generated Node #0,0,0: 26:[48, 112] Operation: 52+60=112 Exploring Operation: 60-48=12, Resulting Numbers: [52, 12] Generated Node #0,0,1: 26:[52, 12] Operation: 60-48=12 Exploring Operation: 60-52=8, Resulting Numbers: [48, 8] Generated Node #0,0,2: 26:[48, 8] Operation: 60-52=8 Exploring Operation: 52-48=4, Resulting Numbers: [60, 4] Generated Node #0,0,3: 26:[60, 4] Operation: 52-48=4 Exploring Operation: 52+48=100, Resulting Numbers: [60, 100] Generated Node #0,0,4: 26:[60, 100] Operation: 52+48=100 Moving to Node #0,4 Current State: 26:[52, 84, 24], Operations: ['60-36=24'] Exploring Operation: 84+24=108, Resulting Numbers: [52, 108] Generated Node #0,4,0: 26:[52, 108] Operation: 84+24=108 Exploring Operation: 84-52=32, Resulting Numbers: [24, 32] Generated Node #0,4,1: 26:[24, 32] Operation: 84-52=32 Exploring Operation: 52+24=76, Resulting Numbers: [84, 76] Generated Node #0,4,2: 26:[84, 76] Operation: 52+24=76 Exploring Operation: 52-24=28, Resulting Numbers: [84, 28] Generated Node #0,4,3: 26:[84, 28] Operation: 52-24=28 Exploring Operation: 84-24=60, Resulting Numbers: [52, 60] Generated Node #0,4,4: 26:[52, 60] Operation: 84-24=60 Moving to Node #0,3,1 Current State: 26:[24, 16], Operations: ['84-60=24', '52-36=16'] Exploring Operation: 24+16=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 24*16=384, Resulting Numbers: [384] 384,26 unequal: No Solution Moving to Node #0,4,1 Current State: 26:[24, 32], Operations: ['60-36=24', '84-52=32'] Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,26 unequal: No Solution Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,26 unequal: No Solution Moving to Node #0,3,3 Current State: 26:[36, 28], Operations: ['84-60=24', '52-24=28'] Exploring Operation: 36+28=64, Resulting Numbers: [64] 64,26 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 36*28=1008, Resulting Numbers: [1008] 1008,26 unequal: No Solution Moving to Node #0,3,2 Current State: 26:[52, 12], Operations: ['84-60=24', '36-24=12'] Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,26 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,26 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[8, 48], Operations: ['60-52=8', '84-36=48'] Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,26 unequal: No Solution Exploring Operation: 8+48=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 8*48=384, Resulting Numbers: [384] 384,26 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[48, 8], Operations: ['84-36=48', '60-52=8'] Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,26 unequal: No Solution Exploring Operation: 48*8=384, Resulting Numbers: [384] 384,26 unequal: No Solution Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[52, 12], Operations: ['84-36=48', '60-48=12'] Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,26 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,26 unequal: No Solution Moving to Node #0,0,3 Current State: 26:[60, 4], Operations: ['84-36=48', '52-48=4'] Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 60*4=240, Resulting Numbers: [240] 240,26 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,26 unequal: No Solution Exploring Operation: 60+4=64, Resulting Numbers: [64] 64,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[84, 28], Operations: ['60-52=8', '36-8=28'] Exploring Operation: 84-28=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 84/28=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 84+28=112, Resulting Numbers: [112] 112,26 unequal: No Solution Exploring Operation: 84*28=2352, Resulting Numbers: [2352] 2352,26 unequal: No Solution Moving to Node #0,4,3 Current State: 26:[84, 28], Operations: ['60-36=24', '52-24=28'] Exploring Operation: 84-28=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 84/28=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 84+28=112, Resulting Numbers: [112] 112,26 unequal: No Solution Exploring Operation: 84*28=2352, Resulting Numbers: [2352] 2352,26 unequal: No Solution Moving to Node #0,2,4 Current State: 26:[36, 76], Operations: ['60-52=8', '84-8=76'] Exploring Operation: 36+76=112, Resulting Numbers: [112] 112,26 unequal: No Solution Exploring Operation: 36*76=2736, Resulting Numbers: [2736] 2736,26 unequal: No Solution Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,26 unequal: No Solution Moving to Node #0,3,4 Current State: 26:[36, 76], Operations: ['84-60=24', '52+24=76'] Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 36*76=2736, Resulting Numbers: [2736] 2736,26 unequal: No Solution Exploring Operation: 36+76=112, Resulting Numbers: [112] 112,26 unequal: No Solution Moving to Node #0,4,4 Current State: 26:[52, 60], Operations: ['60-36=24', '84-24=60'] Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,26 unequal: No Solution Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,26 unequal: No Solution Moving to Node #0,3,0 Current State: 26:[52, 60], Operations: ['84-60=24', '36+24=60'] Exploring Operation: 52*60=3120, Resulting Numbers: [3120] 3120,26 unequal: No Solution Exploring Operation: 60-52=8, Resulting Numbers: [8] 8,26 unequal: No Solution Exploring Operation: 52+60=112, Resulting Numbers: [112] 112,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[84, 44], Operations: ['60-52=8', '36+8=44'] Exploring Operation: 84*44=3696, Resulting Numbers: [3696] 3696,26 unequal: No Solution Exploring Operation: 84+44=128, Resulting Numbers: [128] 128,26 unequal: No Solution Exploring Operation: 84-44=40, Resulting Numbers: [40] 40,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[36, 92], Operations: ['60-52=8', '84+8=92'] Exploring Operation: 92-36=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 36*92=3312, Resulting Numbers: [3312] 3312,26 unequal: No Solution Exploring Operation: 36+92=128, Resulting Numbers: [128] 128,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[48, 112], Operations: ['84-36=48', '52+60=112'] Exploring Operation: 48+112=160, Resulting Numbers: [160] 160,26 unequal: No Solution Exploring Operation: 48*112=5376, Resulting Numbers: [5376] 5376,26 unequal: No Solution Exploring Operation: 112-48=64, Resulting Numbers: [64] 64,26 unequal: No Solution Moving to Node #0,4,2 Current State: 26:[84, 76], Operations: ['60-36=24', '52+24=76'] Exploring Operation: 84*76=6384, Resulting Numbers: [6384] 6384,26 unequal: No Solution Exploring Operation: 84+76=160, Resulting Numbers: [160] 160,26 unequal: No Solution Exploring Operation: 84-76=8, Resulting Numbers: [8] 8,26 unequal: No Solution Moving to Node #0,0,4 Current State: 26:[60, 100], Operations: ['84-36=48', '52+48=100'] Exploring Operation: 60+100=160, Resulting Numbers: [160] 160,26 unequal: No Solution Exploring Operation: 100-60=40, Resulting Numbers: [40] 40,26 unequal: No Solution Exploring Operation: 60*100=6000, Resulting Numbers: [6000] 6000,26 unequal: No Solution Moving to Node #0,4,0 Current State: 26:[52, 108], Operations: ['60-36=24', '84+24=108'] Exploring Operation: 108-52=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 52+108=160, Resulting Numbers: [160] 160,26 unequal: No Solution Exploring Operation: 52*108=5616, Resulting Numbers: [5616] 5616,26 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 12, 11, 1, 4 ]
91
[ "12+11=23", "4*23=92", "92-1=91" ]
Current State: 91:[12, 11, 1, 4], Operations: [] Exploring Operation: 12+11=23, Resulting Numbers: [1, 4, 23] Generated Node #2: [1, 4, 23] from Operation: 12+11=23 Current State: 91:[1, 4, 23], Operations: ['12+11=23'] Exploring Operation: 4*23=92, Resulting Numbers: [1, 92] Generated Node #3: [1, 92] from Operation: 4*23=92 Current State: 91:[1, 92], Operations: ['12+11=23', '4*23=92'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[12, 11, 1, 4], Operations: [] Exploring Operation: 12+1=13, Resulting Numbers: [11, 4, 13] Generated Node #0,0: 91:[11, 4, 13] Operation: 12+1=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[11, 4, 13], Operations: ['12+1=13'] Exploring Operation: 11-4=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 91:[13, 7] Operation: 11-4=7 Moving to Node #0,0,0 Current State: 91:[13, 7], Operations: ['12+1=13', '11-4=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[12, 11, 1, 4], Operations: [] Exploring Operation: 12+1=13, Resulting Numbers: [11, 4, 13] Generated Node #0,0: 91:[11, 4, 13] Operation: 12+1=13 Moving to Node #0,0 Current State: 91:[11, 4, 13], Operations: ['12+1=13'] Exploring Operation: 11-4=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 91:[13, 7] Operation: 11-4=7 Moving to Node #0,0,0 Current State: 91:[13, 7], Operations: ['12+1=13', '11-4=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 83, 84, 60, 40 ]
99
[ "84-83=1", "60+40=100", "100-1=99" ]
Current State: 99:[83, 84, 60, 40], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [60, 40, 1] Generated Node #2: [60, 40, 1] from Operation: 84-83=1 Current State: 99:[60, 40, 1], Operations: ['84-83=1'] Exploring Operation: 60+40=100, Resulting Numbers: [1, 100] Generated Node #3: [1, 100] from Operation: 60+40=100 Current State: 99:[1, 100], Operations: ['84-83=1', '60+40=100'] Exploring Operation: 100-1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[83, 84, 60, 40], Operations: [] Exploring Operation: 84-60=24, Resulting Numbers: [83, 40, 24] Generated Node #0,0: 99:[83, 40, 24] Operation: 84-60=24 Exploring Operation: 83-60=23, Resulting Numbers: [84, 40, 23] Generated Node #0,1: 99:[84, 40, 23] Operation: 83-60=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[83, 40, 24], Operations: ['84-60=24'] Exploring Operation: 83+24=107, Resulting Numbers: [40, 107] Generated Node #0,0,0: 99:[40, 107] Operation: 83+24=107 Exploring Operation: 83-40=43, Resulting Numbers: [24, 43] Generated Node #0,0,1: 99:[24, 43] Operation: 83-40=43 Moving to Node #0,0,0 Current State: 99:[40, 107], Operations: ['84-60=24', '83+24=107'] Exploring Operation: 40+107=147, Resulting Numbers: [147] 147,99 unequal: No Solution Exploring Operation: 107-40=67, Resulting Numbers: [67] 67,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[24, 43], Operations: ['84-60=24', '83-40=43'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,99 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 #0,1 Current State: 99:[84, 40, 23], Operations: ['83-60=23'] Exploring Operation: 84+23=107, Resulting Numbers: [40, 107] Generated Node #0,1,0: 99:[40, 107] Operation: 84+23=107 Exploring Operation: 84-40=44, Resulting Numbers: [23, 44] Generated Node #0,1,1: 99:[23, 44] Operation: 84-40=44 Moving to Node #0,1,0 Current State: 99:[40, 107], Operations: ['83-60=23', '84+23=107'] Exploring Operation: 107-40=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 40+107=147, Resulting Numbers: [147] 147,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[23, 44], Operations: ['83-60=23', '84-40=44'] Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 61, 15, 10, 68 ]
35
[ "68-61=7", "15-10=5", "7*5=35" ]
Current State: 35:[61, 15, 10, 68], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [15, 10, 7] Generated Node #2: [15, 10, 7] from Operation: 68-61=7 Current State: 35:[15, 10, 7], Operations: ['68-61=7'] Exploring Operation: 15-10=5, Resulting Numbers: [7, 5] Generated Node #3: [7, 5] from Operation: 15-10=5 Current State: 35:[7, 5], Operations: ['68-61=7', '15-10=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[61, 15, 10, 68], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [15, 10, 7] Generated Node #0,0: 35:[15, 10, 7] Operation: 68-61=7 Moving to Node #0,0 Current State: 35:[15, 10, 7], Operations: ['68-61=7'] Exploring Operation: 15-10=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 15-10=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['68-61=7', '15-10=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[61, 15, 10, 68], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [15, 10, 7] Generated Node #0,0: 35:[15, 10, 7] Operation: 68-61=7 Moving to Node #0,0 Current State: 35:[15, 10, 7], Operations: ['68-61=7'] Exploring Operation: 15-10=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 15-10=5 Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['68-61=7', '15-10=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 21, 96, 57, 30 ]
12
[ "96-21=75", "57+30=87", "87-75=12" ]
Current State: 12:[21, 96, 57, 30], Operations: [] Exploring Operation: 96-21=75, Resulting Numbers: [57, 30, 75] Generated Node #2: [57, 30, 75] from Operation: 96-21=75 Current State: 12:[57, 30, 75], Operations: ['96-21=75'] Exploring Operation: 57+30=87, Resulting Numbers: [75, 87] Generated Node #3: [75, 87] from Operation: 57+30=87 Current State: 12:[75, 87], Operations: ['96-21=75', '57+30=87'] Exploring Operation: 87-75=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[21, 96, 57, 30], Operations: [] Exploring Operation: 96-30=66, Resulting Numbers: [21, 57, 66] Generated Node #0,0: 12:[21, 57, 66] Operation: 96-30=66 Exploring Operation: 96-57=39, Resulting Numbers: [21, 30, 39] Generated Node #0,1: 12:[21, 30, 39] Operation: 96-57=39 Moving to Node #0,1 Current State: 12:[21, 30, 39], Operations: ['96-57=39'] Exploring Operation: 39-30=9, Resulting Numbers: [21, 9] Generated Node #0,1,0: 12:[21, 9] Operation: 39-30=9 Exploring Operation: 39-21=18, Resulting Numbers: [30, 18] Generated Node #0,1,1: 12:[30, 18] Operation: 39-21=18 Moving to Node #0,0 Current State: 12:[21, 57, 66], Operations: ['96-30=66'] Exploring Operation: 66-57=9, Resulting Numbers: [21, 9] Generated Node #0,0,0: 12:[21, 9] Operation: 66-57=9 Exploring Operation: 57-21=36, Resulting Numbers: [66, 36] Generated Node #0,0,1: 12:[66, 36] Operation: 57-21=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[21, 9], Operations: ['96-30=66', '66-57=9'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[21, 96, 57, 30], Operations: [] Exploring Operation: 96-30=66, Resulting Numbers: [21, 57, 66] Generated Node #0,0: 12:[21, 57, 66] Operation: 96-30=66 Moving to Node #0,0 Current State: 12:[21, 57, 66], Operations: ['96-30=66'] Exploring Operation: 66-57=9, Resulting Numbers: [21, 9] Generated Node #0,0,0: 12:[21, 9] Operation: 66-57=9 Moving to Node #0,0,0 Current State: 12:[21, 9], Operations: ['96-30=66', '66-57=9'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 9, 93, 39, 78 ]
100
[ "9+93=102", "78/39=2", "102-2=100" ]
Current State: 100:[9, 93, 39, 78], Operations: [] Exploring Operation: 9+93=102, Resulting Numbers: [39, 78, 102] Generated Node #2: [39, 78, 102] from Operation: 9+93=102 Current State: 100:[39, 78, 102], Operations: ['9+93=102'] Exploring Operation: 78/39=2, Resulting Numbers: [102, 2] Generated Node #3: [102, 2] from Operation: 78/39=2 Current State: 100:[102, 2], Operations: ['9+93=102', '78/39=2'] Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[9, 93, 39, 78], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [9, 93, 2] Generated Node #0,0: 100:[9, 93, 2] Operation: 78/39=2 Exploring Operation: 93-78=15, Resulting Numbers: [9, 39, 15] Generated Node #0,1: 100:[9, 39, 15] Operation: 93-78=15 Moving to Node #0,0 Current State: 100:[9, 93, 2], Operations: ['78/39=2'] Exploring Operation: 93+2=95, Resulting Numbers: [9, 95] Generated Node #0,0,0: 100:[9, 95] Operation: 93+2=95 Exploring Operation: 9+93=102, Resulting Numbers: [2, 102] Generated Node #0,0,1: 100:[2, 102] Operation: 9+93=102 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[2, 102], Operations: ['78/39=2', '9+93=102'] Exploring Operation: 102/2=51, Resulting Numbers: [51] 51,100 unequal: No Solution Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[9, 93, 39, 78], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [9, 93, 2] Generated Node #0,0: 100:[9, 93, 2] Operation: 78/39=2 Moving to Node #0,0 Current State: 100:[9, 93, 2], Operations: ['78/39=2'] Exploring Operation: 9+93=102, Resulting Numbers: [2, 102] Generated Node #0,0,1: 100:[2, 102] Operation: 9+93=102 Moving to Node #0,0,1 Current State: 100:[2, 102], Operations: ['78/39=2', '9+93=102'] Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 74, 45, 19, 25 ]
73
[ "74-45=29", "19+25=44", "29+44=73" ]
Current State: 73:[74, 45, 19, 25], Operations: [] Exploring Operation: 74-45=29, Resulting Numbers: [19, 25, 29] Generated Node #2: [19, 25, 29] from Operation: 74-45=29 Current State: 73:[19, 25, 29], Operations: ['74-45=29'] Exploring Operation: 19+25=44, Resulting Numbers: [29, 44] Generated Node #3: [29, 44] from Operation: 19+25=44 Current State: 73:[29, 44], Operations: ['74-45=29', '19+25=44'] Exploring Operation: 29+44=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[74, 45, 19, 25], Operations: [] Exploring Operation: 45+19=64, Resulting Numbers: [74, 25, 64] Generated Node #0,0: 73:[74, 25, 64] Operation: 45+19=64 Exploring Operation: 45+25=70, Resulting Numbers: [74, 19, 70] Generated Node #0,1: 73:[74, 19, 70] Operation: 45+25=70 Exploring Operation: 19+25=44, Resulting Numbers: [74, 45, 44] Generated Node #0,2: 73:[74, 45, 44] Operation: 19+25=44 Exploring Operation: 74-19=55, Resulting Numbers: [45, 25, 55] Generated Node #0,3: 73:[45, 25, 55] Operation: 74-19=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[74, 25, 64], Operations: ['45+19=64'] Exploring Operation: 74-25=49, Resulting Numbers: [64, 49] Generated Node #0,0,0: 73:[64, 49] Operation: 74-25=49 Exploring Operation: 64-25=39, Resulting Numbers: [74, 39] Generated Node #0,0,1: 73:[74, 39] Operation: 64-25=39 Exploring Operation: 25+64=89, Resulting Numbers: [74, 89] Generated Node #0,0,2: 73:[74, 89] Operation: 25+64=89 Exploring Operation: 74+25=99, Resulting Numbers: [64, 99] Generated Node #0,0,3: 73:[64, 99] Operation: 74+25=99 Moving to Node #0,0,2 Current State: 73:[74, 89], Operations: ['45+19=64', '25+64=89'] Exploring Operation: 74+89=163, Resulting Numbers: [163] 163,73 unequal: No Solution Exploring Operation: 89-74=15, Resulting Numbers: [15] 15,73 unequal: No Solution Exploring Operation: 74*89=6586, Resulting Numbers: [6586] 6586,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[64, 49], Operations: ['45+19=64', '74-25=49'] Exploring Operation: 64+49=113, Resulting Numbers: [113] 113,73 unequal: No Solution Exploring Operation: 64-49=15, Resulting Numbers: [15] 15,73 unequal: No Solution Exploring Operation: 64*49=3136, Resulting Numbers: [3136] 3136,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[64, 99], Operations: ['45+19=64', '74+25=99'] Exploring Operation: 64*99=6336, Resulting Numbers: [6336] 6336,73 unequal: No Solution Exploring Operation: 99-64=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 64+99=163, Resulting Numbers: [163] 163,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[74, 39], Operations: ['45+19=64', '64-25=39'] Exploring Operation: 74*39=2886, Resulting Numbers: [2886] 2886,73 unequal: No Solution Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,73 unequal: No Solution Exploring Operation: 74+39=113, Resulting Numbers: [113] 113,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[74, 19, 70], Operations: ['45+25=70'] Exploring Operation: 19+70=89, Resulting Numbers: [74, 89] Generated Node #0,1,0: 73:[74, 89] Operation: 19+70=89 Exploring Operation: 74+19=93, Resulting Numbers: [70, 93] Generated Node #0,1,1: 73:[70, 93] Operation: 74+19=93 Exploring Operation: 74-19=55, Resulting Numbers: [70, 55] Generated Node #0,1,2: 73:[70, 55] Operation: 74-19=55 Exploring Operation: 70-19=51, Resulting Numbers: [74, 51] Generated Node #0,1,3: 73:[74, 51] Operation: 70-19=51 Moving to Node #0,1,0 Current State: 73:[74, 89], Operations: ['45+25=70', '19+70=89'] Exploring Operation: 74+89=163, Resulting Numbers: [163] 163,73 unequal: No Solution Exploring Operation: 89-74=15, Resulting Numbers: [15] 15,73 unequal: No Solution Exploring Operation: 74*89=6586, Resulting Numbers: [6586] 6586,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[70, 55], Operations: ['45+25=70', '74-19=55'] Exploring Operation: 70*55=3850, Resulting Numbers: [3850] 3850,73 unequal: No Solution Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,73 unequal: No Solution Exploring Operation: 70+55=125, Resulting Numbers: [125] 125,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[74, 51], Operations: ['45+25=70', '70-19=51'] Exploring Operation: 74*51=3774, Resulting Numbers: [3774] 3774,73 unequal: No Solution Exploring Operation: 74+51=125, Resulting Numbers: [125] 125,73 unequal: No Solution Exploring Operation: 74-51=23, Resulting Numbers: [23] 23,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[70, 93], Operations: ['45+25=70', '74+19=93'] Exploring Operation: 93-70=23, Resulting Numbers: [23] 23,73 unequal: No Solution Exploring Operation: 70*93=6510, Resulting Numbers: [6510] 6510,73 unequal: No Solution Exploring Operation: 70+93=163, Resulting Numbers: [163] 163,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[74, 45, 44], Operations: ['19+25=44'] Exploring Operation: 74-45=29, Resulting Numbers: [44, 29] Generated Node #0,2,0: 73:[44, 29] Operation: 74-45=29 Exploring Operation: 74+44=118, Resulting Numbers: [45, 118] Generated Node #0,2,1: 73:[45, 118] Operation: 74+44=118 Exploring Operation: 74-44=30, Resulting Numbers: [45, 30] Generated Node #0,2,2: 73:[45, 30] Operation: 74-44=30 Exploring Operation: 45+44=89, Resulting Numbers: [74, 89] Generated Node #0,2,3: 73:[74, 89] Operation: 45+44=89 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 73:[74, 89], Operations: ['19+25=44', '45+44=89'] Exploring Operation: 89-74=15, Resulting Numbers: [15] 15,73 unequal: No Solution Exploring Operation: 74+89=163, Resulting Numbers: [163] 163,73 unequal: No Solution Exploring Operation: 74*89=6586, Resulting Numbers: [6586] 6586,73 unequal: No Solution No 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: 73:[45, 30], Operations: ['19+25=44', '74-44=30'] Exploring Operation: 45+30=75, Resulting Numbers: [75] 75,73 unequal: No Solution Exploring Operation: 45*30=1350, Resulting Numbers: [1350] 1350,73 unequal: No Solution Exploring Operation: 45-30=15, Resulting Numbers: [15] 15,73 unequal: No Solution No 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: 73:[44, 29], Operations: ['19+25=44', '74-45=29'] Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,73 unequal: No Solution Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[74, 45, 19, 25], Operations: [] Exploring Operation: 19+25=44, Resulting Numbers: [74, 45, 44] Generated Node #0,2: 73:[74, 45, 44] Operation: 19+25=44 Moving to Node #0,2 Current State: 73:[74, 45, 44], Operations: ['19+25=44'] Exploring Operation: 74-45=29, Resulting Numbers: [44, 29] Generated Node #0,2,0: 73:[44, 29] Operation: 74-45=29 Moving to Node #0,2,0 Current State: 73:[44, 29], Operations: ['19+25=44', '74-45=29'] Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.954861
hs_4
mult_heuristic
[ 32, 91, 13, 52 ]
63
[ "91-32=59", "52/13=4", "59+4=63" ]
Current State: 63:[32, 91, 13, 52], Operations: [] Exploring Operation: 91-32=59, Resulting Numbers: [13, 52, 59] Generated Node #2: [13, 52, 59] from Operation: 91-32=59 Current State: 63:[13, 52, 59], Operations: ['91-32=59'] Exploring Operation: 52/13=4, Resulting Numbers: [59, 4] Generated Node #3: [59, 4] from Operation: 52/13=4 Current State: 63:[59, 4], Operations: ['91-32=59', '52/13=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[32, 91, 13, 52], Operations: [] Exploring Operation: 91/13=7, Resulting Numbers: [32, 52, 7] Generated Node #0,0: 63:[32, 52, 7] Operation: 91/13=7 Exploring Operation: 52-32=20, Resulting Numbers: [91, 13, 20] Generated Node #0,1: 63:[91, 13, 20] Operation: 52-32=20 Exploring Operation: 91-32=59, Resulting Numbers: [13, 52, 59] Generated Node #0,2: 63:[13, 52, 59] Operation: 91-32=59 Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[13, 52, 59], Operations: ['91-32=59'] Exploring Operation: 59-52=7, Resulting Numbers: [13, 7] Generated Node #0,2,0: 63:[13, 7] Operation: 59-52=7 Exploring Operation: 52/13=4, Resulting Numbers: [59, 4] Generated Node #0,2,1: 63:[59, 4] Operation: 52/13=4 Exploring Operation: 13+52=65, Resulting Numbers: [59, 65] Generated Node #0,2,2: 63:[59, 65] Operation: 13+52=65 Moving to Node #0,2,0 Current State: 63:[13, 7], Operations: ['91-32=59', '59-52=7'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,63 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[59, 4], Operations: ['91-32=59', '52/13=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[32, 91, 13, 52], Operations: [] Exploring Operation: 91-32=59, Resulting Numbers: [13, 52, 59] Generated Node #0,2: 63:[13, 52, 59] Operation: 91-32=59 Moving to Node #0,2 Current State: 63:[13, 52, 59], Operations: ['91-32=59'] Exploring Operation: 52/13=4, Resulting Numbers: [59, 4] Generated Node #0,2,1: 63:[59, 4] Operation: 52/13=4 Moving to Node #0,2,1 Current State: 63:[59, 4], Operations: ['91-32=59', '52/13=4'] Exploring Operation: 59+4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 9, 63, 74, 67 ]
47
[ "63-9=54", "74-67=7", "54-7=47" ]
Current State: 47:[9, 63, 74, 67], Operations: [] Exploring Operation: 63-9=54, Resulting Numbers: [74, 67, 54] Generated Node #2: [74, 67, 54] from Operation: 63-9=54 Current State: 47:[74, 67, 54], Operations: ['63-9=54'] Exploring Operation: 74-67=7, Resulting Numbers: [54, 7] Generated Node #3: [54, 7] from Operation: 74-67=7 Current State: 47:[54, 7], Operations: ['63-9=54', '74-67=7'] Exploring Operation: 54-7=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[9, 63, 74, 67], Operations: [] Exploring Operation: 67-9=58, Resulting Numbers: [63, 74, 58] Generated Node #0,0: 47:[63, 74, 58] Operation: 67-9=58 Exploring Operation: 74-9=65, Resulting Numbers: [63, 67, 65] Generated Node #0,1: 47:[63, 67, 65] Operation: 74-9=65 Exploring Operation: 63-9=54, Resulting Numbers: [74, 67, 54] Generated Node #0,2: 47:[74, 67, 54] Operation: 63-9=54 Moving to Node #0,0 Current State: 47:[63, 74, 58], Operations: ['67-9=58'] Exploring Operation: 74-58=16, Resulting Numbers: [63, 16] Generated Node #0,0,0: 47:[63, 16] Operation: 74-58=16 Exploring Operation: 74-63=11, Resulting Numbers: [58, 11] Generated Node #0,0,1: 47:[58, 11] Operation: 74-63=11 Exploring Operation: 63-58=5, Resulting Numbers: [74, 5] Generated Node #0,0,2: 47:[74, 5] Operation: 63-58=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[63, 16], Operations: ['67-9=58', '74-58=16'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[9, 63, 74, 67], Operations: [] Exploring Operation: 67-9=58, Resulting Numbers: [63, 74, 58] Generated Node #0,0: 47:[63, 74, 58] Operation: 67-9=58 Moving to Node #0,0 Current State: 47:[63, 74, 58], Operations: ['67-9=58'] Exploring Operation: 74-58=16, Resulting Numbers: [63, 16] Generated Node #0,0,0: 47:[63, 16] Operation: 74-58=16 Moving to Node #0,0,0 Current State: 47:[63, 16], Operations: ['67-9=58', '74-58=16'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 99, 61, 70, 8 ]
98
[ "99+61=160", "70-8=62", "160-62=98" ]
Current State: 98:[99, 61, 70, 8], Operations: [] Exploring Operation: 99+61=160, Resulting Numbers: [70, 8, 160] Generated Node #2: [70, 8, 160] from Operation: 99+61=160 Current State: 98:[70, 8, 160], Operations: ['99+61=160'] Exploring Operation: 70-8=62, Resulting Numbers: [160, 62] Generated Node #3: [160, 62] from Operation: 70-8=62 Current State: 98:[160, 62], Operations: ['99+61=160', '70-8=62'] Exploring Operation: 160-62=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[99, 61, 70, 8], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [99, 8, 9] Generated Node #0,0: 98:[99, 8, 9] Operation: 70-61=9 Exploring Operation: 99-70=29, Resulting Numbers: [61, 8, 29] Generated Node #0,1: 98:[61, 8, 29] Operation: 99-70=29 Exploring Operation: 70-8=62, Resulting Numbers: [99, 61, 62] Generated Node #0,2: 98:[99, 61, 62] Operation: 70-8=62 Exploring Operation: 99-61=38, Resulting Numbers: [70, 8, 38] Generated Node #0,3: 98:[70, 8, 38] Operation: 99-61=38 Exploring Operation: 61-8=53, Resulting Numbers: [99, 70, 53] Generated Node #0,4: 98:[99, 70, 53] Operation: 61-8=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[99, 8, 9], Operations: ['70-61=9'] Exploring Operation: 99/9=11, Resulting Numbers: [8, 11] Generated Node #0,0,0: 98:[8, 11] Operation: 99/9=11 Exploring Operation: 8+9=17, Resulting Numbers: [99, 17] Generated Node #0,0,1: 98:[99, 17] Operation: 8+9=17 Exploring Operation: 99-8=91, Resulting Numbers: [9, 91] Generated Node #0,0,2: 98:[9, 91] Operation: 99-8=91 Exploring Operation: 9-8=1, Resulting Numbers: [99, 1] Generated Node #0,0,3: 98:[99, 1] Operation: 9-8=1 Exploring Operation: 99-9=90, Resulting Numbers: [8, 90] Generated Node #0,0,4: 98:[8, 90] Operation: 99-9=90 Moving to Node #0,0,3 Current State: 98:[99, 1], Operations: ['70-61=9', '9-8=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,98 unequal: No Solution Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[99, 61, 70, 8], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [99, 8, 9] Generated Node #0,0: 98:[99, 8, 9] Operation: 70-61=9 Moving to Node #0,0 Current State: 98:[99, 8, 9], Operations: ['70-61=9'] Exploring Operation: 9-8=1, Resulting Numbers: [99, 1] Generated Node #0,0,3: 98:[99, 1] Operation: 9-8=1 Moving to Node #0,0,3 Current State: 98:[99, 1], Operations: ['70-61=9', '9-8=1'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 84, 4, 8, 13 ]
80
[ "8*13=104", "104-84=20", "4*20=80" ]
Current State: 80:[84, 4, 8, 13], Operations: [] Exploring Operation: 8*13=104, Resulting Numbers: [84, 4, 104] Generated Node #2: [84, 4, 104] from Operation: 8*13=104 Current State: 80:[84, 4, 104], Operations: ['8*13=104'] Exploring Operation: 104-84=20, Resulting Numbers: [4, 20] Generated Node #3: [4, 20] from Operation: 104-84=20 Current State: 80:[4, 20], Operations: ['8*13=104', '104-84=20'] Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[84, 4, 8, 13], Operations: [] Exploring Operation: 84-4=80, Resulting Numbers: [8, 13, 80] Generated Node #0,0: 80:[8, 13, 80] Operation: 84-4=80 Moving to Node #0,0 Current State: 80:[8, 13, 80], Operations: ['84-4=80'] Exploring Operation: 13-8=5, Resulting Numbers: [80, 5] Generated Node #0,0,0: 80:[80, 5] Operation: 13-8=5 Moving to Node #0,0,0 Current State: 80:[80, 5], Operations: ['84-4=80', '13-8=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,80 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 43, 87, 70, 5 ]
40
[ "43+87=130", "70+130=200", "200/5=40" ]
Current State: 40:[43, 87, 70, 5], Operations: [] Exploring Operation: 43+87=130, Resulting Numbers: [70, 5, 130] Generated Node #2: [70, 5, 130] from Operation: 43+87=130 Current State: 40:[70, 5, 130], Operations: ['43+87=130'] Exploring Operation: 70+130=200, Resulting Numbers: [5, 200] Generated Node #3: [5, 200] from Operation: 70+130=200 Current State: 40:[5, 200], Operations: ['43+87=130', '70+130=200'] Exploring Operation: 200/5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[43, 87, 70, 5], Operations: [] Exploring Operation: 87-70=17, Resulting Numbers: [43, 5, 17] Generated Node #0,0: 40:[43, 5, 17] Operation: 87-70=17 Exploring Operation: 87-43=44, Resulting Numbers: [70, 5, 44] Generated Node #0,1: 40:[70, 5, 44] Operation: 87-43=44 Moving to Node #0,0 Current State: 40:[43, 5, 17], Operations: ['87-70=17'] Exploring Operation: 43-5=38, Resulting Numbers: [17, 38] Generated Node #0,0,0: 40:[17, 38] Operation: 43-5=38 Exploring Operation: 5+17=22, Resulting Numbers: [43, 22] Generated Node #0,0,1: 40:[43, 22] Operation: 5+17=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[17, 38], Operations: ['87-70=17', '43-5=38'] Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,40 unequal: No Solution Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,40 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:[43, 22], Operations: ['87-70=17', '5+17=22'] Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,40 unequal: No Solution Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,40 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:[70, 5, 44], Operations: ['87-43=44'] Exploring Operation: 70-44=26, Resulting Numbers: [5, 26] Generated Node #0,1,0: 40:[5, 26] Operation: 70-44=26 Exploring Operation: 70/5=14, Resulting Numbers: [44, 14] Generated Node #0,1,1: 40:[44, 14] Operation: 70/5=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[5, 26], Operations: ['87-43=44', '70-44=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,40 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[44, 14], Operations: ['87-43=44', '70/5=14'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,40 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,40 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
[ 52, 70, 59, 5 ]
21
[ "59-52=7", "70/5=14", "7+14=21" ]
Current State: 21:[52, 70, 59, 5], Operations: [] Exploring Operation: 59-52=7, Resulting Numbers: [70, 5, 7] Generated Node #2: [70, 5, 7] from Operation: 59-52=7 Current State: 21:[70, 5, 7], Operations: ['59-52=7'] Exploring Operation: 70/5=14, Resulting Numbers: [7, 14] Generated Node #3: [7, 14] from Operation: 70/5=14 Current State: 21:[7, 14], Operations: ['59-52=7', '70/5=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[52, 70, 59, 5], Operations: [] Exploring Operation: 70-59=11, Resulting Numbers: [52, 5, 11] Generated Node #0,0: 21:[52, 5, 11] Operation: 70-59=11 Exploring Operation: 59-52=7, Resulting Numbers: [70, 5, 7] Generated Node #0,1: 21:[70, 5, 7] Operation: 59-52=7 Exploring Operation: 70-52=18, Resulting Numbers: [59, 5, 18] Generated Node #0,2: 21:[59, 5, 18] Operation: 70-52=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[52, 5, 11], Operations: ['70-59=11'] Exploring Operation: 52-11=41, Resulting Numbers: [5, 41] Generated Node #0,0,0: 21:[5, 41] Operation: 52-11=41 Exploring Operation: 52-5=47, Resulting Numbers: [11, 47] Generated Node #0,0,1: 21:[11, 47] Operation: 52-5=47 Exploring Operation: 11-5=6, Resulting Numbers: [52, 6] Generated Node #0,0,2: 21:[52, 6] Operation: 11-5=6 Moving to Node #0,0,0 Current State: 21:[5, 41], Operations: ['70-59=11', '52-11=41'] Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 5*41=205, Resulting Numbers: [205] 205,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[11, 47], Operations: ['70-59=11', '52-5=47'] Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 11*47=517, Resulting Numbers: [517] 517,21 unequal: No Solution Exploring Operation: 11+47=58, Resulting Numbers: [58] 58,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[52, 6], Operations: ['70-59=11', '11-5=6'] Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,21 unequal: No Solution Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,21 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[59, 5, 18], Operations: ['70-52=18'] Exploring Operation: 59-5=54, Resulting Numbers: [18, 54] Generated Node #0,2,0: 21:[18, 54] Operation: 59-5=54 Exploring Operation: 5+18=23, Resulting Numbers: [59, 23] Generated Node #0,2,1: 21:[59, 23] Operation: 5+18=23 Exploring Operation: 59-18=41, Resulting Numbers: [5, 41] Generated Node #0,2,2: 21:[5, 41] Operation: 59-18=41 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 21:[5, 41], Operations: ['70-52=18', '59-18=41'] Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 5*41=205, Resulting Numbers: [205] 205,21 unequal: No Solution No 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: 21:[18, 54], Operations: ['70-52=18', '59-5=54'] Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 18+54=72, Resulting Numbers: [72] 72,21 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,21 unequal: No Solution No 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: 21:[59, 23], Operations: ['70-52=18', '5+18=23'] Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 59*23=1357, Resulting Numbers: [1357] 1357,21 unequal: No Solution Exploring Operation: 59+23=82, Resulting Numbers: [82] 82,21 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: 21:[70, 5, 7], Operations: ['59-52=7'] Exploring Operation: 70/5=14, Resulting Numbers: [7, 14] Generated Node #0,1,0: 21:[7, 14] Operation: 70/5=14 Exploring Operation: 70/7=10, Resulting Numbers: [5, 10] Generated Node #0,1,1: 21:[5, 10] Operation: 70/7=10 Exploring Operation: 70-5=65, Resulting Numbers: [7, 65] Generated Node #0,1,2: 21:[7, 65] Operation: 70-5=65 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 21:[5, 10], Operations: ['59-52=7', '70/7=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,21 unequal: No Solution No 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: 21:[7, 14], Operations: ['59-52=7', '70/5=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[52, 70, 59, 5], Operations: [] Exploring Operation: 59-52=7, Resulting Numbers: [70, 5, 7] Generated Node #0,1: 21:[70, 5, 7] Operation: 59-52=7 Moving to Node #0,1 Current State: 21:[70, 5, 7], Operations: ['59-52=7'] Exploring Operation: 70/5=14, Resulting Numbers: [7, 14] Generated Node #0,1,0: 21:[7, 14] Operation: 70/5=14 Moving to Node #0,1,0 Current State: 21:[7, 14], Operations: ['59-52=7', '70/5=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_3
sum_heuristic
[ 86, 92, 22, 38 ]
51
[ "92*22=2024", "2024-86=1938", "1938/38=51" ]
Current State: 51:[86, 92, 22, 38], Operations: [] Exploring Operation: 92*22=2024, Resulting Numbers: [86, 38, 2024] Generated Node #2: [86, 38, 2024] from Operation: 92*22=2024 Current State: 51:[86, 38, 2024], Operations: ['92*22=2024'] Exploring Operation: 2024-86=1938, Resulting Numbers: [38, 1938] Generated Node #3: [38, 1938] from Operation: 2024-86=1938 Current State: 51:[38, 1938], Operations: ['92*22=2024', '2024-86=1938'] Exploring Operation: 1938/38=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[86, 92, 22, 38], Operations: [] Exploring Operation: 92-38=54, Resulting Numbers: [86, 22, 54] Generated Node #0,0: 51:[86, 22, 54] Operation: 92-38=54 Exploring Operation: 92-86=6, Resulting Numbers: [22, 38, 6] Generated Node #0,1: 51:[22, 38, 6] Operation: 92-86=6 Exploring Operation: 86-22=64, Resulting Numbers: [92, 38, 64] Generated Node #0,2: 51:[92, 38, 64] Operation: 86-22=64 Exploring Operation: 86-38=48, Resulting Numbers: [92, 22, 48] Generated Node #0,3: 51:[92, 22, 48] Operation: 86-38=48 Moving to Node #0,1 Current State: 51:[22, 38, 6], Operations: ['92-86=6'] Exploring Operation: 38+6=44, Resulting Numbers: [22, 44] Generated Node #0,1,0: 51:[22, 44] Operation: 38+6=44 Exploring Operation: 22+38=60, Resulting Numbers: [6, 60] Generated Node #0,1,1: 51:[6, 60] Operation: 22+38=60 Exploring Operation: 38-22=16, Resulting Numbers: [6, 16] Generated Node #0,1,2: 51:[6, 16] Operation: 38-22=16 Exploring Operation: 22-6=16, Resulting Numbers: [38, 16] Generated Node #0,1,3: 51:[38, 16] Operation: 22-6=16 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 51:[6, 16], Operations: ['92-86=6', '38-22=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,51 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 #0,1,0 Current State: 51:[22, 44], Operations: ['92-86=6', '38+6=44'] Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,51 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,51 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,51 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 #0,1,1 Current State: 51:[6, 60], Operations: ['92-86=6', '22+38=60'] Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 6*60=360, Resulting Numbers: [360] 360,51 unequal: No Solution Exploring Operation: 6+60=66, Resulting Numbers: [66] 66,51 unequal: No Solution Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,51 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 #0,1,3 Current State: 51:[38, 16], Operations: ['92-86=6', '22-6=16'] Exploring Operation: 38*16=608, Resulting Numbers: [608] 608,51 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,51 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:[86, 22, 54], Operations: ['92-38=54'] Exploring Operation: 86-54=32, Resulting Numbers: [22, 32] Generated Node #0,0,0: 51:[22, 32] Operation: 86-54=32 Exploring Operation: 54-22=32, Resulting Numbers: [86, 32] Generated Node #0,0,1: 51:[86, 32] Operation: 54-22=32 Exploring Operation: 86+22=108, Resulting Numbers: [54, 108] Generated Node #0,0,2: 51:[54, 108] Operation: 86+22=108 Exploring Operation: 86-22=64, Resulting Numbers: [54, 64] Generated Node #0,0,3: 51:[54, 64] Operation: 86-22=64 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 51:[54, 64], Operations: ['92-38=54', '86-22=64'] Exploring Operation: 54+64=118, Resulting Numbers: [118] 118,51 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 54*64=3456, Resulting Numbers: [3456] 3456,51 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 #0,0,0 Current State: 51:[22, 32], Operations: ['92-38=54', '86-54=32'] Exploring Operation: 22+32=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 22*32=704, Resulting Numbers: [704] 704,51 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 #0,0,1 Current State: 51:[86, 32], Operations: ['92-38=54', '54-22=32'] Exploring Operation: 86+32=118, Resulting Numbers: [118] 118,51 unequal: No Solution Exploring Operation: 86*32=2752, Resulting Numbers: [2752] 2752,51 unequal: No Solution Exploring Operation: 86-32=54, Resulting Numbers: [54] 54,51 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 #0,0,2 Current State: 51:[54, 108], Operations: ['92-38=54', '86+22=108'] Exploring Operation: 108/54=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 54*108=5832, Resulting Numbers: [5832] 5832,51 unequal: No Solution Exploring Operation: 108-54=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 54+108=162, Resulting Numbers: [162] 162,51 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: 51:[92, 22, 48], Operations: ['86-38=48'] Exploring Operation: 92-48=44, Resulting Numbers: [22, 44] Generated Node #0,3,0: 51:[22, 44] Operation: 92-48=44 Exploring Operation: 92-22=70, Resulting Numbers: [48, 70] Generated Node #0,3,1: 51:[48, 70] Operation: 92-22=70 Exploring Operation: 48-22=26, Resulting Numbers: [92, 26] Generated Node #0,3,2: 51:[92, 26] Operation: 48-22=26 Exploring Operation: 22+48=70, Resulting Numbers: [92, 70] Generated Node #0,3,3: 51:[92, 70] Operation: 22+48=70 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 51:[22, 44], Operations: ['86-38=48', '92-48=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,51 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,51 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 51:[48, 70], Operations: ['86-38=48', '92-22=70'] Exploring Operation: 48+70=118, Resulting Numbers: [118] 118,51 unequal: No Solution Exploring Operation: 70-48=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 48*70=3360, Resulting Numbers: [3360] 3360,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 51:[92, 26], Operations: ['86-38=48', '48-22=26'] Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,51 unequal: No Solution Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,51 unequal: No Solution Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 51:[92, 70], Operations: ['86-38=48', '22+48=70'] Exploring Operation: 92*70=6440, Resulting Numbers: [6440] 6440,51 unequal: No Solution Exploring Operation: 92-70=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 92+70=162, Resulting Numbers: [162] 162,51 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: 51:[92, 38, 64], Operations: ['86-22=64'] Exploring Operation: 92-64=28, Resulting Numbers: [38, 28] Generated Node #0,2,0: 51:[38, 28] Operation: 92-64=28 Exploring Operation: 92+38=130, Resulting Numbers: [64, 130] Generated Node #0,2,1: 51:[64, 130] Operation: 92+38=130 Exploring Operation: 92-38=54, Resulting Numbers: [64, 54] Generated Node #0,2,2: 51:[64, 54] Operation: 92-38=54 Exploring Operation: 64-38=26, Resulting Numbers: [92, 26] Generated Node #0,2,3: 51:[92, 26] Operation: 64-38=26 Moving to Node #0,2,2 Current State: 51:[64, 54], Operations: ['86-22=64', '92-38=54'] Exploring Operation: 64+54=118, Resulting Numbers: [118] 118,51 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 64*54=3456, Resulting Numbers: [3456] 3456,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[38, 28], Operations: ['86-22=64', '92-64=28'] Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 38*28=1064, Resulting Numbers: [1064] 1064,51 unequal: No Solution Exploring Operation: 38+28=66, Resulting Numbers: [66] 66,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[92, 26], Operations: ['86-22=64', '64-38=26'] Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,51 unequal: No Solution Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,51 unequal: No Solution Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[64, 130], Operations: ['86-22=64', '92+38=130'] Exploring Operation: 64*130=8320, Resulting Numbers: [8320] 8320,51 unequal: No Solution Exploring Operation: 130-64=66, Resulting Numbers: [66] 66,51 unequal: No Solution Exploring Operation: 64+130=194, Resulting Numbers: [194] 194,51 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 10, 45, 68, 43 ]
18
[ "10*45=450", "68-43=25", "450/25=18" ]
Current State: 18:[10, 45, 68, 43], Operations: [] Exploring Operation: 10*45=450, Resulting Numbers: [68, 43, 450] Generated Node #2: [68, 43, 450] from Operation: 10*45=450 Current State: 18:[68, 43, 450], Operations: ['10*45=450'] Exploring Operation: 68-43=25, Resulting Numbers: [450, 25] Generated Node #3: [450, 25] from Operation: 68-43=25 Current State: 18:[450, 25], Operations: ['10*45=450', '68-43=25'] Exploring Operation: 450/25=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[10, 45, 68, 43], Operations: [] Exploring Operation: 68-45=23, Resulting Numbers: [10, 43, 23] Generated Node #0,0: 18:[10, 43, 23] Operation: 68-45=23 Exploring Operation: 45-43=2, Resulting Numbers: [10, 68, 2] Generated Node #0,1: 18:[10, 68, 2] Operation: 45-43=2 Exploring Operation: 68-43=25, Resulting Numbers: [10, 45, 25] Generated Node #0,2: 18:[10, 45, 25] Operation: 68-43=25 Moving to Node #0,0 Current State: 18:[10, 43, 23], Operations: ['68-45=23'] Exploring Operation: 43-23=20, Resulting Numbers: [10, 20] Generated Node #0,0,0: 18:[10, 20] Operation: 43-23=20 Exploring Operation: 23-10=13, Resulting Numbers: [43, 13] Generated Node #0,0,1: 18:[43, 13] Operation: 23-10=13 Exploring Operation: 43-10=33, Resulting Numbers: [23, 33] Generated Node #0,0,2: 18:[23, 33] Operation: 43-10=33 Moving to Node #0,2 Current State: 18:[10, 45, 25], Operations: ['68-43=25'] Exploring Operation: 45-10=35, Resulting Numbers: [25, 35] Generated Node #0,2,0: 18:[25, 35] Operation: 45-10=35 Exploring Operation: 45-25=20, Resulting Numbers: [10, 20] Generated Node #0,2,1: 18:[10, 20] Operation: 45-25=20 Exploring Operation: 25-10=15, Resulting Numbers: [45, 15] Generated Node #0,2,2: 18:[45, 15] Operation: 25-10=15 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[10, 20], Operations: ['68-43=25', '45-25=20'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[25, 35], Operations: ['68-43=25', '45-10=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 25*35=875, Resulting Numbers: [875] 875,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[45, 15], Operations: ['68-43=25', '25-10=15'] Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 18:[10, 68, 2], Operations: ['45-43=2'] Exploring Operation: 68-2=66, Resulting Numbers: [10, 66] Generated Node #0,1,0: 18:[10, 66] Operation: 68-2=66 Exploring Operation: 68/2=34, Resulting Numbers: [10, 34] Generated Node #0,1,1: 18:[10, 34] Operation: 68/2=34 Exploring Operation: 68-10=58, Resulting Numbers: [2, 58] Generated Node #0,1,2: 18:[2, 58] Operation: 68-10=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[10, 34], Operations: ['45-43=2', '68/2=34'] Exploring Operation: 10+34=44, Resulting Numbers: [44] 44,18 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 10*34=340, Resulting Numbers: [340] 340,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[2, 58], Operations: ['45-43=2', '68-10=58'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[10, 66], Operations: ['45-43=2', '68-2=66'] Exploring Operation: 10+66=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 10*66=660, Resulting Numbers: [660] 660,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 18:[10, 20], Operations: ['68-45=23', '43-23=20'] Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[23, 33], Operations: ['68-45=23', '43-10=33'] Exploring Operation: 23*33=759, Resulting Numbers: [759] 759,18 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[43, 13], Operations: ['68-45=23', '23-10=13'] Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 43*13=559, Resulting Numbers: [559] 559,18 unequal: No Solution Exploring Operation: 43+13=56, Resulting Numbers: [56] 56,18 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 22, 82, 8, 13 ]
28
[ "13-8=5", "22*5=110", "110-82=28" ]
Current State: 28:[22, 82, 8, 13], Operations: [] Exploring Operation: 13-8=5, Resulting Numbers: [22, 82, 5] Generated Node #2: [22, 82, 5] from Operation: 13-8=5 Current State: 28:[22, 82, 5], Operations: ['13-8=5'] Exploring Operation: 22*5=110, Resulting Numbers: [82, 110] Generated Node #3: [82, 110] from Operation: 22*5=110 Current State: 28:[82, 110], Operations: ['13-8=5', '22*5=110'] Exploring Operation: 110-82=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[22, 82, 8, 13], Operations: [] Exploring Operation: 82-13=69, Resulting Numbers: [22, 8, 69] Generated Node #0,0: 28:[22, 8, 69] Operation: 82-13=69 Exploring Operation: 22-8=14, Resulting Numbers: [82, 13, 14] Generated Node #0,1: 28:[82, 13, 14] Operation: 22-8=14 Exploring Operation: 82-8=74, Resulting Numbers: [22, 13, 74] Generated Node #0,2: 28:[22, 13, 74] Operation: 82-8=74 Exploring Operation: 22+8=30, Resulting Numbers: [82, 13, 30] Generated Node #0,3: 28:[82, 13, 30] Operation: 22+8=30 Exploring Operation: 82-22=60, Resulting Numbers: [8, 13, 60] Generated Node #0,4: 28:[8, 13, 60] Operation: 82-22=60 Moving to Node #0,4 Current State: 28:[8, 13, 60], Operations: ['82-22=60'] Exploring Operation: 13-8=5, Resulting Numbers: [60, 5] Generated Node #0,4,0: 28:[60, 5] Operation: 13-8=5 Exploring Operation: 60-13=47, Resulting Numbers: [8, 47] Generated Node #0,4,1: 28:[8, 47] Operation: 60-13=47 Exploring Operation: 8+13=21, Resulting Numbers: [60, 21] Generated Node #0,4,2: 28:[60, 21] Operation: 8+13=21 Exploring Operation: 8+60=68, Resulting Numbers: [13, 68] Generated Node #0,4,3: 28:[13, 68] Operation: 8+60=68 Exploring Operation: 60-8=52, Resulting Numbers: [13, 52] Generated Node #0,4,4: 28:[13, 52] Operation: 60-8=52 Moving to Node #0,0 Current State: 28:[22, 8, 69], Operations: ['82-13=69'] Exploring Operation: 8+69=77, Resulting Numbers: [22, 77] Generated Node #0,0,0: 28:[22, 77] Operation: 8+69=77 Exploring Operation: 22-8=14, Resulting Numbers: [69, 14] Generated Node #0,0,1: 28:[69, 14] Operation: 22-8=14 Exploring Operation: 69-8=61, Resulting Numbers: [22, 61] Generated Node #0,0,2: 28:[22, 61] Operation: 69-8=61 Exploring Operation: 69-22=47, Resulting Numbers: [8, 47] Generated Node #0,0,3: 28:[8, 47] Operation: 69-22=47 Exploring Operation: 22+8=30, Resulting Numbers: [69, 30] Generated Node #0,0,4: 28:[69, 30] Operation: 22+8=30 Moving to Node #0,2 Current State: 28:[22, 13, 74], Operations: ['82-8=74'] Exploring Operation: 74-22=52, Resulting Numbers: [13, 52] Generated Node #0,2,0: 28:[13, 52] Operation: 74-22=52 Exploring Operation: 22-13=9, Resulting Numbers: [74, 9] Generated Node #0,2,1: 28:[74, 9] Operation: 22-13=9 Exploring Operation: 22+13=35, Resulting Numbers: [74, 35] Generated Node #0,2,2: 28:[74, 35] Operation: 22+13=35 Exploring Operation: 13+74=87, Resulting Numbers: [22, 87] Generated Node #0,2,3: 28:[22, 87] Operation: 13+74=87 Exploring Operation: 74-13=61, Resulting Numbers: [22, 61] Generated Node #0,2,4: 28:[22, 61] Operation: 74-13=61 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 28:[13, 52], Operations: ['82-8=74', '74-22=52'] Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 13*52=676, Resulting Numbers: [676] 676,28 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 28:[22, 61], Operations: ['82-8=74', '74-13=61'] Exploring Operation: 22+61=83, Resulting Numbers: [83] 83,28 unequal: No Solution Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 22*61=1342, Resulting Numbers: [1342] 1342,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 28:[74, 9], Operations: ['82-8=74', '22-13=9'] Exploring Operation: 74*9=666, Resulting Numbers: [666] 666,28 unequal: No Solution Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 74+9=83, Resulting Numbers: [83] 83,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 28:[74, 35], Operations: ['82-8=74', '22+13=35'] Exploring Operation: 74*35=2590, Resulting Numbers: [2590] 2590,28 unequal: No Solution Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 74+35=109, Resulting Numbers: [109] 109,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 28:[22, 87], Operations: ['82-8=74', '13+74=87'] Exploring Operation: 22+87=109, Resulting Numbers: [109] 109,28 unequal: No Solution Exploring Operation: 22*87=1914, Resulting Numbers: [1914] 1914,28 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,28 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: 28:[82, 13, 14], Operations: ['22-8=14'] Exploring Operation: 82-13=69, Resulting Numbers: [14, 69] Generated Node #0,1,0: 28:[14, 69] Operation: 82-13=69 Exploring Operation: 13+14=27, Resulting Numbers: [82, 27] Generated Node #0,1,1: 28:[82, 27] Operation: 13+14=27 Exploring Operation: 82-14=68, Resulting Numbers: [13, 68] Generated Node #0,1,2: 28:[13, 68] Operation: 82-14=68 Exploring Operation: 82+13=95, Resulting Numbers: [14, 95] Generated Node #0,1,3: 28:[14, 95] Operation: 82+13=95 Exploring Operation: 14-13=1, Resulting Numbers: [82, 1] Generated Node #0,1,4: 28:[82, 1] Operation: 14-13=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 28:[14, 69], Operations: ['22-8=14', '82-13=69'] Exploring Operation: 14*69=966, Resulting Numbers: [966] 966,28 unequal: No Solution Exploring Operation: 14+69=83, Resulting Numbers: [83] 83,28 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[13, 68], Operations: ['22-8=14', '82-14=68'] Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,28 unequal: No Solution Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[82, 27], Operations: ['22-8=14', '13+14=27'] Exploring Operation: 82+27=109, Resulting Numbers: [109] 109,28 unequal: No Solution Exploring Operation: 82-27=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 82*27=2214, Resulting Numbers: [2214] 2214,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 28:[82, 1], Operations: ['22-8=14', '14-13=1'] Exploring Operation: 82*1=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,28 unequal: No Solution Exploring Operation: 82+1=83, Resulting Numbers: [83] 83,28 unequal: No Solution Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 28:[14, 95], Operations: ['22-8=14', '82+13=95'] Exploring Operation: 14*95=1330, Resulting Numbers: [1330] 1330,28 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 14+95=109, Resulting Numbers: [109] 109,28 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: 28:[82, 13, 30], Operations: ['22+8=30'] Exploring Operation: 30-13=17, Resulting Numbers: [82, 17] Generated Node #0,3,0: 28:[82, 17] Operation: 30-13=17 Exploring Operation: 82-13=69, Resulting Numbers: [30, 69] Generated Node #0,3,1: 28:[30, 69] Operation: 82-13=69 Exploring Operation: 82-30=52, Resulting Numbers: [13, 52] Generated Node #0,3,2: 28:[13, 52] Operation: 82-30=52 Exploring Operation: 82+13=95, Resulting Numbers: [30, 95] Generated Node #0,3,3: 28:[30, 95] Operation: 82+13=95 Exploring Operation: 13+30=43, Resulting Numbers: [82, 43] Generated Node #0,3,4: 28:[82, 43] Operation: 13+30=43 Moving to Node #0,4,1 Current State: 28:[8, 47], Operations: ['82-22=60', '60-13=47'] Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,28 unequal: No Solution Moving to Node #0,0,3 Current State: 28:[8, 47], Operations: ['82-13=69', '69-22=47'] Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,28 unequal: No Solution Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,28 unequal: No Solution Moving to Node #0,4,4 Current State: 28:[13, 52], Operations: ['82-22=60', '60-8=52'] Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 13*52=676, Resulting Numbers: [676] 676,28 unequal: No Solution Moving to Node #0,3,2 Current State: 28:[13, 52], Operations: ['22+8=30', '82-30=52'] Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 13*52=676, Resulting Numbers: [676] 676,28 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,28 unequal: No Solution Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,28 unequal: No Solution Moving to Node #0,4,0 Current State: 28:[60, 5], Operations: ['82-22=60', '13-8=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,28 unequal: No Solution Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 60*5=300, Resulting Numbers: [300] 300,28 unequal: No Solution Moving to Node #0,0,2 Current State: 28:[22, 61], Operations: ['82-13=69', '69-8=61'] Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 22*61=1342, Resulting Numbers: [1342] 1342,28 unequal: No Solution Exploring Operation: 22+61=83, Resulting Numbers: [83] 83,28 unequal: No Solution Moving to Node #0,4,2 Current State: 28:[60, 21], Operations: ['82-22=60', '8+13=21'] Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,28 unequal: No Solution Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,28 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,28 unequal: No Solution Moving to Node #0,4,3 Current State: 28:[13, 68], Operations: ['82-22=60', '8+60=68'] Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,28 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[69, 14], Operations: ['82-13=69', '22-8=14'] Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,28 unequal: No Solution Exploring Operation: 69*14=966, Resulting Numbers: [966] 966,28 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,28 unequal: No Solution Moving to Node #0,3,1 Current State: 28:[30, 69], Operations: ['22+8=30', '82-13=69'] Exploring Operation: 30+69=99, Resulting Numbers: [99] 99,28 unequal: No Solution Exploring Operation: 30*69=2070, Resulting Numbers: [2070] 2070,28 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,28 unequal: No Solution Moving to Node #0,0,4 Current State: 28:[69, 30], Operations: ['82-13=69', '22+8=30'] Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,28 unequal: No Solution Exploring Operation: 69*30=2070, Resulting Numbers: [2070] 2070,28 unequal: No Solution Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[22, 77], Operations: ['82-13=69', '8+69=77'] Exploring Operation: 22*77=1694, Resulting Numbers: [1694] 1694,28 unequal: No Solution Exploring Operation: 77-22=55, Resulting Numbers: [55] 55,28 unequal: No Solution Exploring Operation: 22+77=99, Resulting Numbers: [99] 99,28 unequal: No Solution Moving to Node #0,3,0 Current State: 28:[82, 17], Operations: ['22+8=30', '30-13=17'] Exploring Operation: 82+17=99, Resulting Numbers: [99] 99,28 unequal: No Solution Exploring Operation: 82*17=1394, Resulting Numbers: [1394] 1394,28 unequal: No Solution Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,28 unequal: No Solution Moving to Node #0,3,4 Current State: 28:[82, 43], Operations: ['22+8=30', '13+30=43'] Exploring Operation: 82*43=3526, Resulting Numbers: [3526] 3526,28 unequal: No Solution Exploring Operation: 82+43=125, Resulting Numbers: [125] 125,28 unequal: No Solution Exploring Operation: 82-43=39, Resulting Numbers: [39] 39,28 unequal: No Solution Moving to Node #0,3,3 Current State: 28:[30, 95], Operations: ['22+8=30', '82+13=95'] Exploring Operation: 30*95=2850, Resulting Numbers: [2850] 2850,28 unequal: No Solution Exploring Operation: 95-30=65, Resulting Numbers: [65] 65,28 unequal: No Solution Exploring Operation: 30+95=125, Resulting Numbers: [125] 125,28 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 27, 87, 49, 8 ]
73
[ "27+87=114", "49-8=41", "114-41=73" ]
Current State: 73:[27, 87, 49, 8], Operations: [] Exploring Operation: 27+87=114, Resulting Numbers: [49, 8, 114] Generated Node #2: [49, 8, 114] from Operation: 27+87=114 Current State: 73:[49, 8, 114], Operations: ['27+87=114'] Exploring Operation: 49-8=41, Resulting Numbers: [114, 41] Generated Node #3: [114, 41] from Operation: 49-8=41 Current State: 73:[114, 41], Operations: ['27+87=114', '49-8=41'] Exploring Operation: 114-41=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[27, 87, 49, 8], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [87, 49, 19] Generated Node #0,0: 73:[87, 49, 19] Operation: 27-8=19 Exploring Operation: 27+49=76, Resulting Numbers: [87, 8, 76] Generated Node #0,1: 73:[87, 8, 76] Operation: 27+49=76 Exploring Operation: 27+8=35, Resulting Numbers: [87, 49, 35] Generated Node #0,2: 73:[87, 49, 35] Operation: 27+8=35 Exploring Operation: 87-8=79, Resulting Numbers: [27, 49, 79] Generated Node #0,3: 73:[27, 49, 79] Operation: 87-8=79 Exploring Operation: 49+8=57, Resulting Numbers: [27, 87, 57] Generated Node #0,4: 73:[27, 87, 57] Operation: 49+8=57 Moving to Node #0,2 Current State: 73:[87, 49, 35], Operations: ['27+8=35'] Exploring Operation: 87-35=52, Resulting Numbers: [49, 52] Generated Node #0,2,0: 73:[49, 52] Operation: 87-35=52 Exploring Operation: 49-35=14, Resulting Numbers: [87, 14] Generated Node #0,2,1: 73:[87, 14] Operation: 49-35=14 Exploring Operation: 87+35=122, Resulting Numbers: [49, 122] Generated Node #0,2,2: 73:[49, 122] Operation: 87+35=122 Exploring Operation: 49+35=84, Resulting Numbers: [87, 84] Generated Node #0,2,3: 73:[87, 84] Operation: 49+35=84 Exploring Operation: 87-49=38, Resulting Numbers: [35, 38] Generated Node #0,2,4: 73:[35, 38] Operation: 87-49=38 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 73:[87, 84], Operations: ['27+8=35', '49+35=84'] Exploring Operation: 87+84=171, Resulting Numbers: [171] 171,73 unequal: No Solution Exploring Operation: 87-84=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 87*84=7308, Resulting Numbers: [7308] 7308,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 73:[49, 52], Operations: ['27+8=35', '87-35=52'] Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,73 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 73:[87, 14], Operations: ['27+8=35', '49-35=14'] Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[27, 87, 49, 8], Operations: [] Exploring Operation: 27+8=35, Resulting Numbers: [87, 49, 35] Generated Node #0,2: 73:[87, 49, 35] Operation: 27+8=35 Moving to Node #0,2 Current State: 73:[87, 49, 35], Operations: ['27+8=35'] Exploring Operation: 49-35=14, Resulting Numbers: [87, 14] Generated Node #0,2,1: 73:[87, 14] Operation: 49-35=14 Moving to Node #0,2,1 Current State: 73:[87, 14], Operations: ['27+8=35', '49-35=14'] Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 28, 57, 10, 35 ]
40
[ "28+57=85", "10+35=45", "85-45=40" ]
Current State: 40:[28, 57, 10, 35], Operations: [] Exploring Operation: 28+57=85, Resulting Numbers: [10, 35, 85] Generated Node #2: [10, 35, 85] from Operation: 28+57=85 Current State: 40:[10, 35, 85], Operations: ['28+57=85'] Exploring Operation: 10+35=45, Resulting Numbers: [85, 45] Generated Node #3: [85, 45] from Operation: 10+35=45 Current State: 40:[85, 45], Operations: ['28+57=85', '10+35=45'] Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[28, 57, 10, 35], Operations: [] Exploring Operation: 57-35=22, Resulting Numbers: [28, 10, 22] Generated Node #0,0: 40:[28, 10, 22] Operation: 57-35=22 Exploring Operation: 57-28=29, Resulting Numbers: [10, 35, 29] Generated Node #0,1: 40:[10, 35, 29] Operation: 57-28=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[28, 10, 22], Operations: ['57-35=22'] Exploring Operation: 28+10=38, Resulting Numbers: [22, 38] Generated Node #0,0,0: 40:[22, 38] Operation: 28+10=38 Exploring Operation: 28-22=6, Resulting Numbers: [10, 6] Generated Node #0,0,1: 40:[10, 6] Operation: 28-22=6 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 40:[10, 6], Operations: ['57-35=22', '28-22=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,40 unequal: No Solution No 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: 40:[22, 38], Operations: ['57-35=22', '28+10=38'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,40 unequal: No Solution Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,40 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: 40:[10, 35, 29], Operations: ['57-28=29'] Exploring Operation: 35-29=6, Resulting Numbers: [10, 6] Generated Node #0,1,0: 40:[10, 6] Operation: 35-29=6 Exploring Operation: 10+29=39, Resulting Numbers: [35, 39] Generated Node #0,1,1: 40:[35, 39] Operation: 10+29=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[10, 6], Operations: ['57-28=29', '35-29=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,40 unequal: No Solution No 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: 40:[35, 39], Operations: ['57-28=29', '10+29=39'] Exploring Operation: 35+39=74, Resulting Numbers: [74] 74,40 unequal: No Solution Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 52, 29, 4, 7 ]
70
[ "52+29=81", "4+7=11", "81-11=70" ]
Current State: 70:[52, 29, 4, 7], Operations: [] Exploring Operation: 52+29=81, Resulting Numbers: [4, 7, 81] Generated Node #2: [4, 7, 81] from Operation: 52+29=81 Current State: 70:[4, 7, 81], Operations: ['52+29=81'] Exploring Operation: 4+7=11, Resulting Numbers: [81, 11] Generated Node #3: [81, 11] from Operation: 4+7=11 Current State: 70:[81, 11], Operations: ['52+29=81', '4+7=11'] Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[52, 29, 4, 7], Operations: [] Exploring Operation: 52-29=23, Resulting Numbers: [4, 7, 23] Generated Node #0,0: 70:[4, 7, 23] Operation: 52-29=23 Exploring Operation: 52/4=13, Resulting Numbers: [29, 7, 13] Generated Node #0,1: 70:[29, 7, 13] Operation: 52/4=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[29, 7, 13], Operations: ['52/4=13'] Exploring Operation: 29-13=16, Resulting Numbers: [7, 16] Generated Node #0,1,0: 70:[7, 16] Operation: 29-13=16 Exploring Operation: 29+7=36, Resulting Numbers: [13, 36] Generated Node #0,1,1: 70:[13, 36] Operation: 29+7=36 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 70:[7, 16], Operations: ['52/4=13', '29-13=16'] Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[13, 36], Operations: ['52/4=13', '29+7=36'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[4, 7, 23], Operations: ['52-29=23'] Exploring Operation: 23-7=16, Resulting Numbers: [4, 16] Generated Node #0,0,0: 70:[4, 16] Operation: 23-7=16 Exploring Operation: 23-4=19, Resulting Numbers: [7, 19] Generated Node #0,0,1: 70:[7, 19] Operation: 23-4=19 Moving to Node #0,0,0 Current State: 70:[4, 16], Operations: ['52-29=23', '23-7=16'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[7, 19], Operations: ['52-29=23', '23-4=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 14, 58, 9, 97 ]
61
[ "14*58=812", "9*97=873", "873-812=61" ]
Current State: 61:[14, 58, 9, 97], Operations: [] Exploring Operation: 14*58=812, Resulting Numbers: [9, 97, 812] Generated Node #2: [9, 97, 812] from Operation: 14*58=812 Current State: 61:[9, 97, 812], Operations: ['14*58=812'] Exploring Operation: 9*97=873, Resulting Numbers: [812, 873] Generated Node #3: [812, 873] from Operation: 9*97=873 Current State: 61:[812, 873], Operations: ['14*58=812', '9*97=873'] Exploring Operation: 873-812=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[14, 58, 9, 97], Operations: [] Exploring Operation: 14+9=23, Resulting Numbers: [58, 97, 23] Generated Node #0,0: 61:[58, 97, 23] Operation: 14+9=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[58, 97, 23], Operations: ['14+9=23'] Exploring Operation: 97-23=74, Resulting Numbers: [58, 74] Generated Node #0,0,0: 61:[58, 74] Operation: 97-23=74 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[58, 74], Operations: ['14+9=23', '97-23=74'] Exploring Operation: 74-58=16, Resulting Numbers: [16] 16,61 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
[ 51, 11, 23, 27 ]
66
[ "51+11=62", "27-23=4", "62+4=66" ]
Current State: 66:[51, 11, 23, 27], Operations: [] Exploring Operation: 51+11=62, Resulting Numbers: [23, 27, 62] Generated Node #2: [23, 27, 62] from Operation: 51+11=62 Current State: 66:[23, 27, 62], Operations: ['51+11=62'] Exploring Operation: 27-23=4, Resulting Numbers: [62, 4] Generated Node #3: [62, 4] from Operation: 27-23=4 Current State: 66:[62, 4], Operations: ['51+11=62', '27-23=4'] Exploring Operation: 62+4=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[51, 11, 23, 27], Operations: [] Exploring Operation: 51-27=24, Resulting Numbers: [11, 23, 24] Generated Node #0,0: 66:[11, 23, 24] Operation: 51-27=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[11, 23, 24], Operations: ['51-27=24'] Exploring Operation: 24-23=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 66:[11, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 66:[11, 1], Operations: ['51-27=24', '24-23=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,66 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
[ 48, 35, 60, 20 ]
12
[ "35-20=15", "48*15=720", "720/60=12" ]
Current State: 12:[48, 35, 60, 20], Operations: [] Exploring Operation: 35-20=15, Resulting Numbers: [48, 60, 15] Generated Node #2: [48, 60, 15] from Operation: 35-20=15 Current State: 12:[48, 60, 15], Operations: ['35-20=15'] Exploring Operation: 48*15=720, Resulting Numbers: [60, 720] Generated Node #3: [60, 720] from Operation: 48*15=720 Current State: 12:[60, 720], Operations: ['35-20=15', '48*15=720'] Exploring Operation: 720/60=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[48, 35, 60, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [48, 35, 3] Generated Node #0,0: 12:[48, 35, 3] Operation: 60/20=3 Exploring Operation: 48-35=13, Resulting Numbers: [60, 20, 13] Generated Node #0,1: 12:[60, 20, 13] Operation: 48-35=13 Exploring Operation: 60-48=12, Resulting Numbers: [35, 20, 12] Generated Node #0,2: 12:[35, 20, 12] Operation: 60-48=12 Exploring Operation: 60-35=25, Resulting Numbers: [48, 20, 25] Generated Node #0,3: 12:[48, 20, 25] Operation: 60-35=25 Moving to Node #0,2 Current State: 12:[35, 20, 12], Operations: ['60-48=12'] Exploring Operation: 35+20=55, Resulting Numbers: [12, 55] Generated Node #0,2,0: 12:[12, 55] Operation: 35+20=55 Exploring Operation: 35-20=15, Resulting Numbers: [12, 15] Generated Node #0,2,1: 12:[12, 15] Operation: 35-20=15 Exploring Operation: 20-12=8, Resulting Numbers: [35, 8] Generated Node #0,2,2: 12:[35, 8] Operation: 20-12=8 Exploring Operation: 35-12=23, Resulting Numbers: [20, 23] Generated Node #0,2,3: 12:[20, 23] Operation: 35-12=23 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 12:[12, 15], Operations: ['60-48=12', '35-20=15'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 12:[20, 23], Operations: ['60-48=12', '35-12=23'] Exploring Operation: 20*23=460, Resulting Numbers: [460] 460,12 unequal: No Solution Exploring Operation: 20+23=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 12:[35, 8], Operations: ['60-48=12', '20-12=8'] Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 12:[12, 55], Operations: ['60-48=12', '35+20=55'] Exploring Operation: 12+55=67, Resulting Numbers: [67] 67,12 unequal: No Solution Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 12*55=660, Resulting Numbers: [660] 660,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 12:[48, 20, 25], Operations: ['60-35=25'] Exploring Operation: 25-20=5, Resulting Numbers: [48, 5] Generated Node #0,3,0: 12:[48, 5] Operation: 25-20=5 Exploring Operation: 48+20=68, Resulting Numbers: [25, 68] Generated Node #0,3,1: 12:[25, 68] Operation: 48+20=68 Exploring Operation: 48-25=23, Resulting Numbers: [20, 23] Generated Node #0,3,2: 12:[20, 23] Operation: 48-25=23 Exploring Operation: 48-20=28, Resulting Numbers: [25, 28] Generated Node #0,3,3: 12:[25, 28] Operation: 48-20=28 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 12:[20, 23], Operations: ['60-35=25', '48-25=23'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 20+23=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 20*23=460, Resulting Numbers: [460] 460,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 12:[25, 28], Operations: ['60-35=25', '48-20=28'] Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,12 unequal: No Solution Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 12:[48, 5], Operations: ['60-35=25', '25-20=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 48+5=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 48*5=240, Resulting Numbers: [240] 240,12 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:[25, 68], Operations: ['60-35=25', '48+20=68'] Exploring Operation: 25+68=93, Resulting Numbers: [93] 93,12 unequal: No Solution Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 25*68=1700, Resulting Numbers: [1700] 1700,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 12:[60, 20, 13], Operations: ['48-35=13'] Exploring Operation: 60/20=3, Resulting Numbers: [13, 3] Generated Node #0,1,0: 12:[13, 3] Operation: 60/20=3 Exploring Operation: 60-13=47, Resulting Numbers: [20, 47] Generated Node #0,1,1: 12:[20, 47] Operation: 60-13=47 Exploring Operation: 60-20=40, Resulting Numbers: [13, 40] Generated Node #0,1,2: 12:[13, 40] Operation: 60-20=40 Exploring Operation: 20-13=7, Resulting Numbers: [60, 7] Generated Node #0,1,3: 12:[60, 7] Operation: 20-13=7 Moving to Node #0,0 Current State: 12:[48, 35, 3], Operations: ['60/20=3'] Exploring Operation: 48-3=45, Resulting Numbers: [35, 45] Generated Node #0,0,0: 12:[35, 45] Operation: 48-3=45 Exploring Operation: 48-35=13, Resulting Numbers: [3, 13] Generated Node #0,0,1: 12:[3, 13] Operation: 48-35=13 Exploring Operation: 35-3=32, Resulting Numbers: [48, 32] Generated Node #0,0,2: 12:[48, 32] Operation: 35-3=32 Exploring Operation: 48/3=16, Resulting Numbers: [35, 16] Generated Node #0,0,3: 12:[35, 16] Operation: 48/3=16 Moving to Node #0,1,0 Current State: 12:[13, 3], Operations: ['48-35=13', '60/20=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[3, 13], Operations: ['60/20=3', '48-35=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,12 unequal: No Solution Moving to Node #0,0,3 Current State: 12:[35, 16], Operations: ['60/20=3', '48/3=16'] Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,12 unequal: No Solution Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,12 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[13, 40], Operations: ['48-35=13', '60-20=40'] Exploring Operation: 13*40=520, Resulting Numbers: [520] 520,12 unequal: No Solution Exploring Operation: 13+40=53, Resulting Numbers: [53] 53,12 unequal: No Solution Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[20, 47], Operations: ['48-35=13', '60-13=47'] Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 20*47=940, Resulting Numbers: [940] 940,12 unequal: No Solution Exploring Operation: 20+47=67, Resulting Numbers: [67] 67,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[60, 7], Operations: ['48-35=13', '20-13=7'] Exploring Operation: 60*7=420, Resulting Numbers: [420] 420,12 unequal: No Solution Exploring Operation: 60+7=67, Resulting Numbers: [67] 67,12 unequal: No Solution Exploring Operation: 60-7=53, Resulting Numbers: [53] 53,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[35, 45], Operations: ['60/20=3', '48-3=45'] Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 35*45=1575, Resulting Numbers: [1575] 1575,12 unequal: No Solution Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[48, 32], Operations: ['60/20=3', '35-3=32'] Exploring Operation: 48+32=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 48*32=1536, Resulting Numbers: [1536] 1536,12 unequal: No Solution Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,12 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 14, 30, 23, 69 ]
13
[ "30-14=16", "69/23=3", "16-3=13" ]
Current State: 13:[14, 30, 23, 69], Operations: [] Exploring Operation: 30-14=16, Resulting Numbers: [23, 69, 16] Generated Node #2: [23, 69, 16] from Operation: 30-14=16 Current State: 13:[23, 69, 16], Operations: ['30-14=16'] Exploring Operation: 69/23=3, Resulting Numbers: [16, 3] Generated Node #3: [16, 3] from Operation: 69/23=3 Current State: 13:[16, 3], Operations: ['30-14=16', '69/23=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[14, 30, 23, 69], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [14, 30, 3] Generated Node #0,0: 13:[14, 30, 3] Operation: 69/23=3 Exploring Operation: 69-30=39, Resulting Numbers: [14, 23, 39] Generated Node #0,1: 13:[14, 23, 39] Operation: 69-30=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[14, 30, 3], Operations: ['69/23=3'] Exploring Operation: 30-14=16, Resulting Numbers: [3, 16] Generated Node #0,0,0: 13:[3, 16] Operation: 30-14=16 Exploring Operation: 30/3=10, Resulting Numbers: [14, 10] Generated Node #0,0,1: 13:[14, 10] Operation: 30/3=10 Moving to Node #0,0,1 Current State: 13:[14, 10], Operations: ['69/23=3', '30/3=10'] Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,13 unequal: No Solution Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[3, 16], Operations: ['69/23=3', '30-14=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[14, 30, 23, 69], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [14, 30, 3] Generated Node #0,0: 13:[14, 30, 3] Operation: 69/23=3 Moving to Node #0,0 Current State: 13:[14, 30, 3], Operations: ['69/23=3'] Exploring Operation: 30-14=16, Resulting Numbers: [3, 16] Generated Node #0,0,0: 13:[3, 16] Operation: 30-14=16 Moving to Node #0,0,0 Current State: 13:[3, 16], Operations: ['69/23=3', '30-14=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 44, 80, 1, 49 ]
84
[ "80-44=36", "49-1=48", "36+48=84" ]
Current State: 84:[44, 80, 1, 49], Operations: [] Exploring Operation: 80-44=36, Resulting Numbers: [1, 49, 36] Generated Node #2: [1, 49, 36] from Operation: 80-44=36 Current State: 84:[1, 49, 36], Operations: ['80-44=36'] Exploring Operation: 49-1=48, Resulting Numbers: [36, 48] Generated Node #3: [36, 48] from Operation: 49-1=48 Current State: 84:[36, 48], Operations: ['80-44=36', '49-1=48'] Exploring Operation: 36+48=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[44, 80, 1, 49], Operations: [] Exploring Operation: 80+1=81, Resulting Numbers: [44, 49, 81] Generated Node #0,0: 84:[44, 49, 81] Operation: 80+1=81 Exploring Operation: 44-1=43, Resulting Numbers: [80, 49, 43] Generated Node #0,1: 84:[80, 49, 43] Operation: 44-1=43 Exploring Operation: 49-44=5, Resulting Numbers: [80, 1, 5] Generated Node #0,2: 84:[80, 1, 5] Operation: 49-44=5 Exploring Operation: 80-49=31, Resulting Numbers: [44, 1, 31] Generated Node #0,3: 84:[44, 1, 31] Operation: 80-49=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[80, 1, 5], Operations: ['49-44=5'] Exploring Operation: 80/5=16, Resulting Numbers: [1, 16] Generated Node #0,2,0: 84:[1, 16] Operation: 80/5=16 Exploring Operation: 80+5=85, Resulting Numbers: [1, 85] Generated Node #0,2,1: 84:[1, 85] Operation: 80+5=85 Exploring Operation: 80+1=81, Resulting Numbers: [5, 81] Generated Node #0,2,2: 84:[5, 81] Operation: 80+1=81 Exploring Operation: 1+5=6, Resulting Numbers: [80, 6] Generated Node #0,2,3: 84:[80, 6] Operation: 1+5=6 Moving to Node #0,2,1 Current State: 84:[1, 85], Operations: ['49-44=5', '80+5=85'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[44, 80, 1, 49], Operations: [] Exploring Operation: 49-44=5, Resulting Numbers: [80, 1, 5] Generated Node #0,2: 84:[80, 1, 5] Operation: 49-44=5 Moving to Node #0,2 Current State: 84:[80, 1, 5], Operations: ['49-44=5'] Exploring Operation: 80+5=85, Resulting Numbers: [1, 85] Generated Node #0,2,1: 84:[1, 85] Operation: 80+5=85 Moving to Node #0,2,1 Current State: 84:[1, 85], Operations: ['49-44=5', '80+5=85'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 49, 80, 10, 29 ]
28
[ "49-29=20", "80/10=8", "20+8=28" ]
Current State: 28:[49, 80, 10, 29], Operations: [] Exploring Operation: 49-29=20, Resulting Numbers: [80, 10, 20] Generated Node #2: [80, 10, 20] from Operation: 49-29=20 Current State: 28:[80, 10, 20], Operations: ['49-29=20'] Exploring Operation: 80/10=8, Resulting Numbers: [20, 8] Generated Node #3: [20, 8] from Operation: 80/10=8 Current State: 28:[20, 8], Operations: ['49-29=20', '80/10=8'] Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[49, 80, 10, 29], Operations: [] Exploring Operation: 80-29=51, Resulting Numbers: [49, 10, 51] Generated Node #0,0: 28:[49, 10, 51] Operation: 80-29=51 Exploring Operation: 80/10=8, Resulting Numbers: [49, 29, 8] Generated Node #0,1: 28:[49, 29, 8] Operation: 80/10=8 Exploring Operation: 80-49=31, Resulting Numbers: [10, 29, 31] Generated Node #0,2: 28:[10, 29, 31] Operation: 80-49=31 Moving to Node #0,2 Current State: 28:[10, 29, 31], Operations: ['80-49=31'] Exploring Operation: 31-10=21, Resulting Numbers: [29, 21] Generated Node #0,2,0: 28:[29, 21] Operation: 31-10=21 Exploring Operation: 29-10=19, Resulting Numbers: [31, 19] Generated Node #0,2,1: 28:[31, 19] Operation: 29-10=19 Exploring Operation: 31-29=2, Resulting Numbers: [10, 2] Generated Node #0,2,2: 28:[10, 2] Operation: 31-29=2 Moving to Node #0,1 Current State: 28:[49, 29, 8], Operations: ['80/10=8'] Exploring Operation: 49-29=20, Resulting Numbers: [8, 20] Generated Node #0,1,0: 28:[8, 20] Operation: 49-29=20 Exploring Operation: 49-8=41, Resulting Numbers: [29, 41] Generated Node #0,1,1: 28:[29, 41] Operation: 49-8=41 Exploring Operation: 29-8=21, Resulting Numbers: [49, 21] Generated Node #0,1,2: 28:[49, 21] Operation: 29-8=21 Moving to Node #0,0 Current State: 28:[49, 10, 51], Operations: ['80-29=51'] Exploring Operation: 49-10=39, Resulting Numbers: [51, 39] Generated Node #0,0,0: 28:[51, 39] Operation: 49-10=39 Exploring Operation: 51-49=2, Resulting Numbers: [10, 2] Generated Node #0,0,1: 28:[10, 2] Operation: 51-49=2 Exploring Operation: 51-10=41, Resulting Numbers: [49, 41] Generated Node #0,0,2: 28:[49, 41] Operation: 51-10=41 Moving to Node #0,2,2 Current State: 28:[10, 2], Operations: ['80-49=31', '31-29=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,28 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,28 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[10, 2], Operations: ['80-29=51', '51-49=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,28 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,28 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[8, 20], Operations: ['80/10=8', '49-29=20'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,28 unequal: No Solution Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[49, 80, 10, 29], Operations: [] Exploring Operation: 80/10=8, Resulting Numbers: [49, 29, 8] Generated Node #0,1: 28:[49, 29, 8] Operation: 80/10=8 Moving to Node #0,1 Current State: 28:[49, 29, 8], Operations: ['80/10=8'] Exploring Operation: 49-29=20, Resulting Numbers: [8, 20] Generated Node #0,1,0: 28:[8, 20] Operation: 49-29=20 Moving to Node #0,1,0 Current State: 28:[8, 20], Operations: ['80/10=8', '49-29=20'] Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
0.979167
hs_3
sum_heuristic
[ 73, 88, 3, 35 ]
52
[ "73+35=108", "108/3=36", "88-36=52" ]
Current State: 52:[73, 88, 3, 35], Operations: [] Exploring Operation: 73+35=108, Resulting Numbers: [88, 3, 108] Generated Node #2: [88, 3, 108] from Operation: 73+35=108 Current State: 52:[88, 3, 108], Operations: ['73+35=108'] Exploring Operation: 108/3=36, Resulting Numbers: [88, 36] Generated Node #3: [88, 36] from Operation: 108/3=36 Current State: 52:[88, 36], Operations: ['73+35=108', '108/3=36'] Exploring Operation: 88-36=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[73, 88, 3, 35], Operations: [] Exploring Operation: 88-73=15, Resulting Numbers: [3, 35, 15] Generated Node #0,0: 52:[3, 35, 15] Operation: 88-73=15 Exploring Operation: 88-35=53, Resulting Numbers: [73, 3, 53] Generated Node #0,1: 52:[73, 3, 53] Operation: 88-35=53 Exploring Operation: 73-35=38, Resulting Numbers: [88, 3, 38] Generated Node #0,2: 52:[88, 3, 38] Operation: 73-35=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[3, 35, 15], Operations: ['88-73=15'] Exploring Operation: 35+15=50, Resulting Numbers: [3, 50] Generated Node #0,0,0: 52:[3, 50] Operation: 35+15=50 Exploring Operation: 35-3=32, Resulting Numbers: [15, 32] Generated Node #0,0,1: 52:[15, 32] Operation: 35-3=32 Exploring Operation: 35-15=20, Resulting Numbers: [3, 20] Generated Node #0,0,2: 52:[3, 20] Operation: 35-15=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[3, 50], Operations: ['88-73=15', '35+15=50'] Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,52 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 #0,0,2 Current State: 52:[3, 20], Operations: ['88-73=15', '35-15=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,52 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 #0,0,1 Current State: 52:[15, 32], Operations: ['88-73=15', '35-3=32'] Exploring Operation: 15*32=480, Resulting Numbers: [480] 480,52 unequal: No Solution Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,52 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 #0,1 Current State: 52:[73, 3, 53], Operations: ['88-35=53'] Exploring Operation: 73-53=20, Resulting Numbers: [3, 20] Generated Node #0,1,0: 52:[3, 20] Operation: 73-53=20 Exploring Operation: 73-3=70, Resulting Numbers: [53, 70] Generated Node #0,1,1: 52:[53, 70] Operation: 73-3=70 Exploring Operation: 53-3=50, Resulting Numbers: [73, 50] Generated Node #0,1,2: 52:[73, 50] Operation: 53-3=50 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[3, 20], Operations: ['88-35=53', '73-53=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,52 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:[53, 70], Operations: ['88-35=53', '73-3=70'] Exploring Operation: 53*70=3710, Resulting Numbers: [3710] 3710,52 unequal: No Solution Exploring Operation: 53+70=123, Resulting Numbers: [123] 123,52 unequal: No Solution Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,52 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:[73, 50], Operations: ['88-35=53', '53-3=50'] Exploring Operation: 73+50=123, Resulting Numbers: [123] 123,52 unequal: No Solution Exploring Operation: 73*50=3650, Resulting Numbers: [3650] 3650,52 unequal: No Solution Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,52 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 #0,2 Current State: 52:[88, 3, 38], Operations: ['73-35=38'] Exploring Operation: 88-3=85, Resulting Numbers: [38, 85] Generated Node #0,2,0: 52:[38, 85] Operation: 88-3=85 Exploring Operation: 88-38=50, Resulting Numbers: [3, 50] Generated Node #0,2,1: 52:[3, 50] Operation: 88-38=50 Exploring Operation: 38-3=35, Resulting Numbers: [88, 35] Generated Node #0,2,2: 52:[88, 35] Operation: 38-3=35 Moving to Node #0,2,1 Current State: 52:[3, 50], Operations: ['73-35=38', '88-38=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[38, 85], Operations: ['73-35=38', '88-3=85'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 38+85=123, Resulting Numbers: [123] 123,52 unequal: No Solution Exploring Operation: 38*85=3230, Resulting Numbers: [3230] 3230,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[88, 35], Operations: ['73-35=38', '38-3=35'] Exploring Operation: 88*35=3080, Resulting Numbers: [3080] 3080,52 unequal: No Solution Exploring Operation: 88-35=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 88+35=123, Resulting Numbers: [123] 123,52 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
[ 32, 5, 4, 8 ]
41
[ "32+5=37", "8-4=4", "37+4=41" ]
Current State: 41:[32, 5, 4, 8], Operations: [] Exploring Operation: 32+5=37, Resulting Numbers: [4, 8, 37] Generated Node #2: [4, 8, 37] from Operation: 32+5=37 Current State: 41:[4, 8, 37], Operations: ['32+5=37'] Exploring Operation: 8-4=4, Resulting Numbers: [37, 4] Generated Node #3: [37, 4] from Operation: 8-4=4 Current State: 41:[37, 4], Operations: ['32+5=37', '8-4=4'] Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[32, 5, 4, 8], Operations: [] Exploring Operation: 32+5=37, Resulting Numbers: [4, 8, 37] Generated Node #0,0: 41:[4, 8, 37] Operation: 32+5=37 Exploring Operation: 5*8=40, Resulting Numbers: [32, 4, 40] Generated Node #0,1: 41:[32, 4, 40] Operation: 5*8=40 Exploring Operation: 4*8=32, Resulting Numbers: [32, 5, 32] Generated Node #0,2: 41:[32, 5, 32] Operation: 4*8=32 Exploring Operation: 5*4=20, Resulting Numbers: [32, 8, 20] Generated Node #0,3: 41:[32, 8, 20] Operation: 5*4=20 Moving to Node #0,1 Current State: 41:[32, 4, 40], Operations: ['5*8=40'] Exploring Operation: 40-4=36, Resulting Numbers: [32, 36] Generated Node #0,1,0: 41:[32, 36] Operation: 40-4=36 Exploring Operation: 4+40=44, Resulting Numbers: [32, 44] Generated Node #0,1,1: 41:[32, 44] Operation: 4+40=44 Exploring Operation: 32-4=28, Resulting Numbers: [40, 28] Generated Node #0,1,2: 41:[40, 28] Operation: 32-4=28 Exploring Operation: 32+4=36, Resulting Numbers: [40, 36] Generated Node #0,1,3: 41:[40, 36] Operation: 32+4=36 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[40, 36], Operations: ['5*8=40', '32+4=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,41 unequal: No Solution Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 40*36=1440, Resulting Numbers: [1440] 1440,41 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 #0,1,1 Current State: 41:[32, 44], Operations: ['5*8=40', '4+40=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,41 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,41 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:[32, 36], Operations: ['5*8=40', '40-4=36'] Exploring Operation: 32*36=1152, Resulting Numbers: [1152] 1152,41 unequal: No Solution Exploring Operation: 32+36=68, Resulting Numbers: [68] 68,41 unequal: No Solution Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,41 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:[40, 28], Operations: ['5*8=40', '32-4=28'] Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,41 unequal: No Solution Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,41 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,41 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:[32, 5, 32], Operations: ['4*8=32'] Exploring Operation: 32-5=27, Resulting Numbers: [32, 27] Generated Node #0,2,0: 41:[32, 27] Operation: 32-5=27 Exploring Operation: 32-5=27, Resulting Numbers: [32, 27] Generated Node #0,2,1: 41:[32, 27] Operation: 32-5=27 Exploring Operation: 32+5=37, Resulting Numbers: [32, 37] Generated Node #0,2,2: 41:[32, 37] Operation: 32+5=37 Exploring Operation: 5+32=37, Resulting Numbers: [32, 37] Generated Node #0,2,3: 41:[32, 37] Operation: 5+32=37 Moving to Node #0,3 Current State: 41:[32, 8, 20], Operations: ['5*4=20'] Exploring Operation: 8+20=28, Resulting Numbers: [32, 28] Generated Node #0,3,0: 41:[32, 28] Operation: 8+20=28 Exploring Operation: 32+8=40, Resulting Numbers: [20, 40] Generated Node #0,3,1: 41:[20, 40] Operation: 32+8=40 Exploring Operation: 20-8=12, Resulting Numbers: [32, 12] Generated Node #0,3,2: 41:[32, 12] Operation: 20-8=12 Exploring Operation: 32-8=24, Resulting Numbers: [20, 24] Generated Node #0,3,3: 41:[20, 24] Operation: 32-8=24 Moving to Node #0,0 Current State: 41:[4, 8, 37], Operations: ['32+5=37'] Exploring Operation: 4+8=12, Resulting Numbers: [37, 12] Generated Node #0,0,0: 41:[37, 12] Operation: 4+8=12 Exploring Operation: 4+37=41, Resulting Numbers: [8, 41] Generated Node #0,0,1: 41:[8, 41] Operation: 4+37=41 Exploring Operation: 8-4=4, Resulting Numbers: [37, 4] Generated Node #0,0,2: 41:[37, 4] Operation: 8-4=4 Exploring Operation: 4*8=32, Resulting Numbers: [37, 32] Generated Node #0,0,3: 41:[37, 32] Operation: 4*8=32 Moving to Node #0,2,2 Current State: 41:[32, 37], Operations: ['4*8=32', '32+5=37'] Exploring Operation: 32+37=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 37-32=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 32*37=1184, Resulting Numbers: [1184] 1184,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[32, 37], Operations: ['4*8=32', '5+32=37'] Exploring Operation: 32+37=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 32*37=1184, Resulting Numbers: [1184] 1184,41 unequal: No Solution Exploring Operation: 37-32=5, Resulting Numbers: [5] 5,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[37, 32], Operations: ['32+5=37', '4*8=32'] Exploring Operation: 37*32=1184, Resulting Numbers: [1184] 1184,41 unequal: No Solution Exploring Operation: 37+32=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 37-32=5, Resulting Numbers: [5] 5,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[20, 40], Operations: ['5*4=20', '32+8=40'] Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,41 unequal: No Solution Exploring Operation: 20+40=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 20*40=800, Resulting Numbers: [800] 800,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[32, 28], Operations: ['5*4=20', '8+20=28'] Exploring Operation: 32*28=896, Resulting Numbers: [896] 896,41 unequal: No Solution Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[32, 27], Operations: ['4*8=32', '32-5=27'] Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,41 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[32, 27], Operations: ['4*8=32', '32-5=27'] Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,41 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[8, 41], Operations: ['32+5=37', '4+37=41'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,41 unequal: No Solution Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[37, 12], Operations: ['32+5=37', '4+8=12'] Exploring Operation: 37+12=49, Resulting Numbers: [49] 49,41 unequal: No Solution Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 37*12=444, Resulting Numbers: [444] 444,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[20, 24], Operations: ['5*4=20', '32-8=24'] Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,41 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[32, 12], Operations: ['5*4=20', '20-8=12'] Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,41 unequal: No Solution Exploring Operation: 32*12=384, Resulting Numbers: [384] 384,41 unequal: No Solution Exploring Operation: 32+12=44, Resulting Numbers: [44] 44,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[37, 4], Operations: ['32+5=37', '8-4=4'] Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,41 unequal: No Solution Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[32, 5, 4, 8], Operations: [] Exploring Operation: 32+5=37, Resulting Numbers: [4, 8, 37] Generated Node #0,0: 41:[4, 8, 37] Operation: 32+5=37 Moving to Node #0,0 Current State: 41:[4, 8, 37], Operations: ['32+5=37'] Exploring Operation: 8-4=4, Resulting Numbers: [37, 4] Generated Node #0,0,2: 41:[37, 4] Operation: 8-4=4 Moving to Node #0,0,2 Current State: 41:[37, 4], Operations: ['32+5=37', '8-4=4'] Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
0.9375
hs_4
sum_heuristic
[ 3, 21, 82, 10 ]
96
[ "3+21=24", "82-10=72", "24+72=96" ]
Current State: 96:[3, 21, 82, 10], Operations: [] Exploring Operation: 3+21=24, Resulting Numbers: [82, 10, 24] Generated Node #2: [82, 10, 24] from Operation: 3+21=24 Current State: 96:[82, 10, 24], Operations: ['3+21=24'] Exploring Operation: 82-10=72, Resulting Numbers: [24, 72] Generated Node #3: [24, 72] from Operation: 82-10=72 Current State: 96:[24, 72], Operations: ['3+21=24', '82-10=72'] Exploring Operation: 24+72=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[3, 21, 82, 10], Operations: [] Exploring Operation: 21+82=103, Resulting Numbers: [3, 10, 103] Generated Node #0,0: 96:[3, 10, 103] Operation: 21+82=103 Exploring Operation: 21-10=11, Resulting Numbers: [3, 82, 11] Generated Node #0,1: 96:[3, 82, 11] Operation: 21-10=11 Exploring Operation: 21+10=31, Resulting Numbers: [3, 82, 31] Generated Node #0,2: 96:[3, 82, 31] Operation: 21+10=31 Exploring Operation: 82+10=92, Resulting Numbers: [3, 21, 92] Generated Node #0,3: 96:[3, 21, 92] Operation: 82+10=92 Exploring Operation: 82-21=61, Resulting Numbers: [3, 10, 61] Generated Node #0,4: 96:[3, 10, 61] Operation: 82-21=61 Moving to Node #0,3 Current State: 96:[3, 21, 92], Operations: ['82+10=92'] Exploring Operation: 21/3=7, Resulting Numbers: [92, 7] Generated Node #0,3,0: 96:[92, 7] Operation: 21/3=7 Exploring Operation: 21-3=18, Resulting Numbers: [92, 18] Generated Node #0,3,1: 96:[92, 18] Operation: 21-3=18 Exploring Operation: 3+92=95, Resulting Numbers: [21, 95] Generated Node #0,3,2: 96:[21, 95] Operation: 3+92=95 Exploring Operation: 3+21=24, Resulting Numbers: [92, 24] Generated Node #0,3,3: 96:[92, 24] Operation: 3+21=24 Exploring Operation: 92-3=89, Resulting Numbers: [21, 89] Generated Node #0,3,4: 96:[21, 89] Operation: 92-3=89 Moving to Node #0,0 Current State: 96:[3, 10, 103], Operations: ['21+82=103'] Exploring Operation: 103-10=93, Resulting Numbers: [3, 93] Generated Node #0,0,0: 96:[3, 93] Operation: 103-10=93 Exploring Operation: 103-3=100, Resulting Numbers: [10, 100] Generated Node #0,0,1: 96:[10, 100] Operation: 103-3=100 Exploring Operation: 3+10=13, Resulting Numbers: [103, 13] Generated Node #0,0,2: 96:[103, 13] Operation: 3+10=13 Exploring Operation: 3*10=30, Resulting Numbers: [103, 30] Generated Node #0,0,3: 96:[103, 30] Operation: 3*10=30 Exploring Operation: 10-3=7, Resulting Numbers: [103, 7] Generated Node #0,0,4: 96:[103, 7] Operation: 10-3=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[3, 93], Operations: ['21+82=103', '103-10=93'] Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 3+93=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[3, 21, 82, 10], Operations: [] Exploring Operation: 21+82=103, Resulting Numbers: [3, 10, 103] Generated Node #0,0: 96:[3, 10, 103] Operation: 21+82=103 Moving to Node #0,0 Current State: 96:[3, 10, 103], Operations: ['21+82=103'] Exploring Operation: 103-10=93, Resulting Numbers: [3, 93] Generated Node #0,0,0: 96:[3, 93] Operation: 103-10=93 Moving to Node #0,0,0 Current State: 96:[3, 93], Operations: ['21+82=103', '103-10=93'] Exploring Operation: 3+93=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 65, 44, 75, 15 ]
66
[ "75-65=10", "44*15=660", "660/10=66" ]
Current State: 66:[65, 44, 75, 15], Operations: [] Exploring Operation: 75-65=10, Resulting Numbers: [44, 15, 10] Generated Node #2: [44, 15, 10] from Operation: 75-65=10 Current State: 66:[44, 15, 10], Operations: ['75-65=10'] Exploring Operation: 44*15=660, Resulting Numbers: [10, 660] Generated Node #3: [10, 660] from Operation: 44*15=660 Current State: 66:[10, 660], Operations: ['75-65=10', '44*15=660'] Exploring Operation: 660/10=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[65, 44, 75, 15], Operations: [] Exploring Operation: 75-44=31, Resulting Numbers: [65, 15, 31] Generated Node #0,0: 66:[65, 15, 31] Operation: 75-44=31 Exploring Operation: 65-44=21, Resulting Numbers: [75, 15, 21] Generated Node #0,1: 66:[75, 15, 21] Operation: 65-44=21 Exploring Operation: 75/15=5, Resulting Numbers: [65, 44, 5] Generated Node #0,2: 66:[65, 44, 5] Operation: 75/15=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[65, 15, 31], Operations: ['75-44=31'] Exploring Operation: 15+31=46, Resulting Numbers: [65, 46] Generated Node #0,0,0: 66:[65, 46] Operation: 15+31=46 Exploring Operation: 31-15=16, Resulting Numbers: [65, 16] Generated Node #0,0,1: 66:[65, 16] Operation: 31-15=16 Exploring Operation: 65-31=34, Resulting Numbers: [15, 34] Generated Node #0,0,2: 66:[15, 34] Operation: 65-31=34 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 66:[15, 34], Operations: ['75-44=31', '65-31=34'] Exploring Operation: 15*34=510, Resulting Numbers: [510] 510,66 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,66 unequal: No Solution Exploring Operation: 15+34=49, Resulting Numbers: [49] 49,66 unequal: No Solution No 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: 66:[65, 16], Operations: ['75-44=31', '31-15=16'] Exploring Operation: 65*16=1040, Resulting Numbers: [1040] 1040,66 unequal: No Solution Exploring Operation: 65+16=81, Resulting Numbers: [81] 81,66 unequal: No Solution Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,66 unequal: No Solution No 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: 66:[65, 46], Operations: ['75-44=31', '15+31=46'] Exploring Operation: 65-46=19, Resulting Numbers: [19] 19,66 unequal: No Solution Exploring Operation: 65*46=2990, Resulting Numbers: [2990] 2990,66 unequal: No Solution Exploring Operation: 65+46=111, Resulting Numbers: [111] 111,66 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: 66:[65, 44, 5], Operations: ['75/15=5'] Exploring Operation: 44-5=39, Resulting Numbers: [65, 39] Generated Node #0,2,0: 66:[65, 39] Operation: 44-5=39 Exploring Operation: 65-44=21, Resulting Numbers: [5, 21] Generated Node #0,2,1: 66:[5, 21] Operation: 65-44=21 Exploring Operation: 65/5=13, Resulting Numbers: [44, 13] Generated Node #0,2,2: 66:[44, 13] Operation: 65/5=13 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 66:[5, 21], Operations: ['75/15=5', '65-44=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,66 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,66 unequal: No Solution No 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: 66:[65, 39], Operations: ['75/15=5', '44-5=39'] Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 65+39=104, Resulting Numbers: [104] 104,66 unequal: No Solution Exploring Operation: 65*39=2535, Resulting Numbers: [2535] 2535,66 unequal: No Solution No 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: 66:[44, 13], Operations: ['75/15=5', '65/5=13'] Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,66 unequal: No Solution Exploring Operation: 44*13=572, Resulting Numbers: [572] 572,66 unequal: No Solution Exploring Operation: 44+13=57, Resulting Numbers: [57] 57,66 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: 66:[75, 15, 21], Operations: ['65-44=21'] Exploring Operation: 21-15=6, Resulting Numbers: [75, 6] Generated Node #0,1,0: 66:[75, 6] Operation: 21-15=6 Exploring Operation: 75/15=5, Resulting Numbers: [21, 5] Generated Node #0,1,1: 66:[21, 5] Operation: 75/15=5 Exploring Operation: 75-15=60, Resulting Numbers: [21, 60] Generated Node #0,1,2: 66:[21, 60] Operation: 75-15=60 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[21, 5], Operations: ['65-44=21', '75/15=5'] Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,66 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,66 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,66 unequal: No Solution No 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: 66:[21, 60], Operations: ['65-44=21', '75-15=60'] Exploring Operation: 21*60=1260, Resulting Numbers: [1260] 1260,66 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,66 unequal: No Solution Exploring Operation: 21+60=81, Resulting Numbers: [81] 81,66 unequal: No Solution No 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: 66:[75, 6], Operations: ['65-44=21', '21-15=6'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,66 unequal: No Solution Exploring Operation: 75+6=81, Resulting Numbers: [81] 81,66 unequal: No Solution Exploring Operation: 75*6=450, Resulting Numbers: [450] 450,66 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
[ 39, 80, 32, 96 ]
67
[ "39*32=1248", "1248/96=13", "80-13=67" ]
Current State: 67:[39, 80, 32, 96], Operations: [] Exploring Operation: 39*32=1248, Resulting Numbers: [80, 96, 1248] Generated Node #2: [80, 96, 1248] from Operation: 39*32=1248 Current State: 67:[80, 96, 1248], Operations: ['39*32=1248'] Exploring Operation: 1248/96=13, Resulting Numbers: [80, 13] Generated Node #3: [80, 13] from Operation: 1248/96=13 Current State: 67:[80, 13], Operations: ['39*32=1248', '1248/96=13'] Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[39, 80, 32, 96], Operations: [] Exploring Operation: 39+32=71, Resulting Numbers: [80, 96, 71] Generated Node #0,0: 67:[80, 96, 71] Operation: 39+32=71 Exploring Operation: 96-39=57, Resulting Numbers: [80, 32, 57] Generated Node #0,1: 67:[80, 32, 57] Operation: 96-39=57 Exploring Operation: 96-32=64, Resulting Numbers: [39, 80, 64] Generated Node #0,2: 67:[39, 80, 64] Operation: 96-32=64 Exploring Operation: 80-32=48, Resulting Numbers: [39, 96, 48] Generated Node #0,3: 67:[39, 96, 48] Operation: 80-32=48 Moving to Node #0,2 Current State: 67:[39, 80, 64], Operations: ['96-32=64'] Exploring Operation: 64-39=25, Resulting Numbers: [80, 25] Generated Node #0,2,0: 67:[80, 25] Operation: 64-39=25 Exploring Operation: 39+80=119, Resulting Numbers: [64, 119] Generated Node #0,2,1: 67:[64, 119] Operation: 39+80=119 Exploring Operation: 80-39=41, Resulting Numbers: [64, 41] Generated Node #0,2,2: 67:[64, 41] Operation: 80-39=41 Exploring Operation: 39+64=103, Resulting Numbers: [80, 103] Generated Node #0,2,3: 67:[80, 103] Operation: 39+64=103 Moving to Node #0,0 Current State: 67:[80, 96, 71], Operations: ['39+32=71'] Exploring Operation: 80+96=176, Resulting Numbers: [71, 176] Generated Node #0,0,0: 67:[71, 176] Operation: 80+96=176 Exploring Operation: 96-80=16, Resulting Numbers: [71, 16] Generated Node #0,0,1: 67:[71, 16] Operation: 96-80=16 Exploring Operation: 96-71=25, Resulting Numbers: [80, 25] Generated Node #0,0,2: 67:[80, 25] Operation: 96-71=25 Exploring Operation: 80-71=9, Resulting Numbers: [96, 9] Generated Node #0,0,3: 67:[96, 9] Operation: 80-71=9 Moving to Node #0,1 Current State: 67:[80, 32, 57], Operations: ['96-39=57'] Exploring Operation: 32+57=89, Resulting Numbers: [80, 89] Generated Node #0,1,0: 67:[80, 89] Operation: 32+57=89 Exploring Operation: 80+32=112, Resulting Numbers: [57, 112] Generated Node #0,1,1: 67:[57, 112] Operation: 80+32=112 Exploring Operation: 57-32=25, Resulting Numbers: [80, 25] Generated Node #0,1,2: 67:[80, 25] Operation: 57-32=25 Exploring Operation: 80-32=48, Resulting Numbers: [57, 48] Generated Node #0,1,3: 67:[57, 48] Operation: 80-32=48 Moving to Node #0,3 Current State: 67:[39, 96, 48], Operations: ['80-32=48'] Exploring Operation: 39+48=87, Resulting Numbers: [96, 87] Generated Node #0,3,0: 67:[96, 87] Operation: 39+48=87 Exploring Operation: 96-48=48, Resulting Numbers: [39, 48] Generated Node #0,3,1: 67:[39, 48] Operation: 96-48=48 Exploring Operation: 39+96=135, Resulting Numbers: [48, 135] Generated Node #0,3,2: 67:[48, 135] Operation: 39+96=135 Exploring Operation: 96-39=57, Resulting Numbers: [48, 57] Generated Node #0,3,3: 67:[48, 57] Operation: 96-39=57 Moving to Node #0,2,2 Current State: 67:[64, 41], Operations: ['96-32=64', '80-39=41'] Exploring Operation: 64+41=105, Resulting Numbers: [105] 105,67 unequal: No Solution Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,67 unequal: No Solution Exploring Operation: 64*41=2624, Resulting Numbers: [2624] 2624,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[48, 57], Operations: ['80-32=48', '96-39=57'] Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 48*57=2736, Resulting Numbers: [2736] 2736,67 unequal: No Solution Exploring Operation: 48+57=105, Resulting Numbers: [105] 105,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[57, 48], Operations: ['96-39=57', '80-32=48'] Exploring Operation: 57+48=105, Resulting Numbers: [105] 105,67 unequal: No Solution Exploring Operation: 57*48=2736, Resulting Numbers: [2736] 2736,67 unequal: No Solution Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[80, 89], Operations: ['96-39=57', '32+57=89'] Exploring Operation: 89-80=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 80*89=7120, Resulting Numbers: [7120] 7120,67 unequal: No Solution Exploring Operation: 80+89=169, Resulting Numbers: [169] 169,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[39, 48], Operations: ['80-32=48', '96-48=48'] Exploring Operation: 39*48=1872, Resulting Numbers: [1872] 1872,67 unequal: No Solution Exploring Operation: 48-39=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 39+48=87, Resulting Numbers: [87] 87,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[96, 87], Operations: ['80-32=48', '39+48=87'] Exploring Operation: 96+87=183, Resulting Numbers: [183] 183,67 unequal: No Solution Exploring Operation: 96*87=8352, Resulting Numbers: [8352] 8352,67 unequal: No Solution Exploring Operation: 96-87=9, Resulting Numbers: [9] 9,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[80, 103], Operations: ['96-32=64', '39+64=103'] Exploring Operation: 80*103=8240, Resulting Numbers: [8240] 8240,67 unequal: No Solution Exploring Operation: 103-80=23, Resulting Numbers: [23] 23,67 unequal: No Solution Exploring Operation: 80+103=183, Resulting Numbers: [183] 183,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[80, 25], Operations: ['39+32=71', '96-71=25'] Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,67 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,67 unequal: No Solution Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[80, 25], Operations: ['96-39=57', '57-32=25'] Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,67 unequal: No Solution Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,67 unequal: No Solution Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[80, 25], Operations: ['96-32=64', '64-39=25'] Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,67 unequal: No Solution Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,67 unequal: No Solution Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[57, 112], Operations: ['96-39=57', '80+32=112'] Exploring Operation: 57*112=6384, Resulting Numbers: [6384] 6384,67 unequal: No Solution Exploring Operation: 112-57=55, Resulting Numbers: [55] 55,67 unequal: No Solution Exploring Operation: 57+112=169, Resulting Numbers: [169] 169,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[71, 16], Operations: ['39+32=71', '96-80=16'] Exploring Operation: 71*16=1136, Resulting Numbers: [1136] 1136,67 unequal: No Solution Exploring Operation: 71+16=87, Resulting Numbers: [87] 87,67 unequal: No Solution Exploring Operation: 71-16=55, Resulting Numbers: [55] 55,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[64, 119], Operations: ['96-32=64', '39+80=119'] Exploring Operation: 64+119=183, Resulting Numbers: [183] 183,67 unequal: No Solution Exploring Operation: 119-64=55, Resulting Numbers: [55] 55,67 unequal: No Solution Exploring Operation: 64*119=7616, Resulting Numbers: [7616] 7616,67 unequal: No Solution Moving to Node #0,0,3 Current State: 67:[96, 9], Operations: ['39+32=71', '80-71=9'] Exploring Operation: 96+9=105, Resulting Numbers: [105] 105,67 unequal: No Solution Exploring Operation: 96*9=864, Resulting Numbers: [864] 864,67 unequal: No Solution Exploring Operation: 96-9=87, Resulting Numbers: [87] 87,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[48, 135], Operations: ['80-32=48', '39+96=135'] Exploring Operation: 135-48=87, Resulting Numbers: [87] 87,67 unequal: No Solution Exploring Operation: 48+135=183, Resulting Numbers: [183] 183,67 unequal: No Solution Exploring Operation: 48*135=6480, Resulting Numbers: [6480] 6480,67 unequal: No Solution Moving to Node #0,0,0 Current State: 67:[71, 176], Operations: ['39+32=71', '80+96=176'] Exploring Operation: 71*176=12496, Resulting Numbers: [12496] 12496,67 unequal: No Solution Exploring Operation: 71+176=247, Resulting Numbers: [247] 247,67 unequal: No Solution Exploring Operation: 176-71=105, Resulting Numbers: [105] 105,67 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 23, 2, 2, 73 ]
50
[ "23+2=25", "2+73=75", "75-25=50" ]
Current State: 50:[23, 2, 2, 73], Operations: [] Exploring Operation: 23+2=25, Resulting Numbers: [73, 25] Generated Node #2: [73, 25] from Operation: 23+2=25 Current State: 50:[73, 25], Operations: ['23+2=25'] Exploring Operation: 2+73=75, Resulting Numbers: [25, 75] Generated Node #3: [25, 75] from Operation: 2+73=75 Current State: 50:[25, 75], Operations: ['23+2=25', '2+73=75'] Exploring Operation: 75-25=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[23, 2, 2, 73], Operations: [] Exploring Operation: 73-23=50, Resulting Numbers: [2, 2, 50] Generated Node #0,0: 50:[2, 2, 50] Operation: 73-23=50 Exploring Operation: 23+2=25, Resulting Numbers: [2, 73, 25] Generated Node #0,1: 50:[2, 73, 25] Operation: 23+2=25 Moving to Node #0,0 Current State: 50:[2, 2, 50], Operations: ['73-23=50'] Exploring Operation: 50/2=25, Resulting Numbers: [2, 25] Generated Node #0,0,0: 50:[2, 25] Operation: 50/2=25 Exploring Operation: 50/2=25, Resulting Numbers: [2, 25] Generated Node #0,0,1: 50:[2, 25] Operation: 50/2=25 Moving to Node #0,1 Current State: 50:[2, 73, 25], Operations: ['23+2=25'] Exploring Operation: 73-2=71, Resulting Numbers: [25, 71] Generated Node #0,1,0: 50:[25, 71] Operation: 73-2=71 Exploring Operation: 73-25=48, Resulting Numbers: [2, 48] Generated Node #0,1,1: 50:[2, 48] Operation: 73-25=48 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[2, 48], Operations: ['23+2=25', '73-25=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[23, 2, 2, 73], Operations: [] Exploring Operation: 23+2=25, Resulting Numbers: [2, 73, 25] Generated Node #0,1: 50:[2, 73, 25] Operation: 23+2=25 Moving to Node #0,1 Current State: 50:[2, 73, 25], Operations: ['23+2=25'] Exploring Operation: 73-25=48, Resulting Numbers: [2, 48] Generated Node #0,1,1: 50:[2, 48] Operation: 73-25=48 Moving to Node #0,1,1 Current State: 50:[2, 48], Operations: ['23+2=25', '73-25=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 3, 67, 95, 51 ]
33
[ "95-67=28", "3*28=84", "84-51=33" ]
Current State: 33:[3, 67, 95, 51], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [3, 51, 28] Generated Node #2: [3, 51, 28] from Operation: 95-67=28 Current State: 33:[3, 51, 28], Operations: ['95-67=28'] Exploring Operation: 3*28=84, Resulting Numbers: [51, 84] Generated Node #3: [51, 84] from Operation: 3*28=84 Current State: 33:[51, 84], Operations: ['95-67=28', '3*28=84'] Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[3, 67, 95, 51], Operations: [] Exploring Operation: 95-67=28, Resulting Numbers: [3, 51, 28] Generated Node #0,0: 33:[3, 51, 28] Operation: 95-67=28 Exploring Operation: 95-51=44, Resulting Numbers: [3, 67, 44] Generated Node #0,1: 33:[3, 67, 44] Operation: 95-51=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[3, 51, 28], Operations: ['95-67=28'] Exploring Operation: 51-28=23, Resulting Numbers: [3, 23] Generated Node #0,0,0: 33:[3, 23] Operation: 51-28=23 Exploring Operation: 51/3=17, Resulting Numbers: [28, 17] Generated Node #0,0,1: 33:[28, 17] Operation: 51/3=17 Moving to Node #0,0,0 Current State: 33:[3, 23], Operations: ['95-67=28', '51-28=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,33 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,33 unequal: No Solution Moving to Node #0,0,1 Current State: 33:[28, 17], Operations: ['95-67=28', '51/3=17'] Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 28+17=45, Resulting Numbers: [45] 45,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[3, 67, 44], Operations: ['95-51=44'] Exploring Operation: 67-3=64, Resulting Numbers: [44, 64] Generated Node #0,1,0: 33:[44, 64] Operation: 67-3=64 Exploring Operation: 67-44=23, Resulting Numbers: [3, 23] Generated Node #0,1,1: 33:[3, 23] Operation: 67-44=23 Moving to Node #0,1,1 Current State: 33:[3, 23], Operations: ['95-51=44', '67-44=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,33 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[44, 64], Operations: ['95-51=44', '67-3=64'] Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,33 unequal: No Solution Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,33 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
[ 9, 30, 55, 11 ]
80
[ "11-9=2", "55*2=110", "110-30=80" ]
Current State: 80:[9, 30, 55, 11], Operations: [] Exploring Operation: 11-9=2, Resulting Numbers: [30, 55, 2] Generated Node #2: [30, 55, 2] from Operation: 11-9=2 Current State: 80:[30, 55, 2], Operations: ['11-9=2'] Exploring Operation: 55*2=110, Resulting Numbers: [30, 110] Generated Node #3: [30, 110] from Operation: 55*2=110 Current State: 80:[30, 110], Operations: ['11-9=2', '55*2=110'] Exploring Operation: 110-30=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[9, 30, 55, 11], Operations: [] Exploring Operation: 55-11=44, Resulting Numbers: [9, 30, 44] Generated Node #0,0: 80:[9, 30, 44] Operation: 55-11=44 Exploring Operation: 55/11=5, Resulting Numbers: [9, 30, 5] Generated Node #0,1: 80:[9, 30, 5] Operation: 55/11=5 Exploring Operation: 30+55=85, Resulting Numbers: [9, 11, 85] Generated Node #0,2: 80:[9, 11, 85] Operation: 30+55=85 Exploring Operation: 55-30=25, Resulting Numbers: [9, 11, 25] Generated Node #0,3: 80:[9, 11, 25] Operation: 55-30=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[9, 11, 85], Operations: ['30+55=85'] Exploring Operation: 11-9=2, Resulting Numbers: [85, 2] Generated Node #0,2,0: 80:[85, 2] Operation: 11-9=2 Exploring Operation: 9+11=20, Resulting Numbers: [85, 20] Generated Node #0,2,1: 80:[85, 20] Operation: 9+11=20 Exploring Operation: 85-9=76, Resulting Numbers: [11, 76] Generated Node #0,2,2: 80:[11, 76] Operation: 85-9=76 Exploring Operation: 85-11=74, Resulting Numbers: [9, 74] Generated Node #0,2,3: 80:[9, 74] Operation: 85-11=74 Moving to Node #0,2,0 Current State: 80:[85, 2], Operations: ['30+55=85', '11-9=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 85*2=170, Resulting Numbers: [170] 170,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[11, 76], Operations: ['30+55=85', '85-9=76'] Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 11*76=836, Resulting Numbers: [836] 836,80 unequal: No Solution Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[85, 20], Operations: ['30+55=85', '9+11=20'] Exploring Operation: 85-20=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 85*20=1700, Resulting Numbers: [1700] 1700,80 unequal: No Solution Exploring Operation: 85+20=105, Resulting Numbers: [105] 105,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[9, 74], Operations: ['30+55=85', '85-11=74'] Exploring Operation: 9+74=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 9*74=666, Resulting Numbers: [666] 666,80 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 #0,3 Current State: 80:[9, 11, 25], Operations: ['55-30=25'] Exploring Operation: 25-11=14, Resulting Numbers: [9, 14] Generated Node #0,3,0: 80:[9, 14] Operation: 25-11=14 Exploring Operation: 9+11=20, Resulting Numbers: [25, 20] Generated Node #0,3,1: 80:[25, 20] Operation: 9+11=20 Exploring Operation: 11-9=2, Resulting Numbers: [25, 2] Generated Node #0,3,2: 80:[25, 2] Operation: 11-9=2 Exploring Operation: 25-9=16, Resulting Numbers: [11, 16] Generated Node #0,3,3: 80:[11, 16] Operation: 25-9=16 Moving to Node #0,3,3 Current State: 80:[11, 16], Operations: ['55-30=25', '25-9=16'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,80 unequal: No Solution Exploring Operation: 11*16=176, Resulting Numbers: [176] 176,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[9, 14], Operations: ['55-30=25', '25-11=14'] Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[25, 2], Operations: ['55-30=25', '11-9=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,80 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[25, 20], Operations: ['55-30=25', '9+11=20'] Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,80 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[9, 30, 5], Operations: ['55/11=5'] Exploring Operation: 30-9=21, Resulting Numbers: [5, 21] Generated Node #0,1,0: 80:[5, 21] Operation: 30-9=21 Exploring Operation: 30+5=35, Resulting Numbers: [9, 35] Generated Node #0,1,1: 80:[9, 35] Operation: 30+5=35 Exploring Operation: 9+30=39, Resulting Numbers: [5, 39] Generated Node #0,1,2: 80:[5, 39] Operation: 9+30=39 Exploring Operation: 30/5=6, Resulting Numbers: [9, 6] Generated Node #0,1,3: 80:[9, 6] Operation: 30/5=6 Moving to Node #0,1,0 Current State: 80:[5, 21], Operations: ['55/11=5', '30-9=21'] Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,80 unequal: No Solution Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[5, 39], Operations: ['55/11=5', '9+30=39'] Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,80 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[9, 6], Operations: ['55/11=5', '30/5=6'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,80 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,80 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[9, 35], Operations: ['55/11=5', '30+5=35'] Exploring Operation: 9+35=44, Resulting Numbers: [44] 44,80 unequal: No Solution Exploring Operation: 9*35=315, Resulting Numbers: [315] 315,80 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,80 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 #0,0 Current State: 80:[9, 30, 44], Operations: ['55-11=44'] Exploring Operation: 9+30=39, Resulting Numbers: [44, 39] Generated Node #0,0,0: 80:[44, 39] Operation: 9+30=39 Exploring Operation: 30-9=21, Resulting Numbers: [44, 21] Generated Node #0,0,1: 80:[44, 21] Operation: 30-9=21 Exploring Operation: 30+44=74, Resulting Numbers: [9, 74] Generated Node #0,0,2: 80:[9, 74] Operation: 30+44=74 Exploring Operation: 44-30=14, Resulting Numbers: [9, 14] Generated Node #0,0,3: 80:[9, 14] Operation: 44-30=14 Moving to Node #0,0,3 Current State: 80:[9, 14], Operations: ['55-11=44', '44-30=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,80 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[44, 21], Operations: ['55-11=44', '30-9=21'] Exploring Operation: 44*21=924, Resulting Numbers: [924] 924,80 unequal: No Solution Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[44, 39], Operations: ['55-11=44', '9+30=39'] Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 44*39=1716, Resulting Numbers: [1716] 1716,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[9, 74], Operations: ['55-11=44', '30+44=74'] Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 9+74=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 9*74=666, Resulting Numbers: [666] 666,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 43, 7, 74, 99 ]
66
[ "99-43=56", "56/7=8", "74-8=66" ]
Current State: 66:[43, 7, 74, 99], Operations: [] Exploring Operation: 99-43=56, Resulting Numbers: [7, 74, 56] Generated Node #2: [7, 74, 56] from Operation: 99-43=56 Current State: 66:[7, 74, 56], Operations: ['99-43=56'] Exploring Operation: 56/7=8, Resulting Numbers: [74, 8] Generated Node #3: [74, 8] from Operation: 56/7=8 Current State: 66:[74, 8], Operations: ['99-43=56', '56/7=8'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[43, 7, 74, 99], Operations: [] Exploring Operation: 99-74=25, Resulting Numbers: [43, 7, 25] Generated Node #0,0: 66:[43, 7, 25] Operation: 99-74=25 Moving to Node #0,0 Current State: 66:[43, 7, 25], Operations: ['99-74=25'] Exploring Operation: 43+25=68, Resulting Numbers: [7, 68] Generated Node #0,0,0: 66:[7, 68] Operation: 43+25=68 Moving to Node #0,0,0 Current State: 66:[7, 68], Operations: ['99-74=25', '43+25=68'] Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,66 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 63, 2, 22, 11 ]
50
[ "63-2=61", "22-11=11", "61-11=50" ]
Current State: 50:[63, 2, 22, 11], Operations: [] Exploring Operation: 63-2=61, Resulting Numbers: [22, 11, 61] Generated Node #2: [22, 11, 61] from Operation: 63-2=61 Current State: 50:[22, 11, 61], Operations: ['63-2=61'] Exploring Operation: 22-11=11, Resulting Numbers: [61, 11] Generated Node #3: [61, 11] from Operation: 22-11=11 Current State: 50:[61, 11], Operations: ['63-2=61', '22-11=11'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[63, 2, 22, 11], Operations: [] Exploring Operation: 63-22=41, Resulting Numbers: [2, 11, 41] Generated Node #0,0: 50:[2, 11, 41] Operation: 63-22=41 Exploring Operation: 63-11=52, Resulting Numbers: [2, 22, 52] Generated Node #0,1: 50:[2, 22, 52] Operation: 63-11=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[2, 22, 52], Operations: ['63-11=52'] Exploring Operation: 22/2=11, Resulting Numbers: [52, 11] Generated Node #0,1,0: 50:[52, 11] Operation: 22/2=11 Exploring Operation: 2+22=24, Resulting Numbers: [52, 24] Generated Node #0,1,1: 50:[52, 24] Operation: 2+22=24 Moving to Node #0,1,0 Current State: 50:[52, 11], Operations: ['63-11=52', '22/2=11'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[52, 24], Operations: ['63-11=52', '2+22=24'] Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,50 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[2, 11, 41], Operations: ['63-22=41'] Exploring Operation: 41-11=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 50:[2, 30] Operation: 41-11=30 Exploring Operation: 11+41=52, Resulting Numbers: [2, 52] Generated Node #0,0,1: 50:[2, 52] Operation: 11+41=52 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[2, 52], Operations: ['63-22=41', '11+41=52'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[63, 2, 22, 11], Operations: [] Exploring Operation: 63-22=41, Resulting Numbers: [2, 11, 41] Generated Node #0,0: 50:[2, 11, 41] Operation: 63-22=41 Moving to Node #0,0 Current State: 50:[2, 11, 41], Operations: ['63-22=41'] Exploring Operation: 11+41=52, Resulting Numbers: [2, 52] Generated Node #0,0,1: 50:[2, 52] Operation: 11+41=52 Moving to Node #0,0,1 Current State: 50:[2, 52], Operations: ['63-22=41', '11+41=52'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 22, 3, 2, 99 ]
66
[ "22*3=66", "66/2=33", "99-33=66" ]
Current State: 66:[22, 3, 2, 99], Operations: [] Exploring Operation: 22*3=66, Resulting Numbers: [2, 99, 66] Generated Node #2: [2, 99, 66] from Operation: 22*3=66 Current State: 66:[2, 99, 66], Operations: ['22*3=66'] Exploring Operation: 66/2=33, Resulting Numbers: [99, 33] Generated Node #3: [99, 33] from Operation: 66/2=33 Current State: 66:[99, 33], Operations: ['22*3=66', '66/2=33'] Exploring Operation: 99-33=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[22, 3, 2, 99], Operations: [] Exploring Operation: 99-2=97, Resulting Numbers: [22, 3, 97] Generated Node #0,0: 66:[22, 3, 97] Operation: 99-2=97 Exploring Operation: 99-22=77, Resulting Numbers: [3, 2, 77] Generated Node #0,1: 66:[3, 2, 77] Operation: 99-22=77 Exploring Operation: 99/3=33, Resulting Numbers: [22, 2, 33] Generated Node #0,2: 66:[22, 2, 33] Operation: 99/3=33 Exploring Operation: 99-3=96, Resulting Numbers: [22, 2, 96] Generated Node #0,3: 66:[22, 2, 96] Operation: 99-3=96 Moving to Node #0,2 Current State: 66:[22, 2, 33], Operations: ['99/3=33'] Exploring Operation: 22/2=11, Resulting Numbers: [33, 11] Generated Node #0,2,0: 66:[33, 11] Operation: 22/2=11 Exploring Operation: 2*33=66, Resulting Numbers: [22, 66] Generated Node #0,2,1: 66:[22, 66] Operation: 2*33=66 Exploring Operation: 33-22=11, Resulting Numbers: [2, 11] Generated Node #0,2,2: 66:[2, 11] Operation: 33-22=11 Exploring Operation: 22+2=24, Resulting Numbers: [33, 24] Generated Node #0,2,3: 66:[33, 24] Operation: 22+2=24 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 66:[33, 11], Operations: ['99/3=33', '22/2=11'] Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 33+11=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,66 unequal: No Solution Exploring Operation: 33*11=363, Resulting Numbers: [363] 363,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 66:[22, 66], Operations: ['99/3=33', '2*33=66'] Exploring Operation: 66-22=44, Resulting Numbers: [44] 44,66 unequal: No Solution Exploring Operation: 22+66=88, Resulting Numbers: [88] 88,66 unequal: No Solution Exploring Operation: 22*66=1452, Resulting Numbers: [1452] 1452,66 unequal: No Solution Exploring Operation: 66/22=3, Resulting Numbers: [3] 3,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[2, 11], Operations: ['99/3=33', '33-22=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,66 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 66:[33, 24], Operations: ['99/3=33', '22+2=24'] Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 33+24=57, Resulting Numbers: [57] 57,66 unequal: No Solution Exploring Operation: 33*24=792, Resulting Numbers: [792] 792,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 66:[3, 2, 77], Operations: ['99-22=77'] Exploring Operation: 3+2=5, Resulting Numbers: [77, 5] Generated Node #0,1,0: 66:[77, 5] Operation: 3+2=5 Exploring Operation: 3*2=6, Resulting Numbers: [77, 6] Generated Node #0,1,1: 66:[77, 6] Operation: 3*2=6 Exploring Operation: 77-2=75, Resulting Numbers: [3, 75] Generated Node #0,1,2: 66:[3, 75] Operation: 77-2=75 Exploring Operation: 77-3=74, Resulting Numbers: [2, 74] Generated Node #0,1,3: 66:[2, 74] Operation: 77-3=74 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 66:[2, 74], Operations: ['99-22=77', '77-3=74'] Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,66 unequal: No Solution Exploring Operation: 2*74=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,66 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 66:[3, 75], Operations: ['99-22=77', '77-2=75'] Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,66 unequal: No Solution Exploring Operation: 3*75=225, Resulting Numbers: [225] 225,66 unequal: No Solution Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 3+75=78, Resulting Numbers: [78] 78,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 66:[77, 6], Operations: ['99-22=77', '3*2=6'] Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,66 unequal: No Solution Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,66 unequal: No Solution Exploring Operation: 77*6=462, Resulting Numbers: [462] 462,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 66:[77, 5], Operations: ['99-22=77', '3+2=5'] Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 77+5=82, Resulting Numbers: [82] 82,66 unequal: No Solution Exploring Operation: 77*5=385, Resulting Numbers: [385] 385,66 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: 66:[22, 2, 96], Operations: ['99-3=96'] Exploring Operation: 96/2=48, Resulting Numbers: [22, 48] Generated Node #0,3,0: 66:[22, 48] Operation: 96/2=48 Exploring Operation: 96-2=94, Resulting Numbers: [22, 94] Generated Node #0,3,1: 66:[22, 94] Operation: 96-2=94 Exploring Operation: 22/2=11, Resulting Numbers: [96, 11] Generated Node #0,3,2: 66:[96, 11] Operation: 22/2=11 Exploring Operation: 96-22=74, Resulting Numbers: [2, 74] Generated Node #0,3,3: 66:[2, 74] Operation: 96-22=74 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 66:[2, 74], Operations: ['99-3=96', '96-22=74'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,66 unequal: No Solution Exploring Operation: 2*74=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 66:[22, 48], Operations: ['99-3=96', '96/2=48'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,66 unequal: No Solution Exploring Operation: 22*48=1056, Resulting Numbers: [1056] 1056,66 unequal: No Solution Exploring Operation: 22+48=70, Resulting Numbers: [70] 70,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 66:[22, 94], Operations: ['99-3=96', '96-2=94'] Exploring Operation: 22*94=2068, Resulting Numbers: [2068] 2068,66 unequal: No Solution Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 22+94=116, Resulting Numbers: [116] 116,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 66:[96, 11], Operations: ['99-3=96', '22/2=11'] Exploring Operation: 96*11=1056, Resulting Numbers: [1056] 1056,66 unequal: No Solution Exploring Operation: 96-11=85, Resulting Numbers: [85] 85,66 unequal: No Solution Exploring Operation: 96+11=107, Resulting Numbers: [107] 107,66 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: 66:[22, 3, 97], Operations: ['99-2=97'] Exploring Operation: 97-22=75, Resulting Numbers: [3, 75] Generated Node #0,0,0: 66:[3, 75] Operation: 97-22=75 Exploring Operation: 97-3=94, Resulting Numbers: [22, 94] Generated Node #0,0,1: 66:[22, 94] Operation: 97-3=94 Exploring Operation: 22*3=66, Resulting Numbers: [97, 66] Generated Node #0,0,2: 66:[97, 66] Operation: 22*3=66 Exploring Operation: 22+3=25, Resulting Numbers: [97, 25] Generated Node #0,0,3: 66:[97, 25] Operation: 22+3=25 Moving to Node #0,0,0 Current State: 66:[3, 75], Operations: ['99-2=97', '97-22=75'] Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,66 unequal: No Solution Exploring Operation: 75-3=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 3+75=78, Resulting Numbers: [78] 78,66 unequal: No Solution Exploring Operation: 3*75=225, Resulting Numbers: [225] 225,66 unequal: No Solution Moving to Node #0,0,1 Current State: 66:[22, 94], Operations: ['99-2=97', '97-3=94'] Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 22*94=2068, Resulting Numbers: [2068] 2068,66 unequal: No Solution Exploring Operation: 22+94=116, Resulting Numbers: [116] 116,66 unequal: No Solution Moving to Node #0,0,2 Current State: 66:[97, 66], Operations: ['99-2=97', '22*3=66'] Exploring Operation: 97*66=6402, Resulting Numbers: [6402] 6402,66 unequal: No Solution Exploring Operation: 97-66=31, Resulting Numbers: [31] 31,66 unequal: No Solution Exploring Operation: 97+66=163, Resulting Numbers: [163] 163,66 unequal: No Solution Moving to Node #0,0,3 Current State: 66:[97, 25], Operations: ['99-2=97', '22+3=25'] Exploring Operation: 97-25=72, Resulting Numbers: [72] 72,66 unequal: No Solution Exploring Operation: 97+25=122, Resulting Numbers: [122] 122,66 unequal: No Solution Exploring Operation: 97*25=2425, Resulting Numbers: [2425] 2425,66 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 24, 3, 67, 64 ]
18
[ "24-3=21", "67-64=3", "21-3=18" ]
Current State: 18:[24, 3, 67, 64], Operations: [] Exploring Operation: 24-3=21, Resulting Numbers: [67, 64, 21] Generated Node #2: [67, 64, 21] from Operation: 24-3=21 Current State: 18:[67, 64, 21], Operations: ['24-3=21'] Exploring Operation: 67-64=3, Resulting Numbers: [21, 3] Generated Node #3: [21, 3] from Operation: 67-64=3 Current State: 18:[21, 3], Operations: ['24-3=21', '67-64=3'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[24, 3, 67, 64], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [24, 3, 3] Generated Node #0,0: 18:[24, 3, 3] Operation: 67-64=3 Exploring Operation: 67-24=43, Resulting Numbers: [3, 64, 43] Generated Node #0,1: 18:[3, 64, 43] Operation: 67-24=43 Exploring Operation: 64-24=40, Resulting Numbers: [3, 67, 40] Generated Node #0,2: 18:[3, 67, 40] Operation: 64-24=40 Moving to Node #0,0 Current State: 18:[24, 3, 3], Operations: ['67-64=3'] Exploring Operation: 24-3=21, Resulting Numbers: [3, 21] Generated Node #0,0,0: 18:[3, 21] Operation: 24-3=21 Exploring Operation: 24/3=8, Resulting Numbers: [3, 8] Generated Node #0,0,1: 18:[3, 8] Operation: 24/3=8 Exploring Operation: 24/3=8, Resulting Numbers: [3, 8] Generated Node #0,0,2: 18:[3, 8] Operation: 24/3=8 Moving to Node #0,1 Current State: 18:[3, 64, 43], Operations: ['67-24=43'] Exploring Operation: 64-43=21, Resulting Numbers: [3, 21] Generated Node #0,1,0: 18:[3, 21] Operation: 64-43=21 Exploring Operation: 64-3=61, Resulting Numbers: [43, 61] Generated Node #0,1,1: 18:[43, 61] Operation: 64-3=61 Exploring Operation: 43-3=40, Resulting Numbers: [64, 40] Generated Node #0,1,2: 18:[64, 40] Operation: 43-3=40 Moving to Node #0,2 Current State: 18:[3, 67, 40], Operations: ['64-24=40'] Exploring Operation: 67-40=27, Resulting Numbers: [3, 27] Generated Node #0,2,0: 18:[3, 27] Operation: 67-40=27 Exploring Operation: 67-3=64, Resulting Numbers: [40, 64] Generated Node #0,2,1: 18:[40, 64] Operation: 67-3=64 Exploring Operation: 40-3=37, Resulting Numbers: [67, 37] Generated Node #0,2,2: 18:[67, 37] Operation: 40-3=37 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[3, 27], Operations: ['64-24=40', '67-40=27'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[40, 64], Operations: ['64-24=40', '67-3=64'] Exploring Operation: 64-40=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 40*64=2560, Resulting Numbers: [2560] 2560,18 unequal: No Solution Exploring Operation: 40+64=104, Resulting Numbers: [104] 104,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[67, 37], Operations: ['64-24=40', '40-3=37'] Exploring Operation: 67+37=104, Resulting Numbers: [104] 104,18 unequal: No Solution Exploring Operation: 67*37=2479, Resulting Numbers: [2479] 2479,18 unequal: No Solution Exploring Operation: 67-37=30, Resulting Numbers: [30] 30,18 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: 18:[3, 8], Operations: ['67-64=3', '24/3=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[3, 8], Operations: ['67-64=3', '24/3=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[3, 21], Operations: ['67-64=3', '24-3=21'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[24, 3, 67, 64], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [24, 3, 3] Generated Node #0,0: 18:[24, 3, 3] Operation: 67-64=3 Moving to Node #0,0 Current State: 18:[24, 3, 3], Operations: ['67-64=3'] Exploring Operation: 24-3=21, Resulting Numbers: [3, 21] Generated Node #0,0,0: 18:[3, 21] Operation: 24-3=21 Moving to Node #0,0,0 Current State: 18:[3, 21], Operations: ['67-64=3', '24-3=21'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.970486
hs_3
mult_heuristic
[ 81, 47, 31, 73 ]
70
[ "81-47=34", "31+73=104", "104-34=70" ]
Current State: 70:[81, 47, 31, 73], Operations: [] Exploring Operation: 81-47=34, Resulting Numbers: [31, 73, 34] Generated Node #2: [31, 73, 34] from Operation: 81-47=34 Current State: 70:[31, 73, 34], Operations: ['81-47=34'] Exploring Operation: 31+73=104, Resulting Numbers: [34, 104] Generated Node #3: [34, 104] from Operation: 31+73=104 Current State: 70:[34, 104], Operations: ['81-47=34', '31+73=104'] Exploring Operation: 104-34=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[81, 47, 31, 73], Operations: [] Exploring Operation: 81-73=8, Resulting Numbers: [47, 31, 8] Generated Node #0,0: 70:[47, 31, 8] Operation: 81-73=8 Exploring Operation: 47+31=78, Resulting Numbers: [81, 73, 78] Generated Node #0,1: 70:[81, 73, 78] Operation: 47+31=78 Exploring Operation: 47-31=16, Resulting Numbers: [81, 73, 16] Generated Node #0,2: 70:[81, 73, 16] Operation: 47-31=16 Exploring Operation: 81-47=34, Resulting Numbers: [31, 73, 34] Generated Node #0,3: 70:[31, 73, 34] Operation: 81-47=34 Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[31, 73, 34], Operations: ['81-47=34'] Exploring Operation: 34-31=3, Resulting Numbers: [73, 3] Generated Node #0,3,0: 70:[73, 3] Operation: 34-31=3 Exploring Operation: 31+34=65, Resulting Numbers: [73, 65] Generated Node #0,3,1: 70:[73, 65] Operation: 31+34=65 Exploring Operation: 73-31=42, Resulting Numbers: [34, 42] Generated Node #0,3,2: 70:[34, 42] Operation: 73-31=42 Exploring Operation: 73-34=39, Resulting Numbers: [31, 39] Generated Node #0,3,3: 70:[31, 39] Operation: 73-34=39 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 70:[73, 3], Operations: ['81-47=34', '34-31=3'] Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,70 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[81, 47, 31, 73], Operations: [] Exploring Operation: 81-47=34, Resulting Numbers: [31, 73, 34] Generated Node #0,3: 70:[31, 73, 34] Operation: 81-47=34 Moving to Node #0,3 Current State: 70:[31, 73, 34], Operations: ['81-47=34'] Exploring Operation: 34-31=3, Resulting Numbers: [73, 3] Generated Node #0,3,0: 70:[73, 3] Operation: 34-31=3 Moving to Node #0,3,0 Current State: 70:[73, 3], Operations: ['81-47=34', '34-31=3'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 12, 66, 10, 14 ]
47
[ "12-10=2", "66/2=33", "14+33=47" ]
Current State: 47:[12, 66, 10, 14], Operations: [] Exploring Operation: 12-10=2, Resulting Numbers: [66, 14, 2] Generated Node #2: [66, 14, 2] from Operation: 12-10=2 Current State: 47:[66, 14, 2], Operations: ['12-10=2'] Exploring Operation: 66/2=33, Resulting Numbers: [14, 33] Generated Node #3: [14, 33] from Operation: 66/2=33 Current State: 47:[14, 33], Operations: ['12-10=2', '66/2=33'] Exploring Operation: 14+33=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[12, 66, 10, 14], Operations: [] Exploring Operation: 12+14=26, Resulting Numbers: [66, 10, 26] Generated Node #0,0: 47:[66, 10, 26] Operation: 12+14=26 Exploring Operation: 66-12=54, Resulting Numbers: [10, 14, 54] Generated Node #0,1: 47:[10, 14, 54] Operation: 66-12=54 Exploring Operation: 12+10=22, Resulting Numbers: [66, 14, 22] Generated Node #0,2: 47:[66, 14, 22] Operation: 12+10=22 Moving to Node #0,0 Current State: 47:[66, 10, 26], Operations: ['12+14=26'] Exploring Operation: 10+26=36, Resulting Numbers: [66, 36] Generated Node #0,0,0: 47:[66, 36] Operation: 10+26=36 Exploring Operation: 66-10=56, Resulting Numbers: [26, 56] Generated Node #0,0,1: 47:[26, 56] Operation: 66-10=56 Exploring Operation: 66-26=40, Resulting Numbers: [10, 40] Generated Node #0,0,2: 47:[10, 40] Operation: 66-26=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[66, 36], Operations: ['12+14=26', '10+26=36'] Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,47 unequal: No Solution Exploring Operation: 66*36=2376, Resulting Numbers: [2376] 2376,47 unequal: No Solution Exploring Operation: 66+36=102, Resulting Numbers: [102] 102,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[26, 56], Operations: ['12+14=26', '66-10=56'] Exploring Operation: 26*56=1456, Resulting Numbers: [1456] 1456,47 unequal: No Solution Exploring Operation: 26+56=82, Resulting Numbers: [82] 82,47 unequal: No Solution Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[10, 40], Operations: ['12+14=26', '66-26=40'] Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,47 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: 47:[10, 14, 54], Operations: ['66-12=54'] Exploring Operation: 54-10=44, Resulting Numbers: [14, 44] Generated Node #0,1,0: 47:[14, 44] Operation: 54-10=44 Exploring Operation: 54-14=40, Resulting Numbers: [10, 40] Generated Node #0,1,1: 47:[10, 40] Operation: 54-14=40 Exploring Operation: 10+14=24, Resulting Numbers: [54, 24] Generated Node #0,1,2: 47:[54, 24] Operation: 10+14=24 Moving to Node #0,2 Current State: 47:[66, 14, 22], Operations: ['12+10=22'] Exploring Operation: 66-22=44, Resulting Numbers: [14, 44] Generated Node #0,2,0: 47:[14, 44] Operation: 66-22=44 Exploring Operation: 14+22=36, Resulting Numbers: [66, 36] Generated Node #0,2,1: 47:[66, 36] Operation: 14+22=36 Exploring Operation: 66-14=52, Resulting Numbers: [22, 52] Generated Node #0,2,2: 47:[22, 52] Operation: 66-14=52 Moving to Node #0,1,2 Current State: 47:[54, 24], Operations: ['66-12=54', '10+14=24'] Exploring Operation: 54+24=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 54*24=1296, Resulting Numbers: [1296] 1296,47 unequal: No Solution Exploring Operation: 54-24=30, Resulting Numbers: [30] 30,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[66, 36], Operations: ['12+10=22', '14+22=36'] Exploring Operation: 66+36=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 66*36=2376, Resulting Numbers: [2376] 2376,47 unequal: No Solution Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[22, 52], Operations: ['12+10=22', '66-14=52'] Exploring Operation: 22+52=74, Resulting Numbers: [74] 74,47 unequal: No Solution Exploring Operation: 22*52=1144, Resulting Numbers: [1144] 1144,47 unequal: No Solution Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[14, 44], Operations: ['12+10=22', '66-22=44'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,47 unequal: No Solution Exploring Operation: 14+44=58, Resulting Numbers: [58] 58,47 unequal: No Solution Exploring Operation: 14*44=616, Resulting Numbers: [616] 616,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[14, 44], Operations: ['66-12=54', '54-10=44'] Exploring Operation: 14+44=58, Resulting Numbers: [58] 58,47 unequal: No Solution Exploring Operation: 14*44=616, Resulting Numbers: [616] 616,47 unequal: No Solution Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[10, 40], Operations: ['66-12=54', '54-14=40'] Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,47 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,47 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 30, 71, 18, 91 ]
15
[ "71+18=89", "91-89=2", "30/2=15" ]
Current State: 15:[30, 71, 18, 91], Operations: [] Exploring Operation: 71+18=89, Resulting Numbers: [30, 91, 89] Generated Node #2: [30, 91, 89] from Operation: 71+18=89 Current State: 15:[30, 91, 89], Operations: ['71+18=89'] Exploring Operation: 91-89=2, Resulting Numbers: [30, 2] Generated Node #3: [30, 2] from Operation: 91-89=2 Current State: 15:[30, 2], Operations: ['71+18=89', '91-89=2'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[30, 71, 18, 91], Operations: [] Exploring Operation: 91-71=20, Resulting Numbers: [30, 18, 20] Generated Node #0,0: 15:[30, 18, 20] Operation: 91-71=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[30, 18, 20], Operations: ['91-71=20'] Exploring Operation: 30-18=12, Resulting Numbers: [20, 12] Generated Node #0,0,0: 15:[20, 12] Operation: 30-18=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[20, 12], Operations: ['91-71=20', '30-18=12'] Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,15 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
[ 27, 95, 19, 2 ]
20
[ "27-2=25", "95/19=5", "25-5=20" ]
Current State: 20:[27, 95, 19, 2], Operations: [] Exploring Operation: 27-2=25, Resulting Numbers: [95, 19, 25] Generated Node #2: [95, 19, 25] from Operation: 27-2=25 Current State: 20:[95, 19, 25], Operations: ['27-2=25'] Exploring Operation: 95/19=5, Resulting Numbers: [25, 5] Generated Node #3: [25, 5] from Operation: 95/19=5 Current State: 20:[25, 5], Operations: ['27-2=25', '95/19=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[27, 95, 19, 2], Operations: [] Exploring Operation: 95/19=5, Resulting Numbers: [27, 2, 5] Generated Node #0,0: 20:[27, 2, 5] Operation: 95/19=5 Exploring Operation: 95-27=68, Resulting Numbers: [19, 2, 68] Generated Node #0,1: 20:[19, 2, 68] Operation: 95-27=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[27, 2, 5], Operations: ['95/19=5'] Exploring Operation: 27-5=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 20:[2, 22] Operation: 27-5=22 Exploring Operation: 27-2=25, Resulting Numbers: [5, 25] Generated Node #0,0,1: 20:[5, 25] Operation: 27-2=25 Moving to Node #0,0,0 Current State: 20:[2, 22], Operations: ['95/19=5', '27-5=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[27, 95, 19, 2], Operations: [] Exploring Operation: 95/19=5, Resulting Numbers: [27, 2, 5] Generated Node #0,0: 20:[27, 2, 5] Operation: 95/19=5 Moving to Node #0,0 Current State: 20:[27, 2, 5], Operations: ['95/19=5'] Exploring Operation: 27-5=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 20:[2, 22] Operation: 27-5=22 Moving to Node #0,0,0 Current State: 20:[2, 22], Operations: ['95/19=5', '27-5=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 68, 2, 40, 74 ]
10
[ "68+2=70", "74-70=4", "40/4=10" ]
Current State: 10:[68, 2, 40, 74], Operations: [] Exploring Operation: 68+2=70, Resulting Numbers: [40, 74, 70] Generated Node #2: [40, 74, 70] from Operation: 68+2=70 Current State: 10:[40, 74, 70], Operations: ['68+2=70'] Exploring Operation: 74-70=4, Resulting Numbers: [40, 4] Generated Node #3: [40, 4] from Operation: 74-70=4 Current State: 10:[40, 4], Operations: ['68+2=70', '74-70=4'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[68, 2, 40, 74], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [2, 40, 6] Generated Node #0,0: 10:[2, 40, 6] Operation: 74-68=6 Exploring Operation: 74-40=34, Resulting Numbers: [68, 2, 34] Generated Node #0,1: 10:[68, 2, 34] Operation: 74-40=34 Exploring Operation: 74/2=37, Resulting Numbers: [68, 40, 37] Generated Node #0,2: 10:[68, 40, 37] Operation: 74/2=37 Exploring Operation: 68/2=34, Resulting Numbers: [40, 74, 34] Generated Node #0,3: 10:[40, 74, 34] Operation: 68/2=34 Exploring Operation: 68-40=28, Resulting Numbers: [2, 74, 28] Generated Node #0,4: 10:[2, 74, 28] Operation: 68-40=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[2, 40, 6], Operations: ['74-68=6'] Exploring Operation: 40-2=38, Resulting Numbers: [6, 38] Generated Node #0,0,0: 10:[6, 38] Operation: 40-2=38 Exploring Operation: 40/2=20, Resulting Numbers: [6, 20] Generated Node #0,0,1: 10:[6, 20] Operation: 40/2=20 Exploring Operation: 6-2=4, Resulting Numbers: [40, 4] Generated Node #0,0,2: 10:[40, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [40, 3] Generated Node #0,0,3: 10:[40, 3] Operation: 6/2=3 Exploring Operation: 40-6=34, Resulting Numbers: [2, 34] Generated Node #0,0,4: 10:[2, 34] Operation: 40-6=34 Moving to Node #0,0,1 Current State: 10:[6, 20], Operations: ['74-68=6', '40/2=20'] Exploring Operation: 6*20=120, Resulting Numbers: [120] 120,10 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,10 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,10 unequal: No Solution Moving to Node #0,0,4 Current State: 10:[2, 34], Operations: ['74-68=6', '40-6=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,10 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,10 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,10 unequal: No Solution Moving to Node #0,0,0 Current State: 10:[6, 38], Operations: ['74-68=6', '40-2=38'] Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,10 unequal: No Solution Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,10 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[40, 4], Operations: ['74-68=6', '6-2=4'] Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,10 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,10 unequal: No Solution Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,10 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[68, 2, 40, 74], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [2, 40, 6] Generated Node #0,0: 10:[2, 40, 6] Operation: 74-68=6 Moving to Node #0,0 Current State: 10:[2, 40, 6], Operations: ['74-68=6'] Exploring Operation: 6-2=4, Resulting Numbers: [40, 4] Generated Node #0,0,2: 10:[40, 4] Operation: 6-2=4 Moving to Node #0,0,2 Current State: 10:[40, 4], Operations: ['74-68=6', '6-2=4'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 98, 93, 37, 84 ]
42
[ "98-93=5", "84-37=47", "47-5=42" ]
Current State: 42:[98, 93, 37, 84], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [37, 84, 5] Generated Node #2: [37, 84, 5] from Operation: 98-93=5 Current State: 42:[37, 84, 5], Operations: ['98-93=5'] Exploring Operation: 84-37=47, Resulting Numbers: [5, 47] Generated Node #3: [5, 47] from Operation: 84-37=47 Current State: 42:[5, 47], Operations: ['98-93=5', '84-37=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[98, 93, 37, 84], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [37, 84, 5] Generated Node #0,0: 42:[37, 84, 5] Operation: 98-93=5 Exploring Operation: 98-84=14, Resulting Numbers: [93, 37, 14] Generated Node #0,1: 42:[93, 37, 14] Operation: 98-84=14 Moving to Node #0,0 Current State: 42:[37, 84, 5], Operations: ['98-93=5'] Exploring Operation: 84-37=47, Resulting Numbers: [5, 47] Generated Node #0,0,0: 42:[5, 47] Operation: 84-37=47 Exploring Operation: 37+5=42, Resulting Numbers: [84, 42] Generated Node #0,0,1: 42:[84, 42] Operation: 37+5=42 Moving to Node #0,1 Current State: 42:[93, 37, 14], Operations: ['98-84=14'] Exploring Operation: 93-37=56, Resulting Numbers: [14, 56] Generated Node #0,1,0: 42:[14, 56] Operation: 93-37=56 Exploring Operation: 93-14=79, Resulting Numbers: [37, 79] Generated Node #0,1,1: 42:[37, 79] Operation: 93-14=79 Moving to Node #0,0,0 Current State: 42:[5, 47], Operations: ['98-93=5', '84-37=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[98, 93, 37, 84], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [37, 84, 5] Generated Node #0,0: 42:[37, 84, 5] Operation: 98-93=5 Moving to Node #0,0 Current State: 42:[37, 84, 5], Operations: ['98-93=5'] Exploring Operation: 84-37=47, Resulting Numbers: [5, 47] Generated Node #0,0,0: 42:[5, 47] Operation: 84-37=47 Moving to Node #0,0,0 Current State: 42:[5, 47], Operations: ['98-93=5', '84-37=47'] Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 62, 83, 40, 85 ]
24
[ "83-62=21", "85-40=45", "45-21=24" ]
Current State: 24:[62, 83, 40, 85], Operations: [] Exploring Operation: 83-62=21, Resulting Numbers: [40, 85, 21] Generated Node #2: [40, 85, 21] from Operation: 83-62=21 Current State: 24:[40, 85, 21], Operations: ['83-62=21'] Exploring Operation: 85-40=45, Resulting Numbers: [21, 45] Generated Node #3: [21, 45] from Operation: 85-40=45 Current State: 24:[21, 45], Operations: ['83-62=21', '85-40=45'] Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[62, 83, 40, 85], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [83, 40, 23] Generated Node #0,0: 24:[83, 40, 23] Operation: 85-62=23 Exploring Operation: 85-83=2, Resulting Numbers: [62, 40, 2] Generated Node #0,1: 24:[62, 40, 2] Operation: 85-83=2 Exploring Operation: 83-62=21, Resulting Numbers: [40, 85, 21] Generated Node #0,2: 24:[40, 85, 21] Operation: 83-62=21 Moving to Node #0,1 Current State: 24:[62, 40, 2], Operations: ['85-83=2'] Exploring Operation: 62/2=31, Resulting Numbers: [40, 31] Generated Node #0,1,0: 24:[40, 31] Operation: 62/2=31 Exploring Operation: 40/2=20, Resulting Numbers: [62, 20] Generated Node #0,1,1: 24:[62, 20] Operation: 40/2=20 Exploring Operation: 62-40=22, Resulting Numbers: [2, 22] Generated Node #0,1,2: 24:[2, 22] Operation: 62-40=22 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[2, 22], Operations: ['85-83=2', '62-40=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[62, 83, 40, 85], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [62, 40, 2] Generated Node #0,1: 24:[62, 40, 2] Operation: 85-83=2 Moving to Node #0,1 Current State: 24:[62, 40, 2], Operations: ['85-83=2'] Exploring Operation: 62-40=22, Resulting Numbers: [2, 22] Generated Node #0,1,2: 24:[2, 22] Operation: 62-40=22 Moving to Node #0,1,2 Current State: 24:[2, 22], Operations: ['85-83=2', '62-40=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 32, 14, 98, 45 ]
71
[ "32-14=18", "98-45=53", "18+53=71" ]
Current State: 71:[32, 14, 98, 45], Operations: [] Exploring Operation: 32-14=18, Resulting Numbers: [98, 45, 18] Generated Node #2: [98, 45, 18] from Operation: 32-14=18 Current State: 71:[98, 45, 18], Operations: ['32-14=18'] Exploring Operation: 98-45=53, Resulting Numbers: [18, 53] Generated Node #3: [18, 53] from Operation: 98-45=53 Current State: 71:[18, 53], Operations: ['32-14=18', '98-45=53'] Exploring Operation: 18+53=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[32, 14, 98, 45], Operations: [] Exploring Operation: 14+45=59, Resulting Numbers: [32, 98, 59] Generated Node #0,0: 71:[32, 98, 59] Operation: 14+45=59 Exploring Operation: 32+14=46, Resulting Numbers: [98, 45, 46] Generated Node #0,1: 71:[98, 45, 46] Operation: 32+14=46 Exploring Operation: 98-14=84, Resulting Numbers: [32, 45, 84] Generated Node #0,2: 71:[32, 45, 84] Operation: 98-14=84 Moving to Node #0,0 Current State: 71:[32, 98, 59], Operations: ['14+45=59'] Exploring Operation: 98-32=66, Resulting Numbers: [59, 66] Generated Node #0,0,0: 71:[59, 66] Operation: 98-32=66 Exploring Operation: 32+98=130, Resulting Numbers: [59, 130] Generated Node #0,0,1: 71:[59, 130] Operation: 32+98=130 Exploring Operation: 32+59=91, Resulting Numbers: [98, 91] Generated Node #0,0,2: 71:[98, 91] Operation: 32+59=91 Moving to Node #0,1 Current State: 71:[98, 45, 46], Operations: ['32+14=46'] Exploring Operation: 98-45=53, Resulting Numbers: [46, 53] Generated Node #0,1,0: 71:[46, 53] Operation: 98-45=53 Exploring Operation: 45+46=91, Resulting Numbers: [98, 91] Generated Node #0,1,1: 71:[98, 91] Operation: 45+46=91 Exploring Operation: 98-46=52, Resulting Numbers: [45, 52] Generated Node #0,1,2: 71:[45, 52] Operation: 98-46=52 Moving to Node #0,2 Current State: 71:[32, 45, 84], Operations: ['98-14=84'] Exploring Operation: 45-32=13, Resulting Numbers: [84, 13] Generated Node #0,2,0: 71:[84, 13] Operation: 45-32=13 Exploring Operation: 84-32=52, Resulting Numbers: [45, 52] Generated Node #0,2,1: 71:[45, 52] Operation: 84-32=52 Exploring Operation: 32+45=77, Resulting Numbers: [84, 77] Generated Node #0,2,2: 71:[84, 77] Operation: 32+45=77 Moving to Node #0,0,0 Current State: 71:[59, 66], Operations: ['14+45=59', '98-32=66'] Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,71 unequal: No Solution Exploring Operation: 59*66=3894, Resulting Numbers: [3894] 3894,71 unequal: No Solution Exploring Operation: 59+66=125, Resulting Numbers: [125] 125,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[84, 77], Operations: ['98-14=84', '32+45=77'] Exploring Operation: 84*77=6468, Resulting Numbers: [6468] 6468,71 unequal: No Solution Exploring Operation: 84-77=7, Resulting Numbers: [7] 7,71 unequal: No Solution Exploring Operation: 84+77=161, Resulting Numbers: [161] 161,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[46, 53], Operations: ['32+14=46', '98-45=53'] Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,71 unequal: No Solution Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,71 unequal: No Solution Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[45, 52], Operations: ['32+14=46', '98-46=52'] Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,71 unequal: No Solution Exploring Operation: 45*52=2340, Resulting Numbers: [2340] 2340,71 unequal: No Solution Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[45, 52], Operations: ['98-14=84', '84-32=52'] Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,71 unequal: No Solution Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,71 unequal: No Solution Exploring Operation: 45*52=2340, Resulting Numbers: [2340] 2340,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[98, 91], Operations: ['32+14=46', '45+46=91'] Exploring Operation: 98+91=189, Resulting Numbers: [189] 189,71 unequal: No Solution Exploring Operation: 98-91=7, Resulting Numbers: [7] 7,71 unequal: No Solution Exploring Operation: 98*91=8918, Resulting Numbers: [8918] 8918,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[98, 91], Operations: ['14+45=59', '32+59=91'] Exploring Operation: 98+91=189, Resulting Numbers: [189] 189,71 unequal: No Solution Exploring Operation: 98-91=7, Resulting Numbers: [7] 7,71 unequal: No Solution Exploring Operation: 98*91=8918, Resulting Numbers: [8918] 8918,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[84, 13], Operations: ['98-14=84', '45-32=13'] Exploring Operation: 84*13=1092, Resulting Numbers: [1092] 1092,71 unequal: No Solution Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[32, 14, 98, 45], Operations: [] Exploring Operation: 98-14=84, Resulting Numbers: [32, 45, 84] Generated Node #0,2: 71:[32, 45, 84] Operation: 98-14=84 Moving to Node #0,2 Current State: 71:[32, 45, 84], Operations: ['98-14=84'] Exploring Operation: 45-32=13, Resulting Numbers: [84, 13] Generated Node #0,2,0: 71:[84, 13] Operation: 45-32=13 Moving to Node #0,2,0 Current State: 71:[84, 13], Operations: ['98-14=84', '45-32=13'] Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
0.966146
hs_3
sum_heuristic
[ 49, 1, 41, 5 ]
95
[ "49*1=49", "41+5=46", "49+46=95" ]
Current State: 95:[49, 1, 41, 5], Operations: [] Exploring Operation: 49*1=49, Resulting Numbers: [41, 5, 49] Generated Node #2: [41, 5, 49] from Operation: 49*1=49 Current State: 95:[41, 5, 49], Operations: ['49*1=49'] Exploring Operation: 41+5=46, Resulting Numbers: [49, 46] Generated Node #3: [49, 46] from Operation: 41+5=46 Current State: 95:[49, 46], Operations: ['49*1=49', '41+5=46'] Exploring Operation: 49+46=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[49, 1, 41, 5], Operations: [] Exploring Operation: 49+41=90, Resulting Numbers: [1, 5, 90] Generated Node #0,0: 95:[1, 5, 90] Operation: 49+41=90 Exploring Operation: 49-41=8, Resulting Numbers: [1, 5, 8] Generated Node #0,1: 95:[1, 5, 8] Operation: 49-41=8 Moving to Node #0,1 Current State: 95:[1, 5, 8], Operations: ['49-41=8'] Exploring Operation: 1*5=5, Resulting Numbers: [8, 5] Generated Node #0,1,0: 95:[8, 5] Operation: 1*5=5 Exploring Operation: 8-1=7, Resulting Numbers: [5, 7] Generated Node #0,1,1: 95:[5, 7] Operation: 8-1=7 Moving to Node #0,0 Current State: 95:[1, 5, 90], Operations: ['49+41=90'] Exploring Operation: 1+90=91, Resulting Numbers: [5, 91] Generated Node #0,0,0: 95:[5, 91] Operation: 1+90=91 Exploring Operation: 5+90=95, Resulting Numbers: [1, 95] Generated Node #0,0,1: 95:[1, 95] Operation: 5+90=95 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[5, 91], Operations: ['49+41=90', '1+90=91'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,95 unequal: No Solution Exploring Operation: 5+91=96, Resulting Numbers: [96] 96,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[1, 95], Operations: ['49+41=90', '5+90=95'] Exploring Operation: 1*95=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[49, 1, 41, 5], Operations: [] Exploring Operation: 49+41=90, Resulting Numbers: [1, 5, 90] Generated Node #0,0: 95:[1, 5, 90] Operation: 49+41=90 Moving to Node #0,0 Current State: 95:[1, 5, 90], Operations: ['49+41=90'] Exploring Operation: 5+90=95, Resulting Numbers: [1, 95] Generated Node #0,0,1: 95:[1, 95] Operation: 5+90=95 Moving to Node #0,0,1 Current State: 95:[1, 95], Operations: ['49+41=90', '5+90=95'] Exploring Operation: 1*95=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
sum_heuristic
[ 14, 84, 2, 86 ]
74
[ "14+84=98", "2*86=172", "172-98=74" ]
Current State: 74:[14, 84, 2, 86], Operations: [] Exploring Operation: 14+84=98, Resulting Numbers: [2, 86, 98] Generated Node #2: [2, 86, 98] from Operation: 14+84=98 Current State: 74:[2, 86, 98], Operations: ['14+84=98'] Exploring Operation: 2*86=172, Resulting Numbers: [98, 172] Generated Node #3: [98, 172] from Operation: 2*86=172 Current State: 74:[98, 172], Operations: ['14+84=98', '2*86=172'] Exploring Operation: 172-98=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[14, 84, 2, 86], Operations: [] Exploring Operation: 86-14=72, Resulting Numbers: [84, 2, 72] Generated Node #0,0: 74:[84, 2, 72] Operation: 86-14=72 Moving to Node #0,0 Current State: 74:[84, 2, 72], Operations: ['86-14=72'] Exploring Operation: 84/2=42, Resulting Numbers: [72, 42] Generated Node #0,0,0: 74:[72, 42] Operation: 84/2=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[72, 42], Operations: ['86-14=72', '84/2=42'] Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 70, 2, 7 ]
13
[ "35+70=105", "105/7=15", "15-2=13" ]
Current State: 13:[35, 70, 2, 7], Operations: [] Exploring Operation: 35+70=105, Resulting Numbers: [2, 7, 105] Generated Node #2: [2, 7, 105] from Operation: 35+70=105 Current State: 13:[2, 7, 105], Operations: ['35+70=105'] Exploring Operation: 105/7=15, Resulting Numbers: [2, 15] Generated Node #3: [2, 15] from Operation: 105/7=15 Current State: 13:[2, 15], Operations: ['35+70=105', '105/7=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[35, 70, 2, 7], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [2, 7, 2] Generated Node #0,0: 13:[2, 7, 2] Operation: 70/35=2 Moving to Node #0,0 Current State: 13:[2, 7, 2], Operations: ['70/35=2'] Exploring Operation: 2*7=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 13:[2, 14] Operation: 2*7=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[2, 14], Operations: ['70/35=2', '2*7=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,13 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
[ 90, 71, 8, 61 ]
11
[ "90*8=720", "61+720=781", "781/71=11" ]
Current State: 11:[90, 71, 8, 61], Operations: [] Exploring Operation: 90*8=720, Resulting Numbers: [71, 61, 720] Generated Node #2: [71, 61, 720] from Operation: 90*8=720 Current State: 11:[71, 61, 720], Operations: ['90*8=720'] Exploring Operation: 61+720=781, Resulting Numbers: [71, 781] Generated Node #3: [71, 781] from Operation: 61+720=781 Current State: 11:[71, 781], Operations: ['90*8=720', '61+720=781'] Exploring Operation: 781/71=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[90, 71, 8, 61], Operations: [] Exploring Operation: 90-61=29, Resulting Numbers: [71, 8, 29] Generated Node #0,0: 11:[71, 8, 29] Operation: 90-61=29 Exploring Operation: 90-71=19, Resulting Numbers: [8, 61, 19] Generated Node #0,1: 11:[8, 61, 19] Operation: 90-71=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[8, 61, 19], Operations: ['90-71=19'] Exploring Operation: 61-8=53, Resulting Numbers: [19, 53] Generated Node #0,1,0: 11:[19, 53] Operation: 61-8=53 Exploring Operation: 61-19=42, Resulting Numbers: [8, 42] Generated Node #0,1,1: 11:[8, 42] Operation: 61-19=42 Moving to Node #0,1,1 Current State: 11:[8, 42], Operations: ['90-71=19', '61-19=42'] Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[19, 53], Operations: ['90-71=19', '61-8=53'] Exploring Operation: 19+53=72, Resulting Numbers: [72] 72,11 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,11 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 Current State: 11:[71, 8, 29], Operations: ['90-61=29'] Exploring Operation: 71-29=42, Resulting Numbers: [8, 42] Generated Node #0,0,0: 11:[8, 42] Operation: 71-29=42 Exploring Operation: 71-8=63, Resulting Numbers: [29, 63] Generated Node #0,0,1: 11:[29, 63] Operation: 71-8=63 Moving to Node #0,0,0 Current State: 11:[8, 42], Operations: ['90-61=29', '71-29=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[29, 63], Operations: ['90-61=29', '71-8=63'] Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 29+63=92, Resulting Numbers: [92] 92,11 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
[ 5, 10, 45, 48 ]
44
[ "45-5=40", "40/10=4", "48-4=44" ]
Current State: 44:[5, 10, 45, 48], Operations: [] Exploring Operation: 45-5=40, Resulting Numbers: [10, 48, 40] Generated Node #2: [10, 48, 40] from Operation: 45-5=40 Current State: 44:[10, 48, 40], Operations: ['45-5=40'] Exploring Operation: 40/10=4, Resulting Numbers: [48, 4] Generated Node #3: [48, 4] from Operation: 40/10=4 Current State: 44:[48, 4], Operations: ['45-5=40', '40/10=4'] Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[5, 10, 45, 48], Operations: [] Exploring Operation: 48-5=43, Resulting Numbers: [10, 45, 43] Generated Node #0,0: 44:[10, 45, 43] Operation: 48-5=43 Exploring Operation: 48-45=3, Resulting Numbers: [5, 10, 3] Generated Node #0,1: 44:[5, 10, 3] Operation: 48-45=3 Exploring Operation: 10/5=2, Resulting Numbers: [45, 48, 2] Generated Node #0,2: 44:[45, 48, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [45, 48, 5] Generated Node #0,3: 44:[45, 48, 5] Operation: 10-5=5 Moving to Node #0,0 Current State: 44:[10, 45, 43], Operations: ['48-5=43'] Exploring Operation: 10+45=55, Resulting Numbers: [43, 55] Generated Node #0,0,0: 44:[43, 55] Operation: 10+45=55 Exploring Operation: 45-43=2, Resulting Numbers: [10, 2] Generated Node #0,0,1: 44:[10, 2] Operation: 45-43=2 Exploring Operation: 45-10=35, Resulting Numbers: [43, 35] Generated Node #0,0,2: 44:[43, 35] Operation: 45-10=35 Exploring Operation: 10+43=53, Resulting Numbers: [45, 53] Generated Node #0,0,3: 44:[45, 53] Operation: 10+43=53 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[10, 2], Operations: ['48-5=43', '45-43=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 44:[43, 35], Operations: ['48-5=43', '45-10=35'] Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,44 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 44:[45, 53], Operations: ['48-5=43', '10+43=53'] Exploring Operation: 45+53=98, Resulting Numbers: [98] 98,44 unequal: No Solution Exploring Operation: 45*53=2385, Resulting Numbers: [2385] 2385,44 unequal: No Solution Exploring Operation: 53-45=8, Resulting Numbers: [8] 8,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[43, 55], Operations: ['48-5=43', '10+45=55'] Exploring Operation: 43*55=2365, Resulting Numbers: [2365] 2365,44 unequal: No Solution Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,44 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 44:[5, 10, 3], Operations: ['48-45=3'] Exploring Operation: 10+3=13, Resulting Numbers: [5, 13] Generated Node #0,1,0: 44:[5, 13] Operation: 10+3=13 Exploring Operation: 10/5=2, Resulting Numbers: [3, 2] Generated Node #0,1,1: 44:[3, 2] Operation: 10/5=2 Exploring Operation: 5-3=2, Resulting Numbers: [10, 2] Generated Node #0,1,2: 44:[10, 2] Operation: 5-3=2 Exploring Operation: 10-5=5, Resulting Numbers: [3, 5] Generated Node #0,1,3: 44:[3, 5] Operation: 10-5=5 Moving to Node #0,2 Current State: 44:[45, 48, 2], Operations: ['10/5=2'] Exploring Operation: 48-45=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 44:[2, 3] Operation: 48-45=3 Exploring Operation: 48-2=46, Resulting Numbers: [45, 46] Generated Node #0,2,1: 44:[45, 46] Operation: 48-2=46 Exploring Operation: 48/2=24, Resulting Numbers: [45, 24] Generated Node #0,2,2: 44:[45, 24] Operation: 48/2=24 Exploring Operation: 45-2=43, Resulting Numbers: [48, 43] Generated Node #0,2,3: 44:[48, 43] Operation: 45-2=43 Moving to Node #0,3 Current State: 44:[45, 48, 5], Operations: ['10-5=5'] Exploring Operation: 48-45=3, Resulting Numbers: [5, 3] Generated Node #0,3,0: 44:[5, 3] Operation: 48-45=3 Exploring Operation: 48-5=43, Resulting Numbers: [45, 43] Generated Node #0,3,1: 44:[45, 43] Operation: 48-5=43 Exploring Operation: 45-5=40, Resulting Numbers: [48, 40] Generated Node #0,3,2: 44:[48, 40] Operation: 45-5=40 Exploring Operation: 45/5=9, Resulting Numbers: [48, 9] Generated Node #0,3,3: 44:[48, 9] Operation: 45/5=9 Moving to Node #0,1,1 Current State: 44:[3, 2], Operations: ['48-45=3', '10/5=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[10, 2], Operations: ['48-45=3', '5-3=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[2, 3], Operations: ['10/5=2', '48-45=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[3, 5], Operations: ['48-45=3', '10-5=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,44 unequal: No Solution Moving to Node #0,3,1 Current State: 44:[45, 43], Operations: ['10-5=5', '48-5=43'] Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 45+43=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 45*43=1935, Resulting Numbers: [1935] 1935,44 unequal: No Solution Moving to Node #0,3,0 Current State: 44:[5, 3], Operations: ['10-5=5', '48-45=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[45, 24], Operations: ['10/5=2', '48/2=24'] Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,44 unequal: No Solution Exploring Operation: 45*24=1080, Resulting Numbers: [1080] 1080,44 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[45, 46], Operations: ['10/5=2', '48-2=46'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,44 unequal: No Solution Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,44 unequal: No Solution Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[5, 13], Operations: ['48-45=3', '10+3=13'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,44 unequal: No Solution Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[48, 43], Operations: ['10/5=2', '45-2=43'] Exploring Operation: 48+43=91, Resulting Numbers: [91] 91,44 unequal: No Solution Exploring Operation: 48*43=2064, Resulting Numbers: [2064] 2064,44 unequal: No Solution Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[48, 9], Operations: ['10-5=5', '45/5=9'] Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,44 unequal: No Solution Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,44 unequal: No Solution Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[48, 40], Operations: ['10-5=5', '45-5=40'] Exploring Operation: 48*40=1920, Resulting Numbers: [1920] 1920,44 unequal: No Solution Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,44 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,44 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 76, 75, 79, 48 ]
32
[ "76-75=1", "79-48=31", "1+31=32" ]
Current State: 32:[76, 75, 79, 48], Operations: [] Exploring Operation: 76-75=1, Resulting Numbers: [79, 48, 1] Generated Node #2: [79, 48, 1] from Operation: 76-75=1 Current State: 32:[79, 48, 1], Operations: ['76-75=1'] Exploring Operation: 79-48=31, Resulting Numbers: [1, 31] Generated Node #3: [1, 31] from Operation: 79-48=31 Current State: 32:[1, 31], Operations: ['76-75=1', '79-48=31'] Exploring Operation: 1+31=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[76, 75, 79, 48], Operations: [] Exploring Operation: 76-75=1, Resulting Numbers: [79, 48, 1] Generated Node #0,0: 32:[79, 48, 1] Operation: 76-75=1 Exploring Operation: 79-48=31, Resulting Numbers: [76, 75, 31] Generated Node #0,1: 32:[76, 75, 31] Operation: 79-48=31 Exploring Operation: 76-48=28, Resulting Numbers: [75, 79, 28] Generated Node #0,2: 32:[75, 79, 28] Operation: 76-48=28 Exploring Operation: 79-76=3, Resulting Numbers: [75, 48, 3] Generated Node #0,3: 32:[75, 48, 3] Operation: 79-76=3 Exploring Operation: 79-75=4, Resulting Numbers: [76, 48, 4] Generated Node #0,4: 32:[76, 48, 4] Operation: 79-75=4 Moving to Node #0,3 Current State: 32:[75, 48, 3], Operations: ['79-76=3'] Exploring Operation: 48/3=16, Resulting Numbers: [75, 16] Generated Node #0,3,0: 32:[75, 16] Operation: 48/3=16 Exploring Operation: 75-3=72, Resulting Numbers: [48, 72] Generated Node #0,3,1: 32:[48, 72] Operation: 75-3=72 Exploring Operation: 75/3=25, Resulting Numbers: [48, 25] Generated Node #0,3,2: 32:[48, 25] Operation: 75/3=25 Exploring Operation: 75-48=27, Resulting Numbers: [3, 27] Generated Node #0,3,3: 32:[3, 27] Operation: 75-48=27 Exploring Operation: 48-3=45, Resulting Numbers: [75, 45] Generated Node #0,3,4: 32:[75, 45] Operation: 48-3=45 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 32:[3, 27], Operations: ['79-76=3', '75-48=27'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,32 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,32 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 32:[48, 25], Operations: ['79-76=3', '75/3=25'] Exploring Operation: 48*25=1200, Resulting Numbers: [1200] 1200,32 unequal: No Solution Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,32 unequal: No Solution Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 32:[75, 16], Operations: ['79-76=3', '48/3=16'] Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 75+16=91, Resulting Numbers: [91] 91,32 unequal: No Solution Exploring Operation: 75*16=1200, Resulting Numbers: [1200] 1200,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 32:[48, 72], Operations: ['79-76=3', '75-3=72'] Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 48*72=3456, Resulting Numbers: [3456] 3456,32 unequal: No Solution Exploring Operation: 48+72=120, Resulting Numbers: [120] 120,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 32:[75, 45], Operations: ['79-76=3', '48-3=45'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,32 unequal: No Solution Exploring Operation: 75+45=120, Resulting Numbers: [120] 120,32 unequal: No Solution Exploring Operation: 75*45=3375, Resulting Numbers: [3375] 3375,32 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: 32:[76, 48, 4], Operations: ['79-75=4'] Exploring Operation: 76/4=19, Resulting Numbers: [48, 19] Generated Node #0,4,0: 32:[48, 19] Operation: 76/4=19 Exploring Operation: 76-48=28, Resulting Numbers: [4, 28] Generated Node #0,4,1: 32:[4, 28] Operation: 76-48=28 Exploring Operation: 76-4=72, Resulting Numbers: [48, 72] Generated Node #0,4,2: 32:[48, 72] Operation: 76-4=72 Exploring Operation: 48/4=12, Resulting Numbers: [76, 12] Generated Node #0,4,3: 32:[76, 12] Operation: 48/4=12 Exploring Operation: 48-4=44, Resulting Numbers: [76, 44] Generated Node #0,4,4: 32:[76, 44] Operation: 48-4=44 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 32:[4, 28], Operations: ['79-75=4', '76-48=28'] Exploring Operation: 4*28=112, Resulting Numbers: [112] 112,32 unequal: No Solution Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[76, 75, 79, 48], Operations: [] Exploring Operation: 79-75=4, Resulting Numbers: [76, 48, 4] Generated Node #0,4: 32:[76, 48, 4] Operation: 79-75=4 Moving to Node #0,4 Current State: 32:[76, 48, 4], Operations: ['79-75=4'] Exploring Operation: 76-48=28, Resulting Numbers: [4, 28] Generated Node #0,4,1: 32:[4, 28] Operation: 76-48=28 Moving to Node #0,4,1 Current State: 32:[4, 28], Operations: ['79-75=4', '76-48=28'] Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 68, 39, 86, 58 ]
57
[ "68-39=29", "86-58=28", "29+28=57" ]
Current State: 57:[68, 39, 86, 58], Operations: [] Exploring Operation: 68-39=29, Resulting Numbers: [86, 58, 29] Generated Node #2: [86, 58, 29] from Operation: 68-39=29 Current State: 57:[86, 58, 29], Operations: ['68-39=29'] Exploring Operation: 86-58=28, Resulting Numbers: [29, 28] Generated Node #3: [29, 28] from Operation: 86-58=28 Current State: 57:[29, 28], Operations: ['68-39=29', '86-58=28'] Exploring Operation: 29+28=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[68, 39, 86, 58], Operations: [] Exploring Operation: 86-68=18, Resulting Numbers: [39, 58, 18] Generated Node #0,0: 57:[39, 58, 18] Operation: 86-68=18 Exploring Operation: 86-39=47, Resulting Numbers: [68, 58, 47] Generated Node #0,1: 57:[68, 58, 47] Operation: 86-39=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[39, 58, 18], Operations: ['86-68=18'] Exploring Operation: 39+18=57, Resulting Numbers: [58, 57] Generated Node #0,0,0: 57:[58, 57] Operation: 39+18=57 Exploring Operation: 58-39=19, Resulting Numbers: [18, 19] Generated Node #0,0,1: 57:[18, 19] Operation: 58-39=19 Moving to Node #0,0,0 Current State: 57:[58, 57], Operations: ['86-68=18', '39+18=57'] Exploring Operation: 58-57=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 58+57=115, Resulting Numbers: [115] 115,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[18, 19], Operations: ['86-68=18', '58-39=19'] Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[68, 58, 47], Operations: ['86-39=47'] Exploring Operation: 68-47=21, Resulting Numbers: [58, 21] Generated Node #0,1,0: 57:[58, 21] Operation: 68-47=21 Exploring Operation: 68-58=10, Resulting Numbers: [47, 10] Generated Node #0,1,1: 57:[47, 10] Operation: 68-58=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[58, 21], Operations: ['86-39=47', '68-47=21'] Exploring Operation: 58-21=37, Resulting Numbers: [37] 37,57 unequal: No Solution Exploring Operation: 58+21=79, Resulting Numbers: [79] 79,57 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:[47, 10], Operations: ['86-39=47', '68-58=10'] Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[68, 39, 86, 58], Operations: [] Exploring Operation: 86-39=47, Resulting Numbers: [68, 58, 47] Generated Node #0,1: 57:[68, 58, 47] Operation: 86-39=47 Moving to Node #0,1 Current State: 57:[68, 58, 47], Operations: ['86-39=47'] Exploring Operation: 68-58=10, Resulting Numbers: [47, 10] Generated Node #0,1,1: 57:[47, 10] Operation: 68-58=10 Moving to Node #0,1,1 Current State: 57:[47, 10], Operations: ['86-39=47', '68-58=10'] Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 81, 63, 61, 96 ]
17
[ "81-63=18", "96-61=35", "35-18=17" ]
Current State: 17:[81, 63, 61, 96], Operations: [] Exploring Operation: 81-63=18, Resulting Numbers: [61, 96, 18] Generated Node #2: [61, 96, 18] from Operation: 81-63=18 Current State: 17:[61, 96, 18], Operations: ['81-63=18'] Exploring Operation: 96-61=35, Resulting Numbers: [18, 35] Generated Node #3: [18, 35] from Operation: 96-61=35 Current State: 17:[18, 35], Operations: ['81-63=18', '96-61=35'] Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[81, 63, 61, 96], Operations: [] Exploring Operation: 96-81=15, Resulting Numbers: [63, 61, 15] Generated Node #0,0: 17:[63, 61, 15] Operation: 96-81=15 Moving to Node #0,0 Current State: 17:[63, 61, 15], Operations: ['96-81=15'] Exploring Operation: 63-61=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 17:[15, 2] Operation: 63-61=2 Moving to Node #0,0,0 Current State: 17:[15, 2], Operations: ['96-81=15', '63-61=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[81, 63, 61, 96], Operations: [] Exploring Operation: 96-81=15, Resulting Numbers: [63, 61, 15] Generated Node #0,0: 17:[63, 61, 15] Operation: 96-81=15 Moving to Node #0,0 Current State: 17:[63, 61, 15], Operations: ['96-81=15'] Exploring Operation: 63-61=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 17:[15, 2] Operation: 63-61=2 Moving to Node #0,0,0 Current State: 17:[15, 2], Operations: ['96-81=15', '63-61=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 95, 5, 6, 75 ]
31
[ "95+5=100", "75-6=69", "100-69=31" ]
Current State: 31:[95, 5, 6, 75], Operations: [] Exploring Operation: 95+5=100, Resulting Numbers: [6, 75, 100] Generated Node #2: [6, 75, 100] from Operation: 95+5=100 Current State: 31:[6, 75, 100], Operations: ['95+5=100'] Exploring Operation: 75-6=69, Resulting Numbers: [100, 69] Generated Node #3: [100, 69] from Operation: 75-6=69 Current State: 31:[100, 69], Operations: ['95+5=100', '75-6=69'] Exploring Operation: 100-69=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[95, 5, 6, 75], Operations: [] Exploring Operation: 75/5=15, Resulting Numbers: [95, 6, 15] Generated Node #0,0: 31:[95, 6, 15] Operation: 75/5=15 Exploring Operation: 95/5=19, Resulting Numbers: [6, 75, 19] Generated Node #0,1: 31:[6, 75, 19] Operation: 95/5=19 Exploring Operation: 5*6=30, Resulting Numbers: [95, 75, 30] Generated Node #0,2: 31:[95, 75, 30] Operation: 5*6=30 Exploring Operation: 95-5=90, Resulting Numbers: [6, 75, 90] Generated Node #0,3: 31:[6, 75, 90] Operation: 95-5=90 Exploring Operation: 95-75=20, Resulting Numbers: [5, 6, 20] Generated Node #0,4: 31:[5, 6, 20] Operation: 95-75=20 Moving to Node #0,4 Current State: 31:[5, 6, 20], Operations: ['95-75=20'] Exploring Operation: 6+20=26, Resulting Numbers: [5, 26] Generated Node #0,4,0: 31:[5, 26] Operation: 6+20=26 Exploring Operation: 5+6=11, Resulting Numbers: [20, 11] Generated Node #0,4,1: 31:[20, 11] Operation: 5+6=11 Exploring Operation: 5+20=25, Resulting Numbers: [6, 25] Generated Node #0,4,2: 31:[6, 25] Operation: 5+20=25 Exploring Operation: 6-5=1, Resulting Numbers: [20, 1] Generated Node #0,4,3: 31:[20, 1] Operation: 6-5=1 Exploring Operation: 5*6=30, Resulting Numbers: [20, 30] Generated Node #0,4,4: 31:[20, 30] Operation: 5*6=30 Moving to Node #0,1 Current State: 31:[6, 75, 19], Operations: ['95/5=19'] Exploring Operation: 6+19=25, Resulting Numbers: [75, 25] Generated Node #0,1,0: 31:[75, 25] Operation: 6+19=25 Exploring Operation: 75-19=56, Resulting Numbers: [6, 56] Generated Node #0,1,1: 31:[6, 56] Operation: 75-19=56 Exploring Operation: 6+75=81, Resulting Numbers: [19, 81] Generated Node #0,1,2: 31:[19, 81] Operation: 6+75=81 Exploring Operation: 19-6=13, Resulting Numbers: [75, 13] Generated Node #0,1,3: 31:[75, 13] Operation: 19-6=13 Exploring Operation: 75-6=69, Resulting Numbers: [19, 69] Generated Node #0,1,4: 31:[19, 69] Operation: 75-6=69 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[75, 25], Operations: ['95/5=19', '6+19=25'] Exploring Operation: 75-25=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 75/25=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 75*25=1875, Resulting Numbers: [1875] 1875,31 unequal: No Solution Exploring Operation: 75+25=100, Resulting Numbers: [100] 100,31 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:[6, 56], Operations: ['95/5=19', '75-19=56'] Exploring Operation: 6*56=336, Resulting Numbers: [336] 336,31 unequal: No Solution Exploring Operation: 6+56=62, Resulting Numbers: [62] 62,31 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,31 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:[19, 69], Operations: ['95/5=19', '75-6=69'] Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 19*69=1311, Resulting Numbers: [1311] 1311,31 unequal: No Solution Exploring Operation: 19+69=88, Resulting Numbers: [88] 88,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[19, 81], Operations: ['95/5=19', '6+75=81'] Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,31 unequal: No Solution Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,31 unequal: No Solution Exploring Operation: 19*81=1539, Resulting Numbers: [1539] 1539,31 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:[75, 13], Operations: ['95/5=19', '19-6=13'] Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,31 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,31 unequal: No Solution Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,31 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: 31:[95, 6, 15], Operations: ['75/5=15'] Exploring Operation: 95-6=89, Resulting Numbers: [15, 89] Generated Node #0,0,0: 31:[15, 89] Operation: 95-6=89 Exploring Operation: 95-15=80, Resulting Numbers: [6, 80] Generated Node #0,0,1: 31:[6, 80] Operation: 95-15=80 Exploring Operation: 15-6=9, Resulting Numbers: [95, 9] Generated Node #0,0,2: 31:[95, 9] Operation: 15-6=9 Exploring Operation: 6+15=21, Resulting Numbers: [95, 21] Generated Node #0,0,3: 31:[95, 21] Operation: 6+15=21 Exploring Operation: 95+6=101, Resulting Numbers: [15, 101] Generated Node #0,0,4: 31:[15, 101] Operation: 95+6=101 Moving to Node #0,2 Current State: 31:[95, 75, 30], Operations: ['5*6=30'] Exploring Operation: 95-75=20, Resulting Numbers: [30, 20] Generated Node #0,2,0: 31:[30, 20] Operation: 95-75=20 Exploring Operation: 95-30=65, Resulting Numbers: [75, 65] Generated Node #0,2,1: 31:[75, 65] Operation: 95-30=65 Exploring Operation: 75-30=45, Resulting Numbers: [95, 45] Generated Node #0,2,2: 31:[95, 45] Operation: 75-30=45 Exploring Operation: 95+30=125, Resulting Numbers: [75, 125] Generated Node #0,2,3: 31:[75, 125] Operation: 95+30=125 Exploring Operation: 75+30=105, Resulting Numbers: [95, 105] Generated Node #0,2,4: 31:[95, 105] Operation: 75+30=105 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[30, 20], Operations: ['5*6=30', '95-75=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,31 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,31 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:[75, 65], Operations: ['5*6=30', '95-30=65'] Exploring Operation: 75+65=140, Resulting Numbers: [140] 140,31 unequal: No Solution Exploring Operation: 75-65=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 75*65=4875, Resulting Numbers: [4875] 4875,31 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:[95, 45], Operations: ['5*6=30', '75-30=45'] Exploring Operation: 95+45=140, Resulting Numbers: [140] 140,31 unequal: No Solution Exploring Operation: 95*45=4275, Resulting Numbers: [4275] 4275,31 unequal: No Solution Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,31 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:[75, 125], Operations: ['5*6=30', '95+30=125'] Exploring Operation: 75*125=9375, Resulting Numbers: [9375] 9375,31 unequal: No Solution Exploring Operation: 75+125=200, Resulting Numbers: [200] 200,31 unequal: No Solution Exploring Operation: 125-75=50, Resulting Numbers: [50] 50,31 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 #0,2,4 Current State: 31:[95, 105], Operations: ['5*6=30', '75+30=105'] Exploring Operation: 105-95=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 95*105=9975, Resulting Numbers: [9975] 9975,31 unequal: No Solution Exploring Operation: 95+105=200, Resulting Numbers: [200] 200,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 31:[6, 75, 90], Operations: ['95-5=90'] Exploring Operation: 75-6=69, Resulting Numbers: [90, 69] Generated Node #0,3,0: 31:[90, 69] Operation: 75-6=69 Exploring Operation: 90-75=15, Resulting Numbers: [6, 15] Generated Node #0,3,1: 31:[6, 15] Operation: 90-75=15 Exploring Operation: 6+75=81, Resulting Numbers: [90, 81] Generated Node #0,3,2: 31:[90, 81] Operation: 6+75=81 Exploring Operation: 90-6=84, Resulting Numbers: [75, 84] Generated Node #0,3,3: 31:[75, 84] Operation: 90-6=84 Exploring Operation: 90/6=15, Resulting Numbers: [75, 15] Generated Node #0,3,4: 31:[75, 15] Operation: 90/6=15 Moving to Node #0,4,4 Current State: 31:[20, 30], Operations: ['95-75=20', '5*6=30'] Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,31 unequal: No Solution Moving to Node #0,4,1 Current State: 31:[20, 11], Operations: ['95-75=20', '5+6=11'] Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,31 unequal: No Solution Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[95, 5, 6, 75], Operations: [] Exploring Operation: 95-75=20, Resulting Numbers: [5, 6, 20] Generated Node #0,4: 31:[5, 6, 20] Operation: 95-75=20 Moving to Node #0,4 Current State: 31:[5, 6, 20], Operations: ['95-75=20'] Exploring Operation: 5+6=11, Resulting Numbers: [20, 11] Generated Node #0,4,1: 31:[20, 11] Operation: 5+6=11 Moving to Node #0,4,1 Current State: 31:[20, 11], Operations: ['95-75=20', '5+6=11'] Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.939236
hs_5
sum_heuristic
[ 54, 48, 31, 29 ]
54
[ "54-48=6", "31+29=60", "60-6=54" ]
Current State: 54:[54, 48, 31, 29], Operations: [] Exploring Operation: 54-48=6, Resulting Numbers: [31, 29, 6] Generated Node #2: [31, 29, 6] from Operation: 54-48=6 Current State: 54:[31, 29, 6], Operations: ['54-48=6'] Exploring Operation: 31+29=60, Resulting Numbers: [6, 60] Generated Node #3: [6, 60] from Operation: 31+29=60 Current State: 54:[6, 60], Operations: ['54-48=6', '31+29=60'] Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[54, 48, 31, 29], Operations: [] Exploring Operation: 54-48=6, Resulting Numbers: [31, 29, 6] Generated Node #0,0: 54:[31, 29, 6] Operation: 54-48=6 Exploring Operation: 48-31=17, Resulting Numbers: [54, 29, 17] Generated Node #0,1: 54:[54, 29, 17] Operation: 48-31=17 Exploring Operation: 48-29=19, Resulting Numbers: [54, 31, 19] Generated Node #0,2: 54:[54, 31, 19] Operation: 48-29=19 Moving to Node #0,1 Current State: 54:[54, 29, 17], Operations: ['48-31=17'] Exploring Operation: 29-17=12, Resulting Numbers: [54, 12] Generated Node #0,1,0: 54:[54, 12] Operation: 29-17=12 Exploring Operation: 29+17=46, Resulting Numbers: [54, 46] Generated Node #0,1,1: 54:[54, 46] Operation: 29+17=46 Exploring Operation: 54-29=25, Resulting Numbers: [17, 25] Generated Node #0,1,2: 54:[17, 25] Operation: 54-29=25 Moving to Node #0,2 Current State: 54:[54, 31, 19], Operations: ['48-29=19'] Exploring Operation: 31+19=50, Resulting Numbers: [54, 50] Generated Node #0,2,0: 54:[54, 50] Operation: 31+19=50 Exploring Operation: 54-31=23, Resulting Numbers: [19, 23] Generated Node #0,2,1: 54:[19, 23] Operation: 54-31=23 Exploring Operation: 31-19=12, Resulting Numbers: [54, 12] Generated Node #0,2,2: 54:[54, 12] Operation: 31-19=12 Moving to Node #0,0 Current State: 54:[31, 29, 6], Operations: ['54-48=6'] Exploring Operation: 31-6=25, Resulting Numbers: [29, 25] Generated Node #0,0,0: 54:[29, 25] Operation: 31-6=25 Exploring Operation: 31+29=60, Resulting Numbers: [6, 60] Generated Node #0,0,1: 54:[6, 60] Operation: 31+29=60 Exploring Operation: 31-29=2, Resulting Numbers: [6, 2] Generated Node #0,0,2: 54:[6, 2] Operation: 31-29=2 Moving to Node #0,0,2 Current State: 54:[6, 2], Operations: ['54-48=6', '31-29=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[54, 12], Operations: ['48-31=17', '29-17=12'] Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,54 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[17, 25], Operations: ['48-31=17', '54-29=25'] Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,54 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[54, 12], Operations: ['48-29=19', '31-19=12'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,54 unequal: No Solution Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[54, 50], Operations: ['48-29=19', '31+19=50'] Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 54+50=104, Resulting Numbers: [104] 104,54 unequal: No Solution Exploring Operation: 54*50=2700, Resulting Numbers: [2700] 2700,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[29, 25], Operations: ['54-48=6', '31-6=25'] Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,54 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[54, 48, 31, 29], Operations: [] Exploring Operation: 54-48=6, Resulting Numbers: [31, 29, 6] Generated Node #0,0: 54:[31, 29, 6] Operation: 54-48=6 Moving to Node #0,0 Current State: 54:[31, 29, 6], Operations: ['54-48=6'] Exploring Operation: 31-6=25, Resulting Numbers: [29, 25] Generated Node #0,0,0: 54:[29, 25] Operation: 31-6=25 Moving to Node #0,0,0 Current State: 54:[29, 25], Operations: ['54-48=6', '31-6=25'] Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.970486
hs_3
mult_heuristic
[ 38, 29, 8, 93 ]
76
[ "38-29=9", "93-8=85", "85-9=76" ]
Current State: 76:[38, 29, 8, 93], Operations: [] Exploring Operation: 38-29=9, Resulting Numbers: [8, 93, 9] Generated Node #2: [8, 93, 9] from Operation: 38-29=9 Current State: 76:[8, 93, 9], Operations: ['38-29=9'] Exploring Operation: 93-8=85, Resulting Numbers: [9, 85] Generated Node #3: [9, 85] from Operation: 93-8=85 Current State: 76:[9, 85], Operations: ['38-29=9', '93-8=85'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[38, 29, 8, 93], Operations: [] Exploring Operation: 29+8=37, Resulting Numbers: [38, 93, 37] Generated Node #0,0: 76:[38, 93, 37] Operation: 29+8=37 Exploring Operation: 93-29=64, Resulting Numbers: [38, 8, 64] Generated Node #0,1: 76:[38, 8, 64] Operation: 93-29=64 Exploring Operation: 93-8=85, Resulting Numbers: [38, 29, 85] Generated Node #0,2: 76:[38, 29, 85] Operation: 93-8=85 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[38, 8, 64], Operations: ['93-29=64'] Exploring Operation: 64-38=26, Resulting Numbers: [8, 26] Generated Node #0,1,0: 76:[8, 26] Operation: 64-38=26 Exploring Operation: 64/8=8, Resulting Numbers: [38, 8] Generated Node #0,1,1: 76:[38, 8] Operation: 64/8=8 Exploring Operation: 8+64=72, Resulting Numbers: [38, 72] Generated Node #0,1,2: 76:[38, 72] Operation: 8+64=72 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 76:[38, 8], Operations: ['93-29=64', '64/8=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,76 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:[38, 72], Operations: ['93-29=64', '8+64=72'] Exploring Operation: 38+72=110, Resulting Numbers: [110] 110,76 unequal: No Solution Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 38*72=2736, Resulting Numbers: [2736] 2736,76 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:[8, 26], Operations: ['93-29=64', '64-38=26'] Exploring Operation: 8+26=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 8*26=208, Resulting Numbers: [208] 208,76 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 #0,0 Current State: 76:[38, 93, 37], Operations: ['29+8=37'] Exploring Operation: 38-37=1, Resulting Numbers: [93, 1] Generated Node #0,0,0: 76:[93, 1] Operation: 38-37=1 Exploring Operation: 38+37=75, Resulting Numbers: [93, 75] Generated Node #0,0,1: 76:[93, 75] Operation: 38+37=75 Exploring Operation: 93-38=55, Resulting Numbers: [37, 55] Generated Node #0,0,2: 76:[37, 55] Operation: 93-38=55 Moving to Node #0,0,0 Current State: 76:[93, 1], Operations: ['29+8=37', '38-37=1'] Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,76 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[93, 75], Operations: ['29+8=37', '38+37=75'] Exploring Operation: 93+75=168, Resulting Numbers: [168] 168,76 unequal: No Solution Exploring Operation: 93-75=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 93*75=6975, Resulting Numbers: [6975] 6975,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[37, 55], Operations: ['29+8=37', '93-38=55'] Exploring Operation: 37*55=2035, Resulting Numbers: [2035] 2035,76 unequal: No Solution Exploring Operation: 37+55=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 55-37=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:[38, 29, 85], Operations: ['93-8=85'] Exploring Operation: 38-29=9, Resulting Numbers: [85, 9] Generated Node #0,2,0: 76:[85, 9] Operation: 38-29=9 Exploring Operation: 85-38=47, Resulting Numbers: [29, 47] Generated Node #0,2,1: 76:[29, 47] Operation: 85-38=47 Exploring Operation: 38+29=67, Resulting Numbers: [85, 67] Generated Node #0,2,2: 76:[85, 67] Operation: 38+29=67 Moving to Node #0,2,0 Current State: 76:[85, 9], Operations: ['93-8=85', '38-29=9'] Exploring Operation: 85*9=765, Resulting Numbers: [765] 765,76 unequal: No Solution Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[38, 29, 8, 93], Operations: [] Exploring Operation: 93-8=85, Resulting Numbers: [38, 29, 85] Generated Node #0,2: 76:[38, 29, 85] Operation: 93-8=85 Moving to Node #0,2 Current State: 76:[38, 29, 85], Operations: ['93-8=85'] Exploring Operation: 38-29=9, Resulting Numbers: [85, 9] Generated Node #0,2,0: 76:[85, 9] Operation: 38-29=9 Moving to Node #0,2,0 Current State: 76:[85, 9], Operations: ['93-8=85', '38-29=9'] Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 86, 50, 26, 96 ]
57
[ "86+96=182", "182/26=7", "50+7=57" ]
Current State: 57:[86, 50, 26, 96], Operations: [] Exploring Operation: 86+96=182, Resulting Numbers: [50, 26, 182] Generated Node #2: [50, 26, 182] from Operation: 86+96=182 Current State: 57:[50, 26, 182], Operations: ['86+96=182'] Exploring Operation: 182/26=7, Resulting Numbers: [50, 7] Generated Node #3: [50, 7] from Operation: 182/26=7 Current State: 57:[50, 7], Operations: ['86+96=182', '182/26=7'] Exploring Operation: 50+7=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[86, 50, 26, 96], Operations: [] Exploring Operation: 86-26=60, Resulting Numbers: [50, 96, 60] Generated Node #0,0: 57:[50, 96, 60] Operation: 86-26=60 Exploring Operation: 96-86=10, Resulting Numbers: [50, 26, 10] Generated Node #0,1: 57:[50, 26, 10] Operation: 96-86=10 Exploring Operation: 86-50=36, Resulting Numbers: [26, 96, 36] Generated Node #0,2: 57:[26, 96, 36] Operation: 86-50=36 Exploring Operation: 96-26=70, Resulting Numbers: [86, 50, 70] Generated Node #0,3: 57:[86, 50, 70] Operation: 96-26=70 Exploring Operation: 96-50=46, Resulting Numbers: [86, 26, 46] Generated Node #0,4: 57:[86, 26, 46] Operation: 96-50=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[50, 26, 10], Operations: ['96-86=10'] Exploring Operation: 50-26=24, Resulting Numbers: [10, 24] Generated Node #0,1,0: 57:[10, 24] Operation: 50-26=24 Exploring Operation: 26-10=16, Resulting Numbers: [50, 16] Generated Node #0,1,1: 57:[50, 16] Operation: 26-10=16 Exploring Operation: 50/10=5, Resulting Numbers: [26, 5] Generated Node #0,1,2: 57:[26, 5] Operation: 50/10=5 Exploring Operation: 50-10=40, Resulting Numbers: [26, 40] Generated Node #0,1,3: 57:[26, 40] Operation: 50-10=40 Exploring Operation: 50+10=60, Resulting Numbers: [26, 60] Generated Node #0,1,4: 57:[26, 60] Operation: 50+10=60 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 57:[26, 5], Operations: ['96-86=10', '50/10=5'] Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,57 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,57 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,57 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:[50, 16], Operations: ['96-86=10', '26-10=16'] Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 50+16=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 50*16=800, Resulting Numbers: [800] 800,57 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 #0,1,4 Current State: 57:[26, 60], Operations: ['96-86=10', '50+10=60'] Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,57 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 #0,1,0 Current State: 57:[10, 24], Operations: ['96-86=10', '50-26=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,57 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,57 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:[26, 40], Operations: ['96-86=10', '50-10=40'] Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,57 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 #0,4 Current State: 57:[86, 26, 46], Operations: ['96-50=46'] Exploring Operation: 46-26=20, Resulting Numbers: [86, 20] Generated Node #0,4,0: 57:[86, 20] Operation: 46-26=20 Exploring Operation: 26+46=72, Resulting Numbers: [86, 72] Generated Node #0,4,1: 57:[86, 72] Operation: 26+46=72 Exploring Operation: 86-46=40, Resulting Numbers: [26, 40] Generated Node #0,4,2: 57:[26, 40] Operation: 86-46=40 Exploring Operation: 86-26=60, Resulting Numbers: [46, 60] Generated Node #0,4,3: 57:[46, 60] Operation: 86-26=60 Exploring Operation: 86+26=112, Resulting Numbers: [46, 112] Generated Node #0,4,4: 57:[46, 112] Operation: 86+26=112 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 57:[46, 60], Operations: ['96-50=46', '86-26=60'] Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 46+60=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 46*60=2760, Resulting Numbers: [2760] 2760,57 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 #0,4,2 Current State: 57:[26, 40], Operations: ['96-50=46', '86-46=40'] Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 26+40=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,57 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 #0,4,0 Current State: 57:[86, 20], Operations: ['96-50=46', '46-26=20'] Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,57 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,57 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 #0,4,1 Current State: 57:[86, 72], Operations: ['96-50=46', '26+46=72'] Exploring Operation: 86-72=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 86+72=158, Resulting Numbers: [158] 158,57 unequal: No Solution Exploring Operation: 86*72=6192, Resulting Numbers: [6192] 6192,57 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 #0,4,4 Current State: 57:[46, 112], Operations: ['96-50=46', '86+26=112'] Exploring Operation: 112-46=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 46*112=5152, Resulting Numbers: [5152] 5152,57 unequal: No Solution Exploring Operation: 46+112=158, Resulting Numbers: [158] 158,57 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 #0,0 Current State: 57:[50, 96, 60], Operations: ['86-26=60'] Exploring Operation: 96-50=46, Resulting Numbers: [60, 46] Generated Node #0,0,0: 57:[60, 46] Operation: 96-50=46 Exploring Operation: 96-60=36, Resulting Numbers: [50, 36] Generated Node #0,0,1: 57:[50, 36] Operation: 96-60=36 Exploring Operation: 60-50=10, Resulting Numbers: [96, 10] Generated Node #0,0,2: 57:[96, 10] Operation: 60-50=10 Exploring Operation: 50+96=146, Resulting Numbers: [60, 146] Generated Node #0,0,3: 57:[60, 146] Operation: 50+96=146 Exploring Operation: 50+60=110, Resulting Numbers: [96, 110] Generated Node #0,0,4: 57:[96, 110] Operation: 50+60=110 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[60, 46], Operations: ['86-26=60', '96-50=46'] Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 60*46=2760, Resulting Numbers: [2760] 2760,57 unequal: No Solution Exploring Operation: 60+46=106, Resulting Numbers: [106] 106,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[50, 36], Operations: ['86-26=60', '96-60=36'] Exploring Operation: 50*36=1800, Resulting Numbers: [1800] 1800,57 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 50+36=86, Resulting Numbers: [86] 86,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 57:[96, 10], Operations: ['86-26=60', '60-50=10'] Exploring Operation: 96-10=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 96*10=960, Resulting Numbers: [960] 960,57 unequal: No Solution Exploring Operation: 96+10=106, Resulting Numbers: [106] 106,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 57:[60, 146], Operations: ['86-26=60', '50+96=146'] Exploring Operation: 60*146=8760, Resulting Numbers: [8760] 8760,57 unequal: No Solution Exploring Operation: 146-60=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 60+146=206, Resulting Numbers: [206] 206,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 57:[96, 110], Operations: ['86-26=60', '50+60=110'] Exploring Operation: 96+110=206, Resulting Numbers: [206] 206,57 unequal: No Solution Exploring Operation: 110-96=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 96*110=10560, Resulting Numbers: [10560] 10560,57 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:[86, 50, 70], Operations: ['96-26=70'] Exploring Operation: 50+70=120, Resulting Numbers: [86, 120] Generated Node #0,3,0: 57:[86, 120] Operation: 50+70=120 Exploring Operation: 86-70=16, Resulting Numbers: [50, 16] Generated Node #0,3,1: 57:[50, 16] Operation: 86-70=16 Exploring Operation: 70-50=20, Resulting Numbers: [86, 20] Generated Node #0,3,2: 57:[86, 20] Operation: 70-50=20 Exploring Operation: 86-50=36, Resulting Numbers: [70, 36] Generated Node #0,3,3: 57:[70, 36] Operation: 86-50=36 Exploring Operation: 86+50=136, Resulting Numbers: [70, 136] Generated Node #0,3,4: 57:[70, 136] Operation: 86+50=136 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 57:[50, 16], Operations: ['96-26=70', '86-70=16'] Exploring Operation: 50+16=66, Resulting Numbers: [66] 66,57 unequal: No Solution Exploring Operation: 50*16=800, Resulting Numbers: [800] 800,57 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,57 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 #0,3,2 Current State: 57:[86, 20], Operations: ['96-26=70', '70-50=20'] Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,57 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,57 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 #0,3,3 Current State: 57:[70, 36], Operations: ['96-26=70', '86-50=36'] Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,57 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 70*36=2520, Resulting Numbers: [2520] 2520,57 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 #0,3,0 Current State: 57:[86, 120], Operations: ['96-26=70', '50+70=120'] Exploring Operation: 86*120=10320, Resulting Numbers: [10320] 10320,57 unequal: No Solution Exploring Operation: 86+120=206, Resulting Numbers: [206] 206,57 unequal: No Solution Exploring Operation: 120-86=34, Resulting Numbers: [34] 34,57 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 #0,3,4 Current State: 57:[70, 136], Operations: ['96-26=70', '86+50=136'] Exploring Operation: 70+136=206, Resulting Numbers: [206] 206,57 unequal: No Solution Exploring Operation: 70*136=9520, Resulting Numbers: [9520] 9520,57 unequal: No Solution Exploring Operation: 136-70=66, Resulting Numbers: [66] 66,57 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 #0,2 Current State: 57:[26, 96, 36], Operations: ['86-50=36'] Exploring Operation: 96-36=60, Resulting Numbers: [26, 60] Generated Node #0,2,0: 57:[26, 60] Operation: 96-36=60 Exploring Operation: 26+96=122, Resulting Numbers: [36, 122] Generated Node #0,2,1: 57:[36, 122] Operation: 26+96=122 Exploring Operation: 36-26=10, Resulting Numbers: [96, 10] Generated Node #0,2,2: 57:[96, 10] Operation: 36-26=10 Exploring Operation: 26+36=62, Resulting Numbers: [96, 62] Generated Node #0,2,3: 57:[96, 62] Operation: 26+36=62 Exploring Operation: 96-26=70, Resulting Numbers: [36, 70] Generated Node #0,2,4: 57:[36, 70] Operation: 96-26=70 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 57:[26, 60], Operations: ['86-50=36', '96-36=60'] Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,57 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,57 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 #0,2,4 Current State: 57:[36, 70], Operations: ['86-50=36', '96-26=70'] Exploring Operation: 36*70=2520, Resulting Numbers: [2520] 2520,57 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 36+70=106, Resulting Numbers: [106] 106,57 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 #0,2,3 Current State: 57:[96, 62], Operations: ['86-50=36', '26+36=62'] Exploring Operation: 96+62=158, Resulting Numbers: [158] 158,57 unequal: No Solution Exploring Operation: 96-62=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 96*62=5952, Resulting Numbers: [5952] 5952,57 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 #0,2,2 Current State: 57:[96, 10], Operations: ['86-50=36', '36-26=10'] Exploring Operation: 96-10=86, Resulting Numbers: [86] 86,57 unequal: No Solution Exploring Operation: 96*10=960, Resulting Numbers: [960] 960,57 unequal: No Solution Exploring Operation: 96+10=106, Resulting Numbers: [106] 106,57 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 #0,2,1 Current State: 57:[36, 122], Operations: ['86-50=36', '26+96=122'] Exploring Operation: 36+122=158, Resulting Numbers: [158] 158,57 unequal: No Solution Exploring Operation: 36*122=4392, Resulting Numbers: [4392] 4392,57 unequal: No Solution Exploring Operation: 122-36=86, Resulting Numbers: [86] 86,57 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 No solution found.
0
hs_5
sum_heuristic
[ 85, 2, 79, 53 ]
63
[ "85-53=32", "32/2=16", "79-16=63" ]
Current State: 63:[85, 2, 79, 53], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [2, 79, 32] Generated Node #2: [2, 79, 32] from Operation: 85-53=32 Current State: 63:[2, 79, 32], Operations: ['85-53=32'] Exploring Operation: 32/2=16, Resulting Numbers: [79, 16] Generated Node #3: [79, 16] from Operation: 32/2=16 Current State: 63:[79, 16], Operations: ['85-53=32', '32/2=16'] Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[85, 2, 79, 53], Operations: [] Exploring Operation: 85-2=83, Resulting Numbers: [79, 53, 83] Generated Node #0,0: 63:[79, 53, 83] Operation: 85-2=83 Exploring Operation: 85-79=6, Resulting Numbers: [2, 53, 6] Generated Node #0,1: 63:[2, 53, 6] Operation: 85-79=6 Exploring Operation: 85-53=32, Resulting Numbers: [2, 79, 32] Generated Node #0,2: 63:[2, 79, 32] Operation: 85-53=32 Exploring Operation: 79-2=77, Resulting Numbers: [85, 53, 77] Generated Node #0,3: 63:[85, 53, 77] Operation: 79-2=77 Exploring Operation: 79-53=26, Resulting Numbers: [85, 2, 26] Generated Node #0,4: 63:[85, 2, 26] Operation: 79-53=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[2, 53, 6], Operations: ['85-79=6'] Exploring Operation: 6-2=4, Resulting Numbers: [53, 4] Generated Node #0,1,0: 63:[53, 4] Operation: 6-2=4 Exploring Operation: 2+53=55, Resulting Numbers: [6, 55] Generated Node #0,1,1: 63:[6, 55] Operation: 2+53=55 Exploring Operation: 6/2=3, Resulting Numbers: [53, 3] Generated Node #0,1,2: 63:[53, 3] Operation: 6/2=3 Exploring Operation: 53+6=59, Resulting Numbers: [2, 59] Generated Node #0,1,3: 63:[2, 59] Operation: 53+6=59 Exploring Operation: 2+6=8, Resulting Numbers: [53, 8] Generated Node #0,1,4: 63:[53, 8] Operation: 2+6=8 Moving to Node #0,1,3 Current State: 63:[2, 59], Operations: ['85-79=6', '53+6=59'] Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,63 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,63 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[6, 55], Operations: ['85-79=6', '2+53=55'] Exploring Operation: 6+55=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 55-6=49, Resulting Numbers: [49] 49,63 unequal: No Solution Exploring Operation: 6*55=330, Resulting Numbers: [330] 330,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[53, 3], Operations: ['85-79=6', '6/2=3'] Exploring Operation: 53*3=159, Resulting Numbers: [159] 159,63 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,63 unequal: No Solution Exploring Operation: 53+3=56, Resulting Numbers: [56] 56,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[53, 4], Operations: ['85-79=6', '6-2=4'] Exploring Operation: 53*4=212, Resulting Numbers: [212] 212,63 unequal: No Solution Exploring Operation: 53-4=49, Resulting Numbers: [49] 49,63 unequal: No Solution Exploring Operation: 53+4=57, Resulting Numbers: [57] 57,63 unequal: No Solution Moving to Node #0,1,4 Current State: 63:[53, 8], Operations: ['85-79=6', '2+6=8'] Exploring Operation: 53+8=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,63 unequal: No Solution Exploring Operation: 53*8=424, Resulting Numbers: [424] 424,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[2, 79, 32], Operations: ['85-53=32'] Exploring Operation: 32/2=16, Resulting Numbers: [79, 16] Generated Node #0,2,0: 63:[79, 16] Operation: 32/2=16 Exploring Operation: 79-2=77, Resulting Numbers: [32, 77] Generated Node #0,2,1: 63:[32, 77] Operation: 79-2=77 Exploring Operation: 32-2=30, Resulting Numbers: [79, 30] Generated Node #0,2,2: 63:[79, 30] Operation: 32-2=30 Exploring Operation: 79-32=47, Resulting Numbers: [2, 47] Generated Node #0,2,3: 63:[2, 47] Operation: 79-32=47 Exploring Operation: 2*32=64, Resulting Numbers: [79, 64] Generated Node #0,2,4: 63:[79, 64] Operation: 2*32=64 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 63:[2, 47], Operations: ['85-53=32', '79-32=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,63 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,63 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 63:[79, 64], Operations: ['85-53=32', '2*32=64'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,63 unequal: No Solution Exploring Operation: 79+64=143, Resulting Numbers: [143] 143,63 unequal: No Solution Exploring Operation: 79*64=5056, Resulting Numbers: [5056] 5056,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 63:[79, 16], Operations: ['85-53=32', '32/2=16'] Exploring Operation: 79+16=95, Resulting Numbers: [95] 95,63 unequal: No Solution Exploring Operation: 79*16=1264, Resulting Numbers: [1264] 1264,63 unequal: No Solution Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[85, 2, 79, 53], Operations: [] Exploring Operation: 85-53=32, Resulting Numbers: [2, 79, 32] Generated Node #0,2: 63:[2, 79, 32] Operation: 85-53=32 Moving to Node #0,2 Current State: 63:[2, 79, 32], Operations: ['85-53=32'] Exploring Operation: 32/2=16, Resulting Numbers: [79, 16] Generated Node #0,2,0: 63:[79, 16] Operation: 32/2=16 Moving to Node #0,2,0 Current State: 63:[79, 16], Operations: ['85-53=32', '32/2=16'] Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 62, 32, 32, 37 ]
24
[ "62-37=25", "32/32=1", "25-1=24" ]
Current State: 24:[62, 32, 32, 37], Operations: [] Exploring Operation: 62-37=25, Resulting Numbers: [32, 32, 25] Generated Node #2: [32, 32, 25] from Operation: 62-37=25 Current State: 24:[32, 32, 25], Operations: ['62-37=25'] Exploring Operation: 32/32=1, Resulting Numbers: [25, 1] Generated Node #3: [25, 1] from Operation: 32/32=1 Current State: 24:[25, 1], Operations: ['62-37=25', '32/32=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[62, 32, 32, 37], Operations: [] Exploring Operation: 62-37=25, Resulting Numbers: [32, 32, 25] Generated Node #0,0: 24:[32, 32, 25] Operation: 62-37=25 Exploring Operation: 62-32=30, Resulting Numbers: [32, 37, 30] Generated Node #0,1: 24:[32, 37, 30] Operation: 62-32=30 Exploring Operation: 62-32=30, Resulting Numbers: [32, 37, 30] Generated Node #0,2: 24:[32, 37, 30] Operation: 62-32=30 Moving to Node #0,0 Current State: 24:[32, 32, 25], Operations: ['62-37=25'] Exploring Operation: 32-25=7, Resulting Numbers: [32, 7] Generated Node #0,0,0: 24:[32, 7] Operation: 32-25=7 Exploring Operation: 32-32=0, Resulting Numbers: [25, 0] Generated Node #0,0,1: 24:[25, 0] Operation: 32-32=0 Exploring Operation: 32/32=1, Resulting Numbers: [25, 1] Generated Node #0,0,2: 24:[25, 1] Operation: 32/32=1 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[25, 1], Operations: ['62-37=25', '32/32=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[62, 32, 32, 37], Operations: [] Exploring Operation: 62-37=25, Resulting Numbers: [32, 32, 25] Generated Node #0,0: 24:[32, 32, 25] Operation: 62-37=25 Moving to Node #0,0 Current State: 24:[32, 32, 25], Operations: ['62-37=25'] Exploring Operation: 32/32=1, Resulting Numbers: [25, 1] Generated Node #0,0,2: 24:[25, 1] Operation: 32/32=1 Moving to Node #0,0,2 Current State: 24:[25, 1], Operations: ['62-37=25', '32/32=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 49, 72, 53, 51 ]
25
[ "72-49=23", "53-51=2", "23+2=25" ]
Current State: 25:[49, 72, 53, 51], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [53, 51, 23] Generated Node #2: [53, 51, 23] from Operation: 72-49=23 Current State: 25:[53, 51, 23], Operations: ['72-49=23'] Exploring Operation: 53-51=2, Resulting Numbers: [23, 2] Generated Node #3: [23, 2] from Operation: 53-51=2 Current State: 25:[23, 2], Operations: ['72-49=23', '53-51=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[49, 72, 53, 51], Operations: [] Exploring Operation: 53-49=4, Resulting Numbers: [72, 51, 4] Generated Node #0,0: 25:[72, 51, 4] Operation: 53-49=4 Exploring Operation: 72-53=19, Resulting Numbers: [49, 51, 19] Generated Node #0,1: 25:[49, 51, 19] Operation: 72-53=19 Exploring Operation: 72-51=21, Resulting Numbers: [49, 53, 21] Generated Node #0,2: 25:[49, 53, 21] Operation: 72-51=21 Exploring Operation: 72-49=23, Resulting Numbers: [53, 51, 23] Generated Node #0,3: 25:[53, 51, 23] Operation: 72-49=23 Moving to Node #0,1 Current State: 25:[49, 51, 19], Operations: ['72-53=19'] Exploring Operation: 49+19=68, Resulting Numbers: [51, 68] Generated Node #0,1,0: 25:[51, 68] Operation: 49+19=68 Exploring Operation: 51-49=2, Resulting Numbers: [19, 2] Generated Node #0,1,1: 25:[19, 2] Operation: 51-49=2 Exploring Operation: 51-19=32, Resulting Numbers: [49, 32] Generated Node #0,1,2: 25:[49, 32] Operation: 51-19=32 Exploring Operation: 49-19=30, Resulting Numbers: [51, 30] Generated Node #0,1,3: 25:[51, 30] Operation: 49-19=30 Moving to Node #0,3 Current State: 25:[53, 51, 23], Operations: ['72-49=23'] Exploring Operation: 53-23=30, Resulting Numbers: [51, 30] Generated Node #0,3,0: 25:[51, 30] Operation: 53-23=30 Exploring Operation: 53+23=76, Resulting Numbers: [51, 76] Generated Node #0,3,1: 25:[51, 76] Operation: 53+23=76 Exploring Operation: 53-51=2, Resulting Numbers: [23, 2] Generated Node #0,3,2: 25:[23, 2] Operation: 53-51=2 Exploring Operation: 51-23=28, Resulting Numbers: [53, 28] Generated Node #0,3,3: 25:[53, 28] Operation: 51-23=28 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 25:[23, 2], Operations: ['72-49=23', '53-51=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[49, 72, 53, 51], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [53, 51, 23] Generated Node #0,3: 25:[53, 51, 23] Operation: 72-49=23 Moving to Node #0,3 Current State: 25:[53, 51, 23], Operations: ['72-49=23'] Exploring Operation: 53-51=2, Resulting Numbers: [23, 2] Generated Node #0,3,2: 25:[23, 2] Operation: 53-51=2 Moving to Node #0,3,2 Current State: 25:[23, 2], Operations: ['72-49=23', '53-51=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 64, 6, 98, 6 ]
98
[ "6-6=0", "64*0=0", "98+0=98" ]
Current State: 98:[64, 6, 98, 6], Operations: [] Exploring Operation: 6-6=0, Resulting Numbers: [64, 98, 0] Generated Node #2: [64, 98, 0] from Operation: 6-6=0 Current State: 98:[64, 98, 0], Operations: ['6-6=0'] Exploring Operation: 64*0=0, Resulting Numbers: [98, 0] Generated Node #3: [98, 0] from Operation: 64*0=0 Current State: 98:[98, 0], Operations: ['6-6=0', '64*0=0'] Exploring Operation: 98+0=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[64, 6, 98, 6], Operations: [] Exploring Operation: 64-6=58, Resulting Numbers: [98, 6, 58] Generated Node #0,0: 98:[98, 6, 58] Operation: 64-6=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[98, 6, 58], Operations: ['64-6=58'] Exploring Operation: 58-6=52, Resulting Numbers: [98, 52] Generated Node #0,0,0: 98:[98, 52] Operation: 58-6=52 Moving to Node #0,0,0 Current State: 98:[98, 52], Operations: ['64-6=58', '58-6=52'] Exploring Operation: 98-52=46, Resulting Numbers: [46] 46,98 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
[ 22, 56, 4, 66 ]
20
[ "66/22=3", "56+4=60", "60/3=20" ]
Current State: 20:[22, 56, 4, 66], Operations: [] Exploring Operation: 66/22=3, Resulting Numbers: [56, 4, 3] Generated Node #2: [56, 4, 3] from Operation: 66/22=3 Current State: 20:[56, 4, 3], Operations: ['66/22=3'] Exploring Operation: 56+4=60, Resulting Numbers: [3, 60] Generated Node #3: [3, 60] from Operation: 56+4=60 Current State: 20:[3, 60], Operations: ['66/22=3', '56+4=60'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[22, 56, 4, 66], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [22, 4, 10] Generated Node #0,0: 20:[22, 4, 10] Operation: 66-56=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[22, 4, 10], Operations: ['66-56=10'] Exploring Operation: 22-4=18, Resulting Numbers: [10, 18] Generated Node #0,0,0: 20:[10, 18] Operation: 22-4=18 Moving to Node #0,0,0 Current State: 20:[10, 18], Operations: ['66-56=10', '22-4=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,20 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
[ 90, 16, 91, 55 ]
39
[ "91-90=1", "55-16=39", "1*39=39" ]
Current State: 39:[90, 16, 91, 55], Operations: [] Exploring Operation: 91-90=1, Resulting Numbers: [16, 55, 1] Generated Node #2: [16, 55, 1] from Operation: 91-90=1 Current State: 39:[16, 55, 1], Operations: ['91-90=1'] Exploring Operation: 55-16=39, Resulting Numbers: [1, 39] Generated Node #3: [1, 39] from Operation: 55-16=39 Current State: 39:[1, 39], Operations: ['91-90=1', '55-16=39'] Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[90, 16, 91, 55], Operations: [] Exploring Operation: 91-90=1, Resulting Numbers: [16, 55, 1] Generated Node #0,0: 39:[16, 55, 1] Operation: 91-90=1 Exploring Operation: 91-55=36, Resulting Numbers: [90, 16, 36] Generated Node #0,1: 39:[90, 16, 36] Operation: 91-55=36 Moving to Node #0,0 Current State: 39:[16, 55, 1], Operations: ['91-90=1'] Exploring Operation: 16-1=15, Resulting Numbers: [55, 15] Generated Node #0,0,0: 39:[55, 15] Operation: 16-1=15 Exploring Operation: 55-16=39, Resulting Numbers: [1, 39] Generated Node #0,0,1: 39:[1, 39] Operation: 55-16=39 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[1, 39], Operations: ['91-90=1', '55-16=39'] Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[90, 16, 91, 55], Operations: [] Exploring Operation: 91-90=1, Resulting Numbers: [16, 55, 1] Generated Node #0,0: 39:[16, 55, 1] Operation: 91-90=1 Moving to Node #0,0 Current State: 39:[16, 55, 1], Operations: ['91-90=1'] Exploring Operation: 55-16=39, Resulting Numbers: [1, 39] Generated Node #0,0,1: 39:[1, 39] Operation: 55-16=39 Moving to Node #0,0,1 Current State: 39:[1, 39], Operations: ['91-90=1', '55-16=39'] Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 38, 72, 5, 52 ]
66
[ "38*5=190", "72+52=124", "190-124=66" ]
Current State: 66:[38, 72, 5, 52], Operations: [] Exploring Operation: 38*5=190, Resulting Numbers: [72, 52, 190] Generated Node #2: [72, 52, 190] from Operation: 38*5=190 Current State: 66:[72, 52, 190], Operations: ['38*5=190'] Exploring Operation: 72+52=124, Resulting Numbers: [190, 124] Generated Node #3: [190, 124] from Operation: 72+52=124 Current State: 66:[190, 124], Operations: ['38*5=190', '72+52=124'] Exploring Operation: 190-124=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[38, 72, 5, 52], Operations: [] Exploring Operation: 72-38=34, Resulting Numbers: [5, 52, 34] Generated Node #0,0: 66:[5, 52, 34] Operation: 72-38=34 Exploring Operation: 52-38=14, Resulting Numbers: [72, 5, 14] Generated Node #0,1: 66:[72, 5, 14] Operation: 52-38=14 Exploring Operation: 72-52=20, Resulting Numbers: [38, 5, 20] Generated Node #0,2: 66:[38, 5, 20] Operation: 72-52=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 66:[38, 5, 20], Operations: ['72-52=20'] Exploring Operation: 20/5=4, Resulting Numbers: [38, 4] Generated Node #0,2,0: 66:[38, 4] Operation: 20/5=4 Exploring Operation: 38-5=33, Resulting Numbers: [20, 33] Generated Node #0,2,1: 66:[20, 33] Operation: 38-5=33 Exploring Operation: 38-20=18, Resulting Numbers: [5, 18] Generated Node #0,2,2: 66:[5, 18] Operation: 38-20=18 Moving to Node #0,2,1 Current State: 66:[20, 33], Operations: ['72-52=20', '38-5=33'] Exploring Operation: 20*33=660, Resulting Numbers: [660] 660,66 unequal: No Solution Exploring Operation: 20+33=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,66 unequal: No Solution Moving to Node #0,2,2 Current State: 66:[5, 18], Operations: ['72-52=20', '38-20=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,66 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,66 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,66 unequal: No Solution Moving to Node #0,2,0 Current State: 66:[38, 4], Operations: ['72-52=20', '20/5=4'] Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,66 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,66 unequal: No Solution Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[72, 5, 14], Operations: ['52-38=14'] Exploring Operation: 72-5=67, Resulting Numbers: [14, 67] Generated Node #0,1,0: 66:[14, 67] Operation: 72-5=67 Exploring Operation: 14-5=9, Resulting Numbers: [72, 9] Generated Node #0,1,1: 66:[72, 9] Operation: 14-5=9 Exploring Operation: 72-14=58, Resulting Numbers: [5, 58] Generated Node #0,1,2: 66:[5, 58] Operation: 72-14=58 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 66:[14, 67], Operations: ['52-38=14', '72-5=67'] Exploring Operation: 14*67=938, Resulting Numbers: [938] 938,66 unequal: No Solution Exploring Operation: 67-14=53, Resulting Numbers: [53] 53,66 unequal: No Solution Exploring Operation: 14+67=81, Resulting Numbers: [81] 81,66 unequal: No Solution No 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: 66:[72, 9], Operations: ['52-38=14', '14-5=9'] Exploring Operation: 72/9=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 72-9=63, Resulting Numbers: [63] 63,66 unequal: No Solution Exploring Operation: 72+9=81, Resulting Numbers: [81] 81,66 unequal: No Solution No 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: 66:[5, 58], Operations: ['52-38=14', '72-14=58'] Exploring Operation: 5*58=290, Resulting Numbers: [290] 290,66 unequal: No Solution Exploring Operation: 5+58=63, Resulting Numbers: [63] 63,66 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,66 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: 66:[5, 52, 34], Operations: ['72-38=34'] Exploring Operation: 52-5=47, Resulting Numbers: [34, 47] Generated Node #0,0,0: 66:[34, 47] Operation: 52-5=47 Exploring Operation: 5+52=57, Resulting Numbers: [34, 57] Generated Node #0,0,1: 66:[34, 57] Operation: 5+52=57 Exploring Operation: 52-34=18, Resulting Numbers: [5, 18] Generated Node #0,0,2: 66:[5, 18] Operation: 52-34=18 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 66:[5, 18], Operations: ['72-38=34', '52-34=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,66 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,66 unequal: No Solution No 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: 66:[34, 57], Operations: ['72-38=34', '5+52=57'] Exploring Operation: 34*57=1938, Resulting Numbers: [1938] 1938,66 unequal: No Solution Exploring Operation: 57-34=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 34+57=91, Resulting Numbers: [91] 91,66 unequal: No Solution No 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: 66:[34, 47], Operations: ['72-38=34', '52-5=47'] Exploring Operation: 34*47=1598, Resulting Numbers: [1598] 1598,66 unequal: No Solution Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,66 unequal: No Solution Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,66 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
[ 20, 37, 80, 60 ]
93
[ "80/20=4", "37+60=97", "97-4=93" ]
Current State: 93:[20, 37, 80, 60], Operations: [] Exploring Operation: 80/20=4, Resulting Numbers: [37, 60, 4] Generated Node #2: [37, 60, 4] from Operation: 80/20=4 Current State: 93:[37, 60, 4], Operations: ['80/20=4'] Exploring Operation: 37+60=97, Resulting Numbers: [4, 97] Generated Node #3: [4, 97] from Operation: 37+60=97 Current State: 93:[4, 97], Operations: ['80/20=4', '37+60=97'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[20, 37, 80, 60], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [37, 80, 3] Generated Node #0,0: 93:[37, 80, 3] Operation: 60/20=3 Exploring Operation: 60-20=40, Resulting Numbers: [37, 80, 40] Generated Node #0,1: 93:[37, 80, 40] Operation: 60-20=40 Exploring Operation: 37+60=97, Resulting Numbers: [20, 80, 97] Generated Node #0,2: 93:[20, 80, 97] Operation: 37+60=97 Moving to Node #0,0 Current State: 93:[37, 80, 3], Operations: ['60/20=3'] Exploring Operation: 80+3=83, Resulting Numbers: [37, 83] Generated Node #0,0,0: 93:[37, 83] Operation: 80+3=83 Exploring Operation: 37-3=34, Resulting Numbers: [80, 34] Generated Node #0,0,1: 93:[80, 34] Operation: 37-3=34 Exploring Operation: 80-37=43, Resulting Numbers: [3, 43] Generated Node #0,0,2: 93:[3, 43] Operation: 80-37=43 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 93:[3, 43], Operations: ['60/20=3', '80-37=43'] Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,93 unequal: No Solution Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,93 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[37, 83], Operations: ['60/20=3', '80+3=83'] Exploring Operation: 37*83=3071, Resulting Numbers: [3071] 3071,93 unequal: No Solution Exploring Operation: 83-37=46, Resulting Numbers: [46] 46,93 unequal: No Solution Exploring Operation: 37+83=120, Resulting Numbers: [120] 120,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[80, 34], Operations: ['60/20=3', '37-3=34'] Exploring Operation: 80+34=114, Resulting Numbers: [114] 114,93 unequal: No Solution Exploring Operation: 80-34=46, Resulting Numbers: [46] 46,93 unequal: No Solution Exploring Operation: 80*34=2720, Resulting Numbers: [2720] 2720,93 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: 93:[37, 80, 40], Operations: ['60-20=40'] Exploring Operation: 40-37=3, Resulting Numbers: [80, 3] Generated Node #0,1,0: 93:[80, 3] Operation: 40-37=3 Exploring Operation: 80-40=40, Resulting Numbers: [37, 40] Generated Node #0,1,1: 93:[37, 40] Operation: 80-40=40 Exploring Operation: 80/40=2, Resulting Numbers: [37, 2] Generated Node #0,1,2: 93:[37, 2] Operation: 80/40=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 93:[37, 2], Operations: ['60-20=40', '80/40=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,93 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,93 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 93:[80, 3], Operations: ['60-20=40', '40-37=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,93 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,93 unequal: No Solution Exploring Operation: 80*3=240, Resulting Numbers: [240] 240,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[37, 40], Operations: ['60-20=40', '80-40=40'] Exploring Operation: 37+40=77, Resulting Numbers: [77] 77,93 unequal: No Solution Exploring Operation: 37*40=1480, Resulting Numbers: [1480] 1480,93 unequal: No Solution Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,93 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: 93:[20, 80, 97], Operations: ['37+60=97'] Exploring Operation: 97-80=17, Resulting Numbers: [20, 17] Generated Node #0,2,0: 93:[20, 17] Operation: 97-80=17 Exploring Operation: 80/20=4, Resulting Numbers: [97, 4] Generated Node #0,2,1: 93:[97, 4] Operation: 80/20=4 Exploring Operation: 20+80=100, Resulting Numbers: [97, 100] Generated Node #0,2,2: 93:[97, 100] Operation: 20+80=100 Moving to Node #0,2,1 Current State: 93:[97, 4], Operations: ['37+60=97', '80/20=4'] Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,93 unequal: No Solution Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[20, 37, 80, 60], Operations: [] Exploring Operation: 37+60=97, Resulting Numbers: [20, 80, 97] Generated Node #0,2: 93:[20, 80, 97] Operation: 37+60=97 Moving to Node #0,2 Current State: 93:[20, 80, 97], Operations: ['37+60=97'] Exploring Operation: 80/20=4, Resulting Numbers: [97, 4] Generated Node #0,2,1: 93:[97, 4] Operation: 80/20=4 Moving to Node #0,2,1 Current State: 93:[97, 4], Operations: ['37+60=97', '80/20=4'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.96875
hs_3
sum_heuristic
[ 17, 13, 58, 55 ]
83
[ "17+13=30", "58+55=113", "113-30=83" ]
Current State: 83:[17, 13, 58, 55], Operations: [] Exploring Operation: 17+13=30, Resulting Numbers: [58, 55, 30] Generated Node #2: [58, 55, 30] from Operation: 17+13=30 Current State: 83:[58, 55, 30], Operations: ['17+13=30'] Exploring Operation: 58+55=113, Resulting Numbers: [30, 113] Generated Node #3: [30, 113] from Operation: 58+55=113 Current State: 83:[30, 113], Operations: ['17+13=30', '58+55=113'] Exploring Operation: 113-30=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[17, 13, 58, 55], Operations: [] Exploring Operation: 17+13=30, Resulting Numbers: [58, 55, 30] Generated Node #0,0: 83:[58, 55, 30] Operation: 17+13=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[58, 55, 30], Operations: ['17+13=30'] Exploring Operation: 55+30=85, Resulting Numbers: [58, 85] Generated Node #0,0,0: 83:[58, 85] Operation: 55+30=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[58, 85], Operations: ['17+13=30', '55+30=85'] Exploring Operation: 85-58=27, Resulting Numbers: [27] 27,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 45, 20, 50, 41 ]
25
[ "50-41=9", "45/9=5", "20+5=25" ]
Current State: 25:[45, 20, 50, 41], Operations: [] Exploring Operation: 50-41=9, Resulting Numbers: [45, 20, 9] Generated Node #2: [45, 20, 9] from Operation: 50-41=9 Current State: 25:[45, 20, 9], Operations: ['50-41=9'] Exploring Operation: 45/9=5, Resulting Numbers: [20, 5] Generated Node #3: [20, 5] from Operation: 45/9=5 Current State: 25:[20, 5], Operations: ['50-41=9', '45/9=5'] Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[45, 20, 50, 41], Operations: [] Exploring Operation: 50-45=5, Resulting Numbers: [20, 41, 5] Generated Node #0,0: 25:[20, 41, 5] Operation: 50-45=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[20, 41, 5], Operations: ['50-45=5'] Exploring Operation: 41-20=21, Resulting Numbers: [5, 21] Generated Node #0,0,0: 25:[5, 21] Operation: 41-20=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[5, 21], Operations: ['50-45=5', '41-20=21'] Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 26, 84, 88, 49 ]
79
[ "84-26=58", "88+49=137", "137-58=79" ]
Current State: 79:[26, 84, 88, 49], Operations: [] Exploring Operation: 84-26=58, Resulting Numbers: [88, 49, 58] Generated Node #2: [88, 49, 58] from Operation: 84-26=58 Current State: 79:[88, 49, 58], Operations: ['84-26=58'] Exploring Operation: 88+49=137, Resulting Numbers: [58, 137] Generated Node #3: [58, 137] from Operation: 88+49=137 Current State: 79:[58, 137], Operations: ['84-26=58', '88+49=137'] Exploring Operation: 137-58=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[26, 84, 88, 49], Operations: [] Exploring Operation: 88-26=62, Resulting Numbers: [84, 49, 62] Generated Node #0,0: 79:[84, 49, 62] Operation: 88-26=62 Exploring Operation: 26+49=75, Resulting Numbers: [84, 88, 75] Generated Node #0,1: 79:[84, 88, 75] Operation: 26+49=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[84, 88, 75], Operations: ['26+49=75'] Exploring Operation: 88-84=4, Resulting Numbers: [75, 4] Generated Node #0,1,0: 79:[75, 4] Operation: 88-84=4 Exploring Operation: 88-75=13, Resulting Numbers: [84, 13] Generated Node #0,1,1: 79:[84, 13] Operation: 88-75=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 79:[84, 13], Operations: ['26+49=75', '88-75=13'] Exploring Operation: 84-13=71, Resulting Numbers: [71] 71,79 unequal: No Solution Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,79 unequal: No Solution No 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: 79:[75, 4], Operations: ['26+49=75', '88-84=4'] Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,79 unequal: No Solution Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[26, 84, 88, 49], Operations: [] Exploring Operation: 26+49=75, Resulting Numbers: [84, 88, 75] Generated Node #0,1: 79:[84, 88, 75] Operation: 26+49=75 Moving to Node #0,1 Current State: 79:[84, 88, 75], Operations: ['26+49=75'] Exploring Operation: 88-84=4, Resulting Numbers: [75, 4] Generated Node #0,1,0: 79:[75, 4] Operation: 88-84=4 Moving to Node #0,1,0 Current State: 79:[75, 4], Operations: ['26+49=75', '88-84=4'] Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 68, 34, 72, 68 ]
34
[ "68-68=0", "72*0=0", "34+0=34" ]
Current State: 34:[68, 34, 72, 68], Operations: [] Exploring Operation: 68-68=0, Resulting Numbers: [34, 72, 0] Generated Node #2: [34, 72, 0] from Operation: 68-68=0 Current State: 34:[34, 72, 0], Operations: ['68-68=0'] Exploring Operation: 72*0=0, Resulting Numbers: [34, 0] Generated Node #3: [34, 0] from Operation: 72*0=0 Current State: 34:[34, 0], Operations: ['68-68=0', '72*0=0'] Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[68, 34, 72, 68], Operations: [] Exploring Operation: 68-68=0, Resulting Numbers: [34, 72, 0] Generated Node #0,0: 34:[34, 72, 0] Operation: 68-68=0 Exploring Operation: 68/68=1, Resulting Numbers: [34, 72, 1] Generated Node #0,1: 34:[34, 72, 1] Operation: 68/68=1 Exploring Operation: 72-68=4, Resulting Numbers: [68, 34, 4] Generated Node #0,2: 34:[68, 34, 4] Operation: 72-68=4 Exploring Operation: 72-68=4, Resulting Numbers: [34, 68, 4] Generated Node #0,3: 34:[34, 68, 4] Operation: 72-68=4 Exploring Operation: 68-34=34, Resulting Numbers: [72, 68, 34] Generated Node #0,4: 34:[72, 68, 34] Operation: 68-34=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[68, 34, 4], Operations: ['72-68=4'] Exploring Operation: 68/34=2, Resulting Numbers: [4, 2] Generated Node #0,2,0: 34:[4, 2] Operation: 68/34=2 Exploring Operation: 68/4=17, Resulting Numbers: [34, 17] Generated Node #0,2,1: 34:[34, 17] Operation: 68/4=17 Exploring Operation: 68+4=72, Resulting Numbers: [34, 72] Generated Node #0,2,2: 34:[34, 72] Operation: 68+4=72 Exploring Operation: 68-4=64, Resulting Numbers: [34, 64] Generated Node #0,2,3: 34:[34, 64] Operation: 68-4=64 Exploring Operation: 68-34=34, Resulting Numbers: [4, 34] Generated Node #0,2,4: 34:[4, 34] Operation: 68-34=34 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 34:[34, 17], Operations: ['72-68=4', '68/4=17'] Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,34 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,34 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 34:[4, 2], Operations: ['72-68=4', '68/34=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 34:[4, 34], Operations: ['72-68=4', '68-34=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 34:[34, 64], Operations: ['72-68=4', '68-4=64'] Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 34+64=98, Resulting Numbers: [98] 98,34 unequal: No Solution Exploring Operation: 34*64=2176, Resulting Numbers: [2176] 2176,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 34:[34, 72], Operations: ['72-68=4', '68+4=72'] Exploring Operation: 72-34=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 34*72=2448, Resulting Numbers: [2448] 2448,34 unequal: No Solution Exploring Operation: 34+72=106, Resulting Numbers: [106] 106,34 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: 34:[34, 68, 4], Operations: ['72-68=4'] Exploring Operation: 68/4=17, Resulting Numbers: [34, 17] Generated Node #0,3,0: 34:[34, 17] Operation: 68/4=17 Exploring Operation: 34+4=38, Resulting Numbers: [68, 38] Generated Node #0,3,1: 34:[68, 38] Operation: 34+4=38 Exploring Operation: 68-4=64, Resulting Numbers: [34, 64] Generated Node #0,3,2: 34:[34, 64] Operation: 68-4=64 Exploring Operation: 68-34=34, Resulting Numbers: [4, 34] Generated Node #0,3,3: 34:[4, 34] Operation: 68-34=34 Exploring Operation: 68/34=2, Resulting Numbers: [4, 2] Generated Node #0,3,4: 34:[4, 2] Operation: 68/34=2 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 34:[34, 17], Operations: ['72-68=4', '68/4=17'] Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,34 unequal: No Solution Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,34 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 34:[4, 34], Operations: ['72-68=4', '68-34=34'] Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,34 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 34:[4, 2], Operations: ['72-68=4', '68/34=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,34 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 34:[34, 64], Operations: ['72-68=4', '68-4=64'] Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,34 unequal: No Solution Exploring Operation: 34*64=2176, Resulting Numbers: [2176] 2176,34 unequal: No Solution Exploring Operation: 34+64=98, Resulting Numbers: [98] 98,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 34:[68, 38], Operations: ['72-68=4', '34+4=38'] Exploring Operation: 68*38=2584, Resulting Numbers: [2584] 2584,34 unequal: No Solution Exploring Operation: 68+38=106, Resulting Numbers: [106] 106,34 unequal: No Solution Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,34 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: 34:[34, 72, 1], Operations: ['68/68=1'] Exploring Operation: 72*1=72, Resulting Numbers: [34, 72] Generated Node #0,1,0: 34:[34, 72] Operation: 72*1=72 Exploring Operation: 72-1=71, Resulting Numbers: [34, 71] Generated Node #0,1,1: 34:[34, 71] Operation: 72-1=71 Exploring Operation: 34*1=34, Resulting Numbers: [72, 34] Generated Node #0,1,2: 34:[72, 34] Operation: 34*1=34 Exploring Operation: 72-34=38, Resulting Numbers: [1, 38] Generated Node #0,1,3: 34:[1, 38] Operation: 72-34=38 Exploring Operation: 34/1=34, Resulting Numbers: [72, 34] Generated Node #0,1,4: 34:[72, 34] Operation: 34/1=34 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 34:[1, 38], Operations: ['68/68=1', '72-34=38'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,34 unequal: No Solution Exploring Operation: 1*38=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[34, 71], Operations: ['68/68=1', '72-1=71'] Exploring Operation: 34+71=105, Resulting Numbers: [105] 105,34 unequal: No Solution Exploring Operation: 34*71=2414, Resulting Numbers: [2414] 2414,34 unequal: No Solution Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[34, 72], Operations: ['68/68=1', '72*1=72'] Exploring Operation: 34*72=2448, Resulting Numbers: [2448] 2448,34 unequal: No Solution Exploring Operation: 34+72=106, Resulting Numbers: [106] 106,34 unequal: No Solution Exploring Operation: 72-34=38, Resulting Numbers: [38] 38,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 34:[72, 34], Operations: ['68/68=1', '34*1=34'] Exploring Operation: 72+34=106, Resulting Numbers: [106] 106,34 unequal: No Solution Exploring Operation: 72-34=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 72*34=2448, Resulting Numbers: [2448] 2448,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 34:[72, 34], Operations: ['68/68=1', '34/1=34'] Exploring Operation: 72*34=2448, Resulting Numbers: [2448] 2448,34 unequal: No Solution Exploring Operation: 72-34=38, Resulting Numbers: [38] 38,34 unequal: No Solution Exploring Operation: 72+34=106, Resulting Numbers: [106] 106,34 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: 34:[34, 72, 0], Operations: ['68-68=0'] Exploring Operation: 72*0=0, Resulting Numbers: [34, 0] Generated Node #0,0,0: 34:[34, 0] Operation: 72*0=0 Exploring Operation: 34-0=34, Resulting Numbers: [72, 34] Generated Node #0,0,1: 34:[72, 34] Operation: 34-0=34 Exploring Operation: 34+0=34, Resulting Numbers: [72, 34] Generated Node #0,0,2: 34:[72, 34] Operation: 34+0=34 Exploring Operation: 72-34=38, Resulting Numbers: [0, 38] Generated Node #0,0,3: 34:[0, 38] Operation: 72-34=38 Exploring Operation: 72+0=72, Resulting Numbers: [34, 72] Generated Node #0,0,4: 34:[34, 72] Operation: 72+0=72 Moving to Node #0,0,0 Current State: 34:[34, 0], Operations: ['68-68=0', '72*0=0'] Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[68, 34, 72, 68], Operations: [] Exploring Operation: 68-68=0, Resulting Numbers: [34, 72, 0] Generated Node #0,0: 34:[34, 72, 0] Operation: 68-68=0 Moving to Node #0,0 Current State: 34:[34, 72, 0], Operations: ['68-68=0'] Exploring Operation: 72*0=0, Resulting Numbers: [34, 0] Generated Node #0,0,0: 34:[34, 0] Operation: 72*0=0 Moving to Node #0,0,0 Current State: 34:[34, 0], Operations: ['68-68=0', '72*0=0'] Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.930556
hs_5
mult_heuristic
[ 7, 98, 61, 24 ]
99
[ "98/7=14", "61+24=85", "14+85=99" ]
Current State: 99:[7, 98, 61, 24], Operations: [] Exploring Operation: 98/7=14, Resulting Numbers: [61, 24, 14] Generated Node #2: [61, 24, 14] from Operation: 98/7=14 Current State: 99:[61, 24, 14], Operations: ['98/7=14'] Exploring Operation: 61+24=85, Resulting Numbers: [14, 85] Generated Node #3: [14, 85] from Operation: 61+24=85 Current State: 99:[14, 85], Operations: ['98/7=14', '61+24=85'] Exploring Operation: 14+85=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[7, 98, 61, 24], Operations: [] Exploring Operation: 61-7=54, Resulting Numbers: [98, 24, 54] Generated Node #0,0: 99:[98, 24, 54] Operation: 61-7=54 Exploring Operation: 61+24=85, Resulting Numbers: [7, 98, 85] Generated Node #0,1: 99:[7, 98, 85] Operation: 61+24=85 Exploring Operation: 98-61=37, Resulting Numbers: [7, 24, 37] Generated Node #0,2: 99:[7, 24, 37] Operation: 98-61=37 Exploring Operation: 7+24=31, Resulting Numbers: [98, 61, 31] Generated Node #0,3: 99:[98, 61, 31] Operation: 7+24=31 Exploring Operation: 61-24=37, Resulting Numbers: [7, 98, 37] Generated Node #0,4: 99:[7, 98, 37] Operation: 61-24=37 Moving to Node #0,4 Current State: 99:[7, 98, 37], Operations: ['61-24=37'] Exploring Operation: 7+98=105, Resulting Numbers: [37, 105] Generated Node #0,4,0: 99:[37, 105] Operation: 7+98=105 Exploring Operation: 98-7=91, Resulting Numbers: [37, 91] Generated Node #0,4,1: 99:[37, 91] Operation: 98-7=91 Exploring Operation: 7+37=44, Resulting Numbers: [98, 44] Generated Node #0,4,2: 99:[98, 44] Operation: 7+37=44 Exploring Operation: 37-7=30, Resulting Numbers: [98, 30] Generated Node #0,4,3: 99:[98, 30] Operation: 37-7=30 Exploring Operation: 98/7=14, Resulting Numbers: [37, 14] Generated Node #0,4,4: 99:[37, 14] Operation: 98/7=14 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 99:[98, 30], Operations: ['61-24=37', '37-7=30'] Exploring Operation: 98*30=2940, Resulting Numbers: [2940] 2940,99 unequal: No Solution Exploring Operation: 98-30=68, Resulting Numbers: [68] 68,99 unequal: No Solution Exploring Operation: 98+30=128, Resulting Numbers: [128] 128,99 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 #0,4,4 Current State: 99:[37, 14], Operations: ['61-24=37', '98/7=14'] Exploring Operation: 37*14=518, Resulting Numbers: [518] 518,99 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,99 unequal: No Solution Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,99 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 #0,4,0 Current State: 99:[37, 105], Operations: ['61-24=37', '7+98=105'] Exploring Operation: 37*105=3885, Resulting Numbers: [3885] 3885,99 unequal: No Solution Exploring Operation: 105-37=68, Resulting Numbers: [68] 68,99 unequal: No Solution Exploring Operation: 37+105=142, Resulting Numbers: [142] 142,99 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 #0,4,1 Current State: 99:[37, 91], Operations: ['61-24=37', '98-7=91'] Exploring Operation: 37*91=3367, Resulting Numbers: [3367] 3367,99 unequal: No Solution Exploring Operation: 37+91=128, Resulting Numbers: [128] 128,99 unequal: No Solution Exploring Operation: 91-37=54, Resulting Numbers: [54] 54,99 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 #0,4,2 Current State: 99:[98, 44], Operations: ['61-24=37', '7+37=44'] Exploring Operation: 98*44=4312, Resulting Numbers: [4312] 4312,99 unequal: No Solution Exploring Operation: 98-44=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 98+44=142, Resulting Numbers: [142] 142,99 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: 99:[7, 24, 37], Operations: ['98-61=37'] Exploring Operation: 24-7=17, Resulting Numbers: [37, 17] Generated Node #0,2,0: 99:[37, 17] Operation: 24-7=17 Exploring Operation: 7+37=44, Resulting Numbers: [24, 44] Generated Node #0,2,1: 99:[24, 44] Operation: 7+37=44 Exploring Operation: 37-24=13, Resulting Numbers: [7, 13] Generated Node #0,2,2: 99:[7, 13] Operation: 37-24=13 Exploring Operation: 7+24=31, Resulting Numbers: [37, 31] Generated Node #0,2,3: 99:[37, 31] Operation: 7+24=31 Exploring Operation: 37-7=30, Resulting Numbers: [24, 30] Generated Node #0,2,4: 99:[24, 30] Operation: 37-7=30 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[7, 13], Operations: ['98-61=37', '37-24=13'] Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,99 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 #0,2,3 Current State: 99:[37, 31], Operations: ['98-61=37', '7+24=31'] Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,99 unequal: No Solution Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,99 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 #0,2,0 Current State: 99:[37, 17], Operations: ['98-61=37', '24-7=17'] Exploring Operation: 37*17=629, Resulting Numbers: [629] 629,99 unequal: No Solution Exploring Operation: 37+17=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,99 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 #0,2,4 Current State: 99:[24, 30], Operations: ['98-61=37', '37-7=30'] Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,99 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,99 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 #0,2,1 Current State: 99:[24, 44], Operations: ['98-61=37', '7+37=44'] Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,99 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,99 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,99 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: 99:[7, 98, 85], Operations: ['61+24=85'] Exploring Operation: 98/7=14, Resulting Numbers: [85, 14] Generated Node #0,1,0: 99:[85, 14] Operation: 98/7=14 Exploring Operation: 7+85=92, Resulting Numbers: [98, 92] Generated Node #0,1,1: 99:[98, 92] Operation: 7+85=92 Exploring Operation: 7+98=105, Resulting Numbers: [85, 105] Generated Node #0,1,2: 99:[85, 105] Operation: 7+98=105 Exploring Operation: 98-85=13, Resulting Numbers: [7, 13] Generated Node #0,1,3: 99:[7, 13] Operation: 98-85=13 Exploring Operation: 98-7=91, Resulting Numbers: [85, 91] Generated Node #0,1,4: 99:[85, 91] Operation: 98-7=91 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[7, 13], Operations: ['61+24=85', '98-85=13'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,99 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,99 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 #0,1,1 Current State: 99:[98, 92], Operations: ['61+24=85', '7+85=92'] Exploring Operation: 98+92=190, Resulting Numbers: [190] 190,99 unequal: No Solution Exploring Operation: 98-92=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 98*92=9016, Resulting Numbers: [9016] 9016,99 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 #0,1,0 Current State: 99:[85, 14], Operations: ['61+24=85', '98/7=14'] Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,99 unequal: No Solution Exploring Operation: 85*14=1190, Resulting Numbers: [1190] 1190,99 unequal: No Solution Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[7, 98, 61, 24], Operations: [] Exploring Operation: 61+24=85, Resulting Numbers: [7, 98, 85] Generated Node #0,1: 99:[7, 98, 85] Operation: 61+24=85 Moving to Node #0,1 Current State: 99:[7, 98, 85], Operations: ['61+24=85'] Exploring Operation: 98/7=14, Resulting Numbers: [85, 14] Generated Node #0,1,0: 99:[85, 14] Operation: 98/7=14 Moving to Node #0,1,0 Current State: 99:[85, 14], Operations: ['61+24=85', '98/7=14'] Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_5
mult_heuristic
[ 79, 40, 20, 29 ]
16
[ "79-29=50", "40*20=800", "800/50=16" ]
Current State: 16:[79, 40, 20, 29], Operations: [] Exploring Operation: 79-29=50, Resulting Numbers: [40, 20, 50] Generated Node #2: [40, 20, 50] from Operation: 79-29=50 Current State: 16:[40, 20, 50], Operations: ['79-29=50'] Exploring Operation: 40*20=800, Resulting Numbers: [50, 800] Generated Node #3: [50, 800] from Operation: 40*20=800 Current State: 16:[50, 800], Operations: ['79-29=50', '40*20=800'] Exploring Operation: 800/50=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[79, 40, 20, 29], Operations: [] Exploring Operation: 40/20=2, Resulting Numbers: [79, 29, 2] Generated Node #0,0: 16:[79, 29, 2] Operation: 40/20=2 Exploring Operation: 79-29=50, Resulting Numbers: [40, 20, 50] Generated Node #0,1: 16:[40, 20, 50] Operation: 79-29=50 Exploring Operation: 79-40=39, Resulting Numbers: [20, 29, 39] Generated Node #0,2: 16:[20, 29, 39] Operation: 79-40=39 Exploring Operation: 40-29=11, Resulting Numbers: [79, 20, 11] Generated Node #0,3: 16:[79, 20, 11] Operation: 40-29=11 Moving to Node #0,2 Current State: 16:[20, 29, 39], Operations: ['79-40=39'] Exploring Operation: 29-20=9, Resulting Numbers: [39, 9] Generated Node #0,2,0: 16:[39, 9] Operation: 29-20=9 Exploring Operation: 20+29=49, Resulting Numbers: [39, 49] Generated Node #0,2,1: 16:[39, 49] Operation: 20+29=49 Exploring Operation: 39-20=19, Resulting Numbers: [29, 19] Generated Node #0,2,2: 16:[29, 19] Operation: 39-20=19 Exploring Operation: 39-29=10, Resulting Numbers: [20, 10] Generated Node #0,2,3: 16:[20, 10] Operation: 39-29=10 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 16:[20, 10], Operations: ['79-40=39', '39-29=10'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,16 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,16 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 #0,2,2 Current State: 16:[29, 19], Operations: ['79-40=39', '39-20=19'] Exploring Operation: 29*19=551, Resulting Numbers: [551] 551,16 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,16 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 #0,2,0 Current State: 16:[39, 9], Operations: ['79-40=39', '29-20=9'] Exploring Operation: 39+9=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 39*9=351, Resulting Numbers: [351] 351,16 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 #0,2,1 Current State: 16:[39, 49], Operations: ['79-40=39', '20+29=49'] Exploring Operation: 49-39=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 39+49=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 39*49=1911, Resulting Numbers: [1911] 1911,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 16:[40, 20, 50], Operations: ['79-29=50'] Exploring Operation: 40-20=20, Resulting Numbers: [50, 20] Generated Node #0,1,0: 16:[50, 20] Operation: 40-20=20 Exploring Operation: 50-20=30, Resulting Numbers: [40, 30] Generated Node #0,1,1: 16:[40, 30] Operation: 50-20=30 Exploring Operation: 50-40=10, Resulting Numbers: [20, 10] Generated Node #0,1,2: 16:[20, 10] Operation: 50-40=10 Exploring Operation: 40/20=2, Resulting Numbers: [50, 2] Generated Node #0,1,3: 16:[50, 2] Operation: 40/20=2 Moving to Node #0,3 Current State: 16:[79, 20, 11], Operations: ['40-29=11'] Exploring Operation: 20-11=9, Resulting Numbers: [79, 9] Generated Node #0,3,0: 16:[79, 9] Operation: 20-11=9 Exploring Operation: 79-20=59, Resulting Numbers: [11, 59] Generated Node #0,3,1: 16:[11, 59] Operation: 79-20=59 Exploring Operation: 79+11=90, Resulting Numbers: [20, 90] Generated Node #0,3,2: 16:[20, 90] Operation: 79+11=90 Exploring Operation: 79-11=68, Resulting Numbers: [20, 68] Generated Node #0,3,3: 16:[20, 68] Operation: 79-11=68 Moving to Node #0,0 Current State: 16:[79, 29, 2], Operations: ['40/20=2'] Exploring Operation: 29-2=27, Resulting Numbers: [79, 27] Generated Node #0,0,0: 16:[79, 27] Operation: 29-2=27 Exploring Operation: 79-29=50, Resulting Numbers: [2, 50] Generated Node #0,0,1: 16:[2, 50] Operation: 79-29=50 Exploring Operation: 79+2=81, Resulting Numbers: [29, 81] Generated Node #0,0,2: 16:[29, 81] Operation: 79+2=81 Exploring Operation: 79-2=77, Resulting Numbers: [29, 77] Generated Node #0,0,3: 16:[29, 77] Operation: 79-2=77 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[2, 50], Operations: ['40/20=2', '79-29=50'] Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[79, 27], Operations: ['40/20=2', '29-2=27'] Exploring Operation: 79-27=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 79*27=2133, Resulting Numbers: [2133] 2133,16 unequal: No Solution Exploring Operation: 79+27=106, Resulting Numbers: [106] 106,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[29, 77], Operations: ['40/20=2', '79-2=77'] Exploring Operation: 29+77=106, Resulting Numbers: [106] 106,16 unequal: No Solution Exploring Operation: 29*77=2233, Resulting Numbers: [2233] 2233,16 unequal: No Solution Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[29, 81], Operations: ['40/20=2', '79+2=81'] Exploring Operation: 29*81=2349, Resulting Numbers: [2349] 2349,16 unequal: No Solution Exploring Operation: 81-29=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 29+81=110, Resulting Numbers: [110] 110,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 16:[20, 10], Operations: ['79-29=50', '50-40=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[50, 2], Operations: ['79-29=50', '40/20=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,16 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[50, 20], Operations: ['79-29=50', '40-20=20'] Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 50*20=1000, Resulting Numbers: [1000] 1000,16 unequal: No Solution Exploring Operation: 50+20=70, Resulting Numbers: [70] 70,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[40, 30], Operations: ['79-29=50', '50-20=30'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,16 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[11, 59], Operations: ['40-29=11', '79-20=59'] Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 11*59=649, Resulting Numbers: [649] 649,16 unequal: No Solution Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[20, 68], Operations: ['40-29=11', '79-11=68'] Exploring Operation: 20+68=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 20*68=1360, Resulting Numbers: [1360] 1360,16 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[79, 9], Operations: ['40-29=11', '20-11=9'] Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,16 unequal: No Solution Exploring Operation: 79+9=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 79*9=711, Resulting Numbers: [711] 711,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[20, 90], Operations: ['40-29=11', '79+11=90'] Exploring Operation: 20*90=1800, Resulting Numbers: [1800] 1800,16 unequal: No Solution Exploring Operation: 90-20=70, Resulting Numbers: [70] 70,16 unequal: No Solution Exploring Operation: 20+90=110, Resulting Numbers: [110] 110,16 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 20, 83, 6, 40 ]
37
[ "40-20=20", "6*20=120", "120-83=37" ]
Current State: 37:[20, 83, 6, 40], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [83, 6, 20] Generated Node #2: [83, 6, 20] from Operation: 40-20=20 Current State: 37:[83, 6, 20], Operations: ['40-20=20'] Exploring Operation: 6*20=120, Resulting Numbers: [83, 120] Generated Node #3: [83, 120] from Operation: 6*20=120 Current State: 37:[83, 120], Operations: ['40-20=20', '6*20=120'] Exploring Operation: 120-83=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[20, 83, 6, 40], Operations: [] Exploring Operation: 83-40=43, Resulting Numbers: [20, 6, 43] Generated Node #0,0: 37:[20, 6, 43] Operation: 83-40=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[20, 6, 43], Operations: ['83-40=43'] Exploring Operation: 20+6=26, Resulting Numbers: [43, 26] Generated Node #0,0,0: 37:[43, 26] Operation: 20+6=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[43, 26], Operations: ['83-40=43', '20+6=26'] Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 76, 78, 74, 46 ]
18
[ "78-76=2", "46*2=92", "92-74=18" ]
Current State: 18:[76, 78, 74, 46], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [74, 46, 2] Generated Node #2: [74, 46, 2] from Operation: 78-76=2 Current State: 18:[74, 46, 2], Operations: ['78-76=2'] Exploring Operation: 46*2=92, Resulting Numbers: [74, 92] Generated Node #3: [74, 92] from Operation: 46*2=92 Current State: 18:[74, 92], Operations: ['78-76=2', '46*2=92'] Exploring Operation: 92-74=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[76, 78, 74, 46], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [78, 46, 2] Generated Node #0,0: 18:[78, 46, 2] Operation: 76-74=2 Exploring Operation: 78-74=4, Resulting Numbers: [76, 46, 4] Generated Node #0,1: 18:[76, 46, 4] Operation: 78-74=4 Exploring Operation: 78-76=2, Resulting Numbers: [74, 46, 2] Generated Node #0,2: 18:[74, 46, 2] Operation: 78-76=2 Exploring Operation: 76-46=30, Resulting Numbers: [78, 74, 30] Generated Node #0,3: 18:[78, 74, 30] Operation: 76-46=30 Moving to Node #0,2 Current State: 18:[74, 46, 2], Operations: ['78-76=2'] Exploring Operation: 74-2=72, Resulting Numbers: [46, 72] Generated Node #0,2,0: 18:[46, 72] Operation: 74-2=72 Exploring Operation: 74-46=28, Resulting Numbers: [2, 28] Generated Node #0,2,1: 18:[2, 28] Operation: 74-46=28 Exploring Operation: 74/2=37, Resulting Numbers: [46, 37] Generated Node #0,2,2: 18:[46, 37] Operation: 74/2=37 Exploring Operation: 46/2=23, Resulting Numbers: [74, 23] Generated Node #0,2,3: 18:[74, 23] Operation: 46/2=23 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[2, 28], Operations: ['78-76=2', '74-46=28'] Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,18 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[46, 37], Operations: ['78-76=2', '74/2=37'] Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 46*37=1702, Resulting Numbers: [1702] 1702,18 unequal: No Solution Exploring Operation: 46+37=83, Resulting Numbers: [83] 83,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[74, 23], Operations: ['78-76=2', '46/2=23'] Exploring Operation: 74*23=1702, Resulting Numbers: [1702] 1702,18 unequal: No Solution Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 74+23=97, Resulting Numbers: [97] 97,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[46, 72], Operations: ['78-76=2', '74-2=72'] Exploring Operation: 46+72=118, Resulting Numbers: [118] 118,18 unequal: No Solution Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 46*72=3312, Resulting Numbers: [3312] 3312,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 18:[76, 46, 4], Operations: ['78-74=4'] Exploring Operation: 76-46=30, Resulting Numbers: [4, 30] Generated Node #0,1,0: 18:[4, 30] Operation: 76-46=30 Exploring Operation: 76/4=19, Resulting Numbers: [46, 19] Generated Node #0,1,1: 18:[46, 19] Operation: 76/4=19 Exploring Operation: 76-4=72, Resulting Numbers: [46, 72] Generated Node #0,1,2: 18:[46, 72] Operation: 76-4=72 Exploring Operation: 46-4=42, Resulting Numbers: [76, 42] Generated Node #0,1,3: 18:[76, 42] Operation: 46-4=42 Moving to Node #0,0 Current State: 18:[78, 46, 2], Operations: ['76-74=2'] Exploring Operation: 78-2=76, Resulting Numbers: [46, 76] Generated Node #0,0,0: 18:[46, 76] Operation: 78-2=76 Exploring Operation: 46/2=23, Resulting Numbers: [78, 23] Generated Node #0,0,1: 18:[78, 23] Operation: 46/2=23 Exploring Operation: 78-46=32, Resulting Numbers: [2, 32] Generated Node #0,0,2: 18:[2, 32] Operation: 78-46=32 Exploring Operation: 78/2=39, Resulting Numbers: [46, 39] Generated Node #0,0,3: 18:[46, 39] Operation: 78/2=39 Moving to Node #0,3 Current State: 18:[78, 74, 30], Operations: ['76-46=30'] Exploring Operation: 78-30=48, Resulting Numbers: [74, 48] Generated Node #0,3,0: 18:[74, 48] Operation: 78-30=48 Exploring Operation: 78+74=152, Resulting Numbers: [30, 152] Generated Node #0,3,1: 18:[30, 152] Operation: 78+74=152 Exploring Operation: 78-74=4, Resulting Numbers: [30, 4] Generated Node #0,3,2: 18:[30, 4] Operation: 78-74=4 Exploring Operation: 74-30=44, Resulting Numbers: [78, 44] Generated Node #0,3,3: 18:[78, 44] Operation: 74-30=44 Moving to Node #0,1,0 Current State: 18:[4, 30], Operations: ['78-74=4', '76-46=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,18 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[30, 4], Operations: ['76-46=30', '78-74=4'] Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,18 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[2, 32], Operations: ['76-74=2', '78-46=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,18 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,18 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[46, 19], Operations: ['78-74=4', '76/4=19'] Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,18 unequal: No Solution Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,18 unequal: No Solution Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[46, 39], Operations: ['76-74=2', '78/2=39'] Exploring Operation: 46+39=85, Resulting Numbers: [85] 85,18 unequal: No Solution Exploring Operation: 46*39=1794, Resulting Numbers: [1794] 1794,18 unequal: No Solution Exploring Operation: 46-39=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[78, 23], Operations: ['76-74=2', '46/2=23'] Exploring Operation: 78+23=101, Resulting Numbers: [101] 101,18 unequal: No Solution Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,18 unequal: No Solution Exploring Operation: 78*23=1794, Resulting Numbers: [1794] 1794,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[46, 72], Operations: ['78-74=4', '76-4=72'] Exploring Operation: 46*72=3312, Resulting Numbers: [3312] 3312,18 unequal: No Solution Exploring Operation: 46+72=118, Resulting Numbers: [118] 118,18 unequal: No Solution Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,18 unequal: No Solution Moving to Node #0,1,3 Current State: 18:[76, 42], Operations: ['78-74=4', '46-4=42'] Exploring Operation: 76*42=3192, Resulting Numbers: [3192] 3192,18 unequal: No Solution Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 76+42=118, Resulting Numbers: [118] 118,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[78, 44], Operations: ['76-46=30', '74-30=44'] Exploring Operation: 78*44=3432, Resulting Numbers: [3432] 3432,18 unequal: No Solution Exploring Operation: 78+44=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 78-44=34, Resulting Numbers: [34] 34,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[74, 48], Operations: ['76-46=30', '78-30=48'] Exploring Operation: 74*48=3552, Resulting Numbers: [3552] 3552,18 unequal: No Solution Exploring Operation: 74+48=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 74-48=26, Resulting Numbers: [26] 26,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[46, 76], Operations: ['76-74=2', '78-2=76'] Exploring Operation: 46*76=3496, Resulting Numbers: [3496] 3496,18 unequal: No Solution Exploring Operation: 46+76=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[30, 152], Operations: ['76-46=30', '78+74=152'] Exploring Operation: 152-30=122, Resulting Numbers: [122] 122,18 unequal: No Solution Exploring Operation: 30*152=4560, Resulting Numbers: [4560] 4560,18 unequal: No Solution Exploring Operation: 30+152=182, Resulting Numbers: [182] 182,18 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 59, 78, 83, 63 ]
17
[ "59*83=4897", "78*63=4914", "4914-4897=17" ]
Current State: 17:[59, 78, 83, 63], Operations: [] Exploring Operation: 59*83=4897, Resulting Numbers: [78, 63, 4897] Generated Node #2: [78, 63, 4897] from Operation: 59*83=4897 Current State: 17:[78, 63, 4897], Operations: ['59*83=4897'] Exploring Operation: 78*63=4914, Resulting Numbers: [4897, 4914] Generated Node #3: [4897, 4914] from Operation: 78*63=4914 Current State: 17:[4897, 4914], Operations: ['59*83=4897', '78*63=4914'] Exploring Operation: 4914-4897=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[59, 78, 83, 63], Operations: [] Exploring Operation: 78-63=15, Resulting Numbers: [59, 83, 15] Generated Node #0,0: 17:[59, 83, 15] Operation: 78-63=15 Exploring Operation: 83-63=20, Resulting Numbers: [59, 78, 20] Generated Node #0,1: 17:[59, 78, 20] Operation: 83-63=20 Exploring Operation: 83-78=5, Resulting Numbers: [59, 63, 5] Generated Node #0,2: 17:[59, 63, 5] Operation: 83-78=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[59, 63, 5], Operations: ['83-78=5'] Exploring Operation: 63-5=58, Resulting Numbers: [59, 58] Generated Node #0,2,0: 17:[59, 58] Operation: 63-5=58 Exploring Operation: 63-59=4, Resulting Numbers: [5, 4] Generated Node #0,2,1: 17:[5, 4] Operation: 63-59=4 Exploring Operation: 59-5=54, Resulting Numbers: [63, 54] Generated Node #0,2,2: 17:[63, 54] Operation: 59-5=54 Moving to Node #0,2,1 Current State: 17:[5, 4], Operations: ['83-78=5', '63-59=4'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,17 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[59, 58], Operations: ['83-78=5', '63-5=58'] Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 59*58=3422, Resulting Numbers: [3422] 3422,17 unequal: No Solution Exploring Operation: 59+58=117, Resulting Numbers: [117] 117,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[63, 54], Operations: ['83-78=5', '59-5=54'] Exploring Operation: 63+54=117, Resulting Numbers: [117] 117,17 unequal: No Solution Exploring Operation: 63*54=3402, Resulting Numbers: [3402] 3402,17 unequal: No Solution Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[59, 78, 20], Operations: ['83-63=20'] Exploring Operation: 59-20=39, Resulting Numbers: [78, 39] Generated Node #0,1,0: 17:[78, 39] Operation: 59-20=39 Exploring Operation: 78-20=58, Resulting Numbers: [59, 58] Generated Node #0,1,1: 17:[59, 58] Operation: 78-20=58 Exploring Operation: 78-59=19, Resulting Numbers: [20, 19] Generated Node #0,1,2: 17:[20, 19] Operation: 78-59=19 Moving to Node #0,1,2 Current State: 17:[20, 19], Operations: ['83-63=20', '78-59=19'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,17 unequal: No Solution Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[78, 39], Operations: ['83-63=20', '59-20=39'] Exploring Operation: 78/39=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 78+39=117, Resulting Numbers: [117] 117,17 unequal: No Solution Exploring Operation: 78-39=39, Resulting Numbers: [39] 39,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[59, 58], Operations: ['83-63=20', '78-20=58'] Exploring Operation: 59-58=1, Resulting Numbers: [1] 1,17 unequal: No Solution Exploring Operation: 59+58=117, Resulting Numbers: [117] 117,17 unequal: No Solution Exploring Operation: 59*58=3422, Resulting Numbers: [3422] 3422,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[59, 83, 15], Operations: ['78-63=15'] Exploring Operation: 83-15=68, Resulting Numbers: [59, 68] Generated Node #0,0,0: 17:[59, 68] Operation: 83-15=68 Exploring Operation: 59-15=44, Resulting Numbers: [83, 44] Generated Node #0,0,1: 17:[83, 44] Operation: 59-15=44 Exploring Operation: 83-59=24, Resulting Numbers: [15, 24] Generated Node #0,0,2: 17:[15, 24] Operation: 83-59=24 Moving to Node #0,0,2 Current State: 17:[15, 24], Operations: ['78-63=15', '83-59=24'] Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,17 unequal: No Solution Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,17 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[59, 68], Operations: ['78-63=15', '83-15=68'] Exploring Operation: 59+68=127, Resulting Numbers: [127] 127,17 unequal: No Solution Exploring Operation: 68-59=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 59*68=4012, Resulting Numbers: [4012] 4012,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[83, 44], Operations: ['78-63=15', '59-15=44'] Exploring Operation: 83*44=3652, Resulting Numbers: [3652] 3652,17 unequal: No Solution Exploring Operation: 83+44=127, Resulting Numbers: [127] 127,17 unequal: No Solution Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,17 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
[ 15, 33, 35, 38 ]
15
[ "33-15=18", "38-35=3", "18-3=15" ]
Current State: 15:[15, 33, 35, 38], Operations: [] Exploring Operation: 33-15=18, Resulting Numbers: [35, 38, 18] Generated Node #2: [35, 38, 18] from Operation: 33-15=18 Current State: 15:[35, 38, 18], Operations: ['33-15=18'] Exploring Operation: 38-35=3, Resulting Numbers: [18, 3] Generated Node #3: [18, 3] from Operation: 38-35=3 Current State: 15:[18, 3], Operations: ['33-15=18', '38-35=3'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[15, 33, 35, 38], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [15, 35, 5] Generated Node #0,0: 15:[15, 35, 5] Operation: 38-33=5 Exploring Operation: 35-33=2, Resulting Numbers: [15, 38, 2] Generated Node #0,1: 15:[15, 38, 2] Operation: 35-33=2 Exploring Operation: 38-35=3, Resulting Numbers: [15, 33, 3] Generated Node #0,2: 15:[15, 33, 3] Operation: 38-35=3 Exploring Operation: 35-15=20, Resulting Numbers: [33, 38, 20] Generated Node #0,3: 15:[33, 38, 20] Operation: 35-15=20 Exploring Operation: 33-15=18, Resulting Numbers: [35, 38, 18] Generated Node #0,4: 15:[35, 38, 18] Operation: 33-15=18 Moving to Node #0,2 Current State: 15:[15, 33, 3], Operations: ['38-35=3'] Exploring Operation: 15+3=18, Resulting Numbers: [33, 18] Generated Node #0,2,0: 15:[33, 18] Operation: 15+3=18 Exploring Operation: 15/3=5, Resulting Numbers: [33, 5] Generated Node #0,2,1: 15:[33, 5] Operation: 15/3=5 Exploring Operation: 33-15=18, Resulting Numbers: [3, 18] Generated Node #0,2,2: 15:[3, 18] Operation: 33-15=18 Exploring Operation: 33-3=30, Resulting Numbers: [15, 30] Generated Node #0,2,3: 15:[15, 30] Operation: 33-3=30 Exploring Operation: 33/3=11, Resulting Numbers: [15, 11] Generated Node #0,2,4: 15:[15, 11] Operation: 33/3=11 Moving to Node #0,0 Current State: 15:[15, 35, 5], Operations: ['38-33=5'] Exploring Operation: 35/5=7, Resulting Numbers: [15, 7] Generated Node #0,0,0: 15:[15, 7] Operation: 35/5=7 Exploring Operation: 35-5=30, Resulting Numbers: [15, 30] Generated Node #0,0,1: 15:[15, 30] Operation: 35-5=30 Exploring Operation: 15+5=20, Resulting Numbers: [35, 20] Generated Node #0,0,2: 15:[35, 20] Operation: 15+5=20 Exploring Operation: 35-15=20, Resulting Numbers: [5, 20] Generated Node #0,0,3: 15:[5, 20] Operation: 35-15=20 Exploring Operation: 15/5=3, Resulting Numbers: [35, 3] Generated Node #0,0,4: 15:[35, 3] Operation: 15/5=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[15, 7], Operations: ['38-33=5', '35/5=7'] Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 15*7=105, Resulting Numbers: [105] 105,15 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:[5, 20], Operations: ['38-33=5', '35-15=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,15 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,15 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[15, 33, 35, 38], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [15, 35, 5] Generated Node #0,0: 15:[15, 35, 5] Operation: 38-33=5 Moving to Node #0,0 Current State: 15:[15, 35, 5], Operations: ['38-33=5'] Exploring Operation: 35-15=20, Resulting Numbers: [5, 20] Generated Node #0,0,3: 15:[5, 20] Operation: 35-15=20 Moving to Node #0,0,3 Current State: 15:[5, 20], Operations: ['38-33=5', '35-15=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 23, 6, 88, 62 ]
18
[ "88-23=65", "65-62=3", "6*3=18" ]
Current State: 18:[23, 6, 88, 62], Operations: [] Exploring Operation: 88-23=65, Resulting Numbers: [6, 62, 65] Generated Node #2: [6, 62, 65] from Operation: 88-23=65 Current State: 18:[6, 62, 65], Operations: ['88-23=65'] Exploring Operation: 65-62=3, Resulting Numbers: [6, 3] Generated Node #3: [6, 3] from Operation: 65-62=3 Current State: 18:[6, 3], Operations: ['88-23=65', '65-62=3'] Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[23, 6, 88, 62], Operations: [] Exploring Operation: 62-23=39, Resulting Numbers: [6, 88, 39] Generated Node #0,0: 18:[6, 88, 39] Operation: 62-23=39 Exploring Operation: 88-23=65, Resulting Numbers: [6, 62, 65] Generated Node #0,1: 18:[6, 62, 65] Operation: 88-23=65 Exploring Operation: 88-62=26, Resulting Numbers: [23, 6, 26] Generated Node #0,2: 18:[23, 6, 26] Operation: 88-62=26 Exploring Operation: 88-6=82, Resulting Numbers: [23, 62, 82] Generated Node #0,3: 18:[23, 62, 82] Operation: 88-6=82 Moving to Node #0,2 Current State: 18:[23, 6, 26], Operations: ['88-62=26'] Exploring Operation: 23+6=29, Resulting Numbers: [26, 29] Generated Node #0,2,0: 18:[26, 29] Operation: 23+6=29 Exploring Operation: 26-23=3, Resulting Numbers: [6, 3] Generated Node #0,2,1: 18:[6, 3] Operation: 26-23=3 Exploring Operation: 26-6=20, Resulting Numbers: [23, 20] Generated Node #0,2,2: 18:[23, 20] Operation: 26-6=20 Exploring Operation: 23-6=17, Resulting Numbers: [26, 17] Generated Node #0,2,3: 18:[26, 17] Operation: 23-6=17 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[6, 3], Operations: ['88-62=26', '26-23=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[23, 6, 88, 62], Operations: [] Exploring Operation: 88-62=26, Resulting Numbers: [23, 6, 26] Generated Node #0,2: 18:[23, 6, 26] Operation: 88-62=26 Moving to Node #0,2 Current State: 18:[23, 6, 26], Operations: ['88-62=26'] Exploring Operation: 26-23=3, Resulting Numbers: [6, 3] Generated Node #0,2,1: 18:[6, 3] Operation: 26-23=3 Moving to Node #0,2,1 Current State: 18:[6, 3], Operations: ['88-62=26', '26-23=3'] Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 9, 92, 27, 89 ]
15
[ "9+92=101", "27+89=116", "116-101=15" ]
Current State: 15:[9, 92, 27, 89], Operations: [] Exploring Operation: 9+92=101, Resulting Numbers: [27, 89, 101] Generated Node #2: [27, 89, 101] from Operation: 9+92=101 Current State: 15:[27, 89, 101], Operations: ['9+92=101'] Exploring Operation: 27+89=116, Resulting Numbers: [101, 116] Generated Node #3: [101, 116] from Operation: 27+89=116 Current State: 15:[101, 116], Operations: ['9+92=101', '27+89=116'] Exploring Operation: 116-101=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[9, 92, 27, 89], Operations: [] Exploring Operation: 92-27=65, Resulting Numbers: [9, 89, 65] Generated Node #0,0: 15:[9, 89, 65] Operation: 92-27=65 Exploring Operation: 27/9=3, Resulting Numbers: [92, 89, 3] Generated Node #0,1: 15:[92, 89, 3] Operation: 27/9=3 Exploring Operation: 92-89=3, Resulting Numbers: [9, 27, 3] Generated Node #0,2: 15:[9, 27, 3] Operation: 92-89=3 Exploring Operation: 89-27=62, Resulting Numbers: [9, 92, 62] Generated Node #0,3: 15:[9, 92, 62] Operation: 89-27=62 Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[9, 27, 3], Operations: ['92-89=3'] Exploring Operation: 27/3=9, Resulting Numbers: [9, 9] Generated Node #0,2,0: 15:[9, 9] Operation: 27/3=9 Exploring Operation: 27-9=18, Resulting Numbers: [3, 18] Generated Node #0,2,1: 15:[3, 18] Operation: 27-9=18 Exploring Operation: 9/3=3, Resulting Numbers: [27, 3] Generated Node #0,2,2: 15:[27, 3] Operation: 9/3=3 Exploring Operation: 27/9=3, Resulting Numbers: [3, 3] Generated Node #0,2,3: 15:[3, 3] Operation: 27/9=3 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 15:[3, 3], Operations: ['92-89=3', '27/9=3'] Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,15 unequal: No Solution No 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: 15:[3, 18], Operations: ['92-89=3', '27-9=18'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,15 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[9, 92, 27, 89], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [9, 27, 3] Generated Node #0,2: 15:[9, 27, 3] Operation: 92-89=3 Moving to Node #0,2 Current State: 15:[9, 27, 3], Operations: ['92-89=3'] Exploring Operation: 27-9=18, Resulting Numbers: [3, 18] Generated Node #0,2,1: 15:[3, 18] Operation: 27-9=18 Moving to Node #0,2,1 Current State: 15:[3, 18], Operations: ['92-89=3', '27-9=18'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 85, 3, 3, 40 ]
85
[ "3-3=0", "40*0=0", "85+0=85" ]
Current State: 85:[85, 3, 3, 40], Operations: [] Exploring Operation: 3-3=0, Resulting Numbers: [85, 40, 0] Generated Node #2: [85, 40, 0] from Operation: 3-3=0 Current State: 85:[85, 40, 0], Operations: ['3-3=0'] Exploring Operation: 40*0=0, Resulting Numbers: [85, 0] Generated Node #3: [85, 0] from Operation: 40*0=0 Current State: 85:[85, 0], Operations: ['3-3=0', '40*0=0'] Exploring Operation: 85+0=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[85, 3, 3, 40], Operations: [] Exploring Operation: 40-3=37, Resulting Numbers: [85, 3, 37] Generated Node #0,0: 85:[85, 3, 37] Operation: 40-3=37 Moving to Node #0,0 Current State: 85:[85, 3, 37], Operations: ['40-3=37'] Exploring Operation: 37-3=34, Resulting Numbers: [85, 34] Generated Node #0,0,0: 85:[85, 34] Operation: 37-3=34 Moving to Node #0,0,0 Current State: 85:[85, 34], Operations: ['40-3=37', '37-3=34'] Exploring Operation: 85+34=119, Resulting Numbers: [119] 119,85 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 62, 22, 67, 94 ]
77
[ "62+22=84", "67+94=161", "161-84=77" ]
Current State: 77:[62, 22, 67, 94], Operations: [] Exploring Operation: 62+22=84, Resulting Numbers: [67, 94, 84] Generated Node #2: [67, 94, 84] from Operation: 62+22=84 Current State: 77:[67, 94, 84], Operations: ['62+22=84'] Exploring Operation: 67+94=161, Resulting Numbers: [84, 161] Generated Node #3: [84, 161] from Operation: 67+94=161 Current State: 77:[84, 161], Operations: ['62+22=84', '67+94=161'] Exploring Operation: 161-84=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[62, 22, 67, 94], Operations: [] Exploring Operation: 94-22=72, Resulting Numbers: [62, 67, 72] Generated Node #0,0: 77:[62, 67, 72] Operation: 94-22=72 Exploring Operation: 67-62=5, Resulting Numbers: [22, 94, 5] Generated Node #0,1: 77:[22, 94, 5] Operation: 67-62=5 Moving to Node #0,0 Current State: 77:[62, 67, 72], Operations: ['94-22=72'] Exploring Operation: 72-62=10, Resulting Numbers: [67, 10] Generated Node #0,0,0: 77:[67, 10] Operation: 72-62=10 Exploring Operation: 67-62=5, Resulting Numbers: [72, 5] Generated Node #0,0,1: 77:[72, 5] Operation: 67-62=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[72, 5], Operations: ['94-22=72', '67-62=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[62, 22, 67, 94], Operations: [] Exploring Operation: 94-22=72, Resulting Numbers: [62, 67, 72] Generated Node #0,0: 77:[62, 67, 72] Operation: 94-22=72 Moving to Node #0,0 Current State: 77:[62, 67, 72], Operations: ['94-22=72'] Exploring Operation: 67-62=5, Resulting Numbers: [72, 5] Generated Node #0,0,1: 77:[72, 5] Operation: 67-62=5 Moving to Node #0,0,1 Current State: 77:[72, 5], Operations: ['94-22=72', '67-62=5'] Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 38, 36, 36, 43 ]
29
[ "38-36=2", "36*2=72", "72-43=29" ]
Current State: 29:[38, 36, 36, 43], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [43, 2] Generated Node #2: [43, 2] from Operation: 38-36=2 Current State: 29:[43, 2], Operations: ['38-36=2'] Exploring Operation: 36*2=72, Resulting Numbers: [43, 72] Generated Node #3: [43, 72] from Operation: 36*2=72 Current State: 29:[43, 72], Operations: ['38-36=2', '36*2=72'] Exploring Operation: 72-43=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[38, 36, 36, 43], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [38, 36, 7] Generated Node #0,0: 29:[38, 36, 7] Operation: 43-36=7 Exploring Operation: 43-38=5, Resulting Numbers: [36, 36, 5] Generated Node #0,1: 29:[36, 36, 5] Operation: 43-38=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[38, 36, 7], Operations: ['43-36=7'] Exploring Operation: 36-7=29, Resulting Numbers: [38, 29] Generated Node #0,0,0: 29:[38, 29] Operation: 36-7=29 Exploring Operation: 38-7=31, Resulting Numbers: [36, 31] Generated Node #0,0,1: 29:[36, 31] Operation: 38-7=31 Moving to Node #0,0,0 Current State: 29:[38, 29], Operations: ['43-36=7', '36-7=29'] Exploring Operation: 38+29=67, Resulting Numbers: [67] 67,29 unequal: No Solution Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[36, 31], Operations: ['43-36=7', '38-7=31'] Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,29 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[36, 36, 5], Operations: ['43-38=5'] Exploring Operation: 36-5=31, Resulting Numbers: [36, 31] Generated Node #0,1,0: 29:[36, 31] Operation: 36-5=31 Exploring Operation: 36-5=31, Resulting Numbers: [36, 31] Generated Node #0,1,1: 29:[36, 31] Operation: 36-5=31 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[36, 31], Operations: ['43-38=5', '36-5=31'] Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 29:[36, 31], Operations: ['43-38=5', '36-5=31'] Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,29 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 87, 58, 83, 54 ]
61
[ "83-54=29", "87/29=3", "58+3=61" ]
Current State: 61:[87, 58, 83, 54], Operations: [] Exploring Operation: 83-54=29, Resulting Numbers: [87, 58, 29] Generated Node #2: [87, 58, 29] from Operation: 83-54=29 Current State: 61:[87, 58, 29], Operations: ['83-54=29'] Exploring Operation: 87/29=3, Resulting Numbers: [58, 3] Generated Node #3: [58, 3] from Operation: 87/29=3 Current State: 61:[58, 3], Operations: ['83-54=29', '87/29=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[87, 58, 83, 54], Operations: [] Exploring Operation: 87-54=33, Resulting Numbers: [58, 83, 33] Generated Node #0,0: 61:[58, 83, 33] Operation: 87-54=33 Moving to Node #0,0 Current State: 61:[58, 83, 33], Operations: ['87-54=33'] Exploring Operation: 83-33=50, Resulting Numbers: [58, 50] Generated Node #0,0,0: 61:[58, 50] Operation: 83-33=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[58, 50], Operations: ['87-54=33', '83-33=50'] Exploring Operation: 58+50=108, Resulting Numbers: [108] 108,61 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
[ 2, 83, 52, 39 ]
98
[ "2+83=85", "52-39=13", "85+13=98" ]
Current State: 98:[2, 83, 52, 39], Operations: [] Exploring Operation: 2+83=85, Resulting Numbers: [52, 39, 85] Generated Node #2: [52, 39, 85] from Operation: 2+83=85 Current State: 98:[52, 39, 85], Operations: ['2+83=85'] Exploring Operation: 52-39=13, Resulting Numbers: [85, 13] Generated Node #3: [85, 13] from Operation: 52-39=13 Current State: 98:[85, 13], Operations: ['2+83=85', '52-39=13'] Exploring Operation: 85+13=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[2, 83, 52, 39], Operations: [] Exploring Operation: 83-39=44, Resulting Numbers: [2, 52, 44] Generated Node #0,0: 98:[2, 52, 44] Operation: 83-39=44 Moving to Node #0,0 Current State: 98:[2, 52, 44], Operations: ['83-39=44'] Exploring Operation: 52-44=8, Resulting Numbers: [2, 8] Generated Node #0,0,0: 98:[2, 8] Operation: 52-44=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[2, 8], Operations: ['83-39=44', '52-44=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 74, 73, 17, 2 ]
29
[ "73+17=90", "90/2=45", "74-45=29" ]
Current State: 29:[74, 73, 17, 2], Operations: [] Exploring Operation: 73+17=90, Resulting Numbers: [74, 2, 90] Generated Node #2: [74, 2, 90] from Operation: 73+17=90 Current State: 29:[74, 2, 90], Operations: ['73+17=90'] Exploring Operation: 90/2=45, Resulting Numbers: [74, 45] Generated Node #3: [74, 45] from Operation: 90/2=45 Current State: 29:[74, 45], Operations: ['73+17=90', '90/2=45'] Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[74, 73, 17, 2], Operations: [] Exploring Operation: 74-17=57, Resulting Numbers: [73, 2, 57] Generated Node #0,0: 29:[73, 2, 57] Operation: 74-17=57 Exploring Operation: 74-73=1, Resulting Numbers: [17, 2, 1] Generated Node #0,1: 29:[17, 2, 1] Operation: 74-73=1 Exploring Operation: 17*2=34, Resulting Numbers: [74, 73, 34] Generated Node #0,2: 29:[74, 73, 34] Operation: 17*2=34 Exploring Operation: 74/2=37, Resulting Numbers: [73, 17, 37] Generated Node #0,3: 29:[73, 17, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,3 Current State: 29:[73, 17, 37], Operations: ['74/2=37'] Exploring Operation: 37-17=20, Resulting Numbers: [73, 20] Generated Node #0,3,0: 29:[73, 20] Operation: 37-17=20 Exploring Operation: 73+17=90, Resulting Numbers: [37, 90] Generated Node #0,3,1: 29:[37, 90] Operation: 73+17=90 Exploring Operation: 73-37=36, Resulting Numbers: [17, 36] Generated Node #0,3,2: 29:[17, 36] Operation: 73-37=36 Exploring Operation: 73-17=56, Resulting Numbers: [37, 56] Generated Node #0,3,3: 29:[37, 56] Operation: 73-17=56 Moving to Node #0,3,2 Current State: 29:[17, 36], Operations: ['74/2=37', '73-37=36'] Exploring Operation: 17*36=612, Resulting Numbers: [612] 612,29 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,29 unequal: No Solution Exploring Operation: 17+36=53, Resulting Numbers: [53] 53,29 unequal: No Solution Moving to Node #0,3,3 Current State: 29:[37, 56], Operations: ['74/2=37', '73-17=56'] Exploring Operation: 37+56=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 37*56=2072, Resulting Numbers: [2072] 2072,29 unequal: No Solution Exploring Operation: 56-37=19, Resulting Numbers: [19] 19,29 unequal: No Solution Moving to Node #0,3,0 Current State: 29:[73, 20], Operations: ['74/2=37', '37-17=20'] Exploring Operation: 73+20=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,29 unequal: No Solution Exploring Operation: 73*20=1460, Resulting Numbers: [1460] 1460,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[37, 90], Operations: ['74/2=37', '73+17=90'] Exploring Operation: 90-37=53, Resulting Numbers: [53] 53,29 unequal: No Solution Exploring Operation: 37*90=3330, Resulting Numbers: [3330] 3330,29 unequal: No Solution Exploring Operation: 37+90=127, Resulting Numbers: [127] 127,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[17, 2, 1], Operations: ['74-73=1'] Exploring Operation: 17*2=34, Resulting Numbers: [1, 34] Generated Node #0,1,0: 29:[1, 34] Operation: 17*2=34 Exploring Operation: 2+1=3, Resulting Numbers: [17, 3] Generated Node #0,1,1: 29:[17, 3] Operation: 2+1=3 Exploring Operation: 17+1=18, Resulting Numbers: [2, 18] Generated Node #0,1,2: 29:[2, 18] Operation: 17+1=18 Exploring Operation: 17+2=19, Resulting Numbers: [1, 19] Generated Node #0,1,3: 29:[1, 19] Operation: 17+2=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[1, 34], Operations: ['74-73=1', '17*2=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,29 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,29 unequal: No Solution Exploring Operation: 1+34=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 29:[17, 3], Operations: ['74-73=1', '2+1=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,29 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 29:[2, 18], Operations: ['74-73=1', '17+1=18'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 29:[1, 19], Operations: ['74-73=1', '17+2=19'] Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,29 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 1+19=20, Resulting Numbers: [20] 20,29 unequal: No Solution Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[74, 73, 34], Operations: ['17*2=34'] Exploring Operation: 74-73=1, Resulting Numbers: [34, 1] Generated Node #0,2,0: 29:[34, 1] Operation: 74-73=1 Exploring Operation: 74-34=40, Resulting Numbers: [73, 40] Generated Node #0,2,1: 29:[73, 40] Operation: 74-34=40 Exploring Operation: 74+73=147, Resulting Numbers: [34, 147] Generated Node #0,2,2: 29:[34, 147] Operation: 74+73=147 Exploring Operation: 73-34=39, Resulting Numbers: [74, 39] Generated Node #0,2,3: 29:[74, 39] Operation: 73-34=39 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 29:[34, 1], Operations: ['17*2=34', '74-73=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,29 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,29 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 29:[73, 40], Operations: ['17*2=34', '74-34=40'] Exploring Operation: 73+40=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,29 unequal: No Solution Exploring Operation: 73*40=2920, Resulting Numbers: [2920] 2920,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 29:[74, 39], Operations: ['17*2=34', '73-34=39'] Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 74+39=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 74*39=2886, Resulting Numbers: [2886] 2886,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 29:[34, 147], Operations: ['17*2=34', '74+73=147'] Exploring Operation: 34*147=4998, Resulting Numbers: [4998] 4998,29 unequal: No Solution Exploring Operation: 147-34=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 34+147=181, Resulting Numbers: [181] 181,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[73, 2, 57], Operations: ['74-17=57'] Exploring Operation: 57-2=55, Resulting Numbers: [73, 55] Generated Node #0,0,0: 29:[73, 55] Operation: 57-2=55 Exploring Operation: 73-57=16, Resulting Numbers: [2, 16] Generated Node #0,0,1: 29:[2, 16] Operation: 73-57=16 Exploring Operation: 73-2=71, Resulting Numbers: [57, 71] Generated Node #0,0,2: 29:[57, 71] Operation: 73-2=71 Exploring Operation: 73+2=75, Resulting Numbers: [57, 75] Generated Node #0,0,3: 29:[57, 75] Operation: 73+2=75 Moving to Node #0,0,1 Current State: 29:[2, 16], Operations: ['74-17=57', '73-57=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,29 unequal: No Solution Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,29 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[57, 71], Operations: ['74-17=57', '73-2=71'] Exploring Operation: 57*71=4047, Resulting Numbers: [4047] 4047,29 unequal: No Solution Exploring Operation: 71-57=14, Resulting Numbers: [14] 14,29 unequal: No Solution Exploring Operation: 57+71=128, Resulting Numbers: [128] 128,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[73, 55], Operations: ['74-17=57', '57-2=55'] Exploring Operation: 73*55=4015, Resulting Numbers: [4015] 4015,29 unequal: No Solution Exploring Operation: 73+55=128, Resulting Numbers: [128] 128,29 unequal: No Solution Exploring Operation: 73-55=18, Resulting Numbers: [18] 18,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[57, 75], Operations: ['74-17=57', '73+2=75'] Exploring Operation: 57+75=132, Resulting Numbers: [132] 132,29 unequal: No Solution Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 57*75=4275, Resulting Numbers: [4275] 4275,29 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
[ 84, 2, 22, 95 ]
22
[ "84+22=106", "106-95=11", "2*11=22" ]
Current State: 22:[84, 2, 22, 95], Operations: [] Exploring Operation: 84+22=106, Resulting Numbers: [2, 95, 106] Generated Node #2: [2, 95, 106] from Operation: 84+22=106 Current State: 22:[2, 95, 106], Operations: ['84+22=106'] Exploring Operation: 106-95=11, Resulting Numbers: [2, 11] Generated Node #3: [2, 11] from Operation: 106-95=11 Current State: 22:[2, 11], Operations: ['84+22=106', '106-95=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[84, 2, 22, 95], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [22, 95, 42] Generated Node #0,0: 22:[22, 95, 42] Operation: 84/2=42 Exploring Operation: 84-22=62, Resulting Numbers: [2, 95, 62] Generated Node #0,1: 22:[2, 95, 62] Operation: 84-22=62 Exploring Operation: 95-84=11, Resulting Numbers: [2, 22, 11] Generated Node #0,2: 22:[2, 22, 11] Operation: 95-84=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[2, 22, 11], Operations: ['95-84=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22, 22] Generated Node #0,2,0: 22:[22, 22] Operation: 2*11=22 Exploring Operation: 22-11=11, Resulting Numbers: [2, 11] Generated Node #0,2,1: 22:[2, 11] Operation: 22-11=11 Exploring Operation: 22/2=11, Resulting Numbers: [11, 11] Generated Node #0,2,2: 22:[11, 11] Operation: 22/2=11 Moving to Node #0,2,0 Current State: 22:[22, 22], Operations: ['95-84=11', '2*11=22'] Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,22 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[2, 11], Operations: ['95-84=11', '22-11=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,22 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[84, 2, 22, 95], Operations: [] Exploring Operation: 95-84=11, Resulting Numbers: [2, 22, 11] Generated Node #0,2: 22:[2, 22, 11] Operation: 95-84=11 Moving to Node #0,2 Current State: 22:[2, 22, 11], Operations: ['95-84=11'] Exploring Operation: 22-11=11, Resulting Numbers: [2, 11] Generated Node #0,2,1: 22:[2, 11] Operation: 22-11=11 Moving to Node #0,2,1 Current State: 22:[2, 11], Operations: ['95-84=11', '22-11=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 81, 53, 14, 96 ]
48
[ "81-53=28", "14*96=1344", "1344/28=48" ]
Current State: 48:[81, 53, 14, 96], Operations: [] Exploring Operation: 81-53=28, Resulting Numbers: [14, 96, 28] Generated Node #2: [14, 96, 28] from Operation: 81-53=28 Current State: 48:[14, 96, 28], Operations: ['81-53=28'] Exploring Operation: 14*96=1344, Resulting Numbers: [28, 1344] Generated Node #3: [28, 1344] from Operation: 14*96=1344 Current State: 48:[28, 1344], Operations: ['81-53=28', '14*96=1344'] Exploring Operation: 1344/28=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[81, 53, 14, 96], Operations: [] Exploring Operation: 96-53=43, Resulting Numbers: [81, 14, 43] Generated Node #0,0: 48:[81, 14, 43] Operation: 96-53=43 Exploring Operation: 81-53=28, Resulting Numbers: [14, 96, 28] Generated Node #0,1: 48:[14, 96, 28] Operation: 81-53=28 Exploring Operation: 81-14=67, Resulting Numbers: [53, 96, 67] Generated Node #0,2: 48:[53, 96, 67] Operation: 81-14=67 Exploring Operation: 96-14=82, Resulting Numbers: [81, 53, 82] Generated Node #0,3: 48:[81, 53, 82] Operation: 96-14=82 Exploring Operation: 96-81=15, Resulting Numbers: [53, 14, 15] Generated Node #0,4: 48:[53, 14, 15] Operation: 96-81=15 Moving to Node #0,4 Current State: 48:[53, 14, 15], Operations: ['96-81=15'] Exploring Operation: 15-14=1, Resulting Numbers: [53, 1] Generated Node #0,4,0: 48:[53, 1] Operation: 15-14=1 Exploring Operation: 14+15=29, Resulting Numbers: [53, 29] Generated Node #0,4,1: 48:[53, 29] Operation: 14+15=29 Exploring Operation: 53-14=39, Resulting Numbers: [15, 39] Generated Node #0,4,2: 48:[15, 39] Operation: 53-14=39 Exploring Operation: 53-15=38, Resulting Numbers: [14, 38] Generated Node #0,4,3: 48:[14, 38] Operation: 53-15=38 Exploring Operation: 53+14=67, Resulting Numbers: [15, 67] Generated Node #0,4,4: 48:[15, 67] Operation: 53+14=67 Moving to Node #0,0 Current State: 48:[81, 14, 43], Operations: ['96-53=43'] Exploring Operation: 14+43=57, Resulting Numbers: [81, 57] Generated Node #0,0,0: 48:[81, 57] Operation: 14+43=57 Exploring Operation: 81-14=67, Resulting Numbers: [43, 67] Generated Node #0,0,1: 48:[43, 67] Operation: 81-14=67 Exploring Operation: 81-43=38, Resulting Numbers: [14, 38] Generated Node #0,0,2: 48:[14, 38] Operation: 81-43=38 Exploring Operation: 81+14=95, Resulting Numbers: [43, 95] Generated Node #0,0,3: 48:[43, 95] Operation: 81+14=95 Exploring Operation: 43-14=29, Resulting Numbers: [81, 29] Generated Node #0,0,4: 48:[81, 29] Operation: 43-14=29 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 48:[14, 38], Operations: ['96-53=43', '81-43=38'] Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,48 unequal: No Solution Exploring Operation: 14*38=532, Resulting Numbers: [532] 532,48 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,48 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 #0,0,1 Current State: 48:[43, 67], Operations: ['96-53=43', '81-14=67'] Exploring Operation: 43*67=2881, Resulting Numbers: [2881] 2881,48 unequal: No Solution Exploring Operation: 67-43=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 43+67=110, Resulting Numbers: [110] 110,48 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 #0,0,4 Current State: 48:[81, 29], Operations: ['96-53=43', '43-14=29'] Exploring Operation: 81-29=52, Resulting Numbers: [52] 52,48 unequal: No Solution Exploring Operation: 81+29=110, Resulting Numbers: [110] 110,48 unequal: No Solution Exploring Operation: 81*29=2349, Resulting Numbers: [2349] 2349,48 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 #0,0,0 Current State: 48:[81, 57], Operations: ['96-53=43', '14+43=57'] Exploring Operation: 81+57=138, Resulting Numbers: [138] 138,48 unequal: No Solution Exploring Operation: 81-57=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 81*57=4617, Resulting Numbers: [4617] 4617,48 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 #0,0,3 Current State: 48:[43, 95], Operations: ['96-53=43', '81+14=95'] Exploring Operation: 43*95=4085, Resulting Numbers: [4085] 4085,48 unequal: No Solution Exploring Operation: 95-43=52, Resulting Numbers: [52] 52,48 unequal: No Solution Exploring Operation: 43+95=138, Resulting Numbers: [138] 138,48 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: 48:[14, 96, 28], Operations: ['81-53=28'] Exploring Operation: 96-28=68, Resulting Numbers: [14, 68] Generated Node #0,1,0: 48:[14, 68] Operation: 96-28=68 Exploring Operation: 14+28=42, Resulting Numbers: [96, 42] Generated Node #0,1,1: 48:[96, 42] Operation: 14+28=42 Exploring Operation: 96-14=82, Resulting Numbers: [28, 82] Generated Node #0,1,2: 48:[28, 82] Operation: 96-14=82 Exploring Operation: 28/14=2, Resulting Numbers: [96, 2] Generated Node #0,1,3: 48:[96, 2] Operation: 28/14=2 Exploring Operation: 28-14=14, Resulting Numbers: [96, 14] Generated Node #0,1,4: 48:[96, 14] Operation: 28-14=14 Moving to Node #0,2 Current State: 48:[53, 96, 67], Operations: ['81-14=67'] Exploring Operation: 96-53=43, Resulting Numbers: [67, 43] Generated Node #0,2,0: 48:[67, 43] Operation: 96-53=43 Exploring Operation: 96-67=29, Resulting Numbers: [53, 29] Generated Node #0,2,1: 48:[53, 29] Operation: 96-67=29 Exploring Operation: 67-53=14, Resulting Numbers: [96, 14] Generated Node #0,2,2: 48:[96, 14] Operation: 67-53=14 Exploring Operation: 53+67=120, Resulting Numbers: [96, 120] Generated Node #0,2,3: 48:[96, 120] Operation: 53+67=120 Exploring Operation: 53+96=149, Resulting Numbers: [67, 149] Generated Node #0,2,4: 48:[67, 149] Operation: 53+96=149 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 48:[53, 29], Operations: ['81-14=67', '96-67=29'] Exploring Operation: 53-29=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 53*29=1537, Resulting Numbers: [1537] 1537,48 unequal: No Solution Exploring Operation: 53+29=82, Resulting Numbers: [82] 82,48 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 #0,2,0 Current State: 48:[67, 43], Operations: ['81-14=67', '96-53=43'] Exploring Operation: 67+43=110, Resulting Numbers: [110] 110,48 unequal: No Solution Exploring Operation: 67*43=2881, Resulting Numbers: [2881] 2881,48 unequal: No Solution Exploring Operation: 67-43=24, Resulting Numbers: [24] 24,48 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 #0,2,2 Current State: 48:[96, 14], Operations: ['81-14=67', '67-53=14'] Exploring Operation: 96+14=110, Resulting Numbers: [110] 110,48 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,48 unequal: No Solution Exploring Operation: 96*14=1344, Resulting Numbers: [1344] 1344,48 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 #0,2,3 Current State: 48:[96, 120], Operations: ['81-14=67', '53+67=120'] Exploring Operation: 96+120=216, Resulting Numbers: [216] 216,48 unequal: No Solution Exploring Operation: 96*120=11520, Resulting Numbers: [11520] 11520,48 unequal: No Solution Exploring Operation: 120-96=24, Resulting Numbers: [24] 24,48 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 #0,2,4 Current State: 48:[67, 149], Operations: ['81-14=67', '53+96=149'] Exploring Operation: 67+149=216, Resulting Numbers: [216] 216,48 unequal: No Solution Exploring Operation: 67*149=9983, Resulting Numbers: [9983] 9983,48 unequal: No Solution Exploring Operation: 149-67=82, Resulting Numbers: [82] 82,48 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: 48:[81, 53, 82], Operations: ['96-14=82'] Exploring Operation: 81-53=28, Resulting Numbers: [82, 28] Generated Node #0,3,0: 48:[82, 28] Operation: 81-53=28 Exploring Operation: 81+82=163, Resulting Numbers: [53, 163] Generated Node #0,3,1: 48:[53, 163] Operation: 81+82=163 Exploring Operation: 82-53=29, Resulting Numbers: [81, 29] Generated Node #0,3,2: 48:[81, 29] Operation: 82-53=29 Exploring Operation: 81+53=134, Resulting Numbers: [82, 134] Generated Node #0,3,3: 48:[82, 134] Operation: 81+53=134 Exploring Operation: 82-81=1, Resulting Numbers: [53, 1] Generated Node #0,3,4: 48:[53, 1] Operation: 82-81=1 Moving to Node #0,4,0 Current State: 48:[53, 1], Operations: ['96-81=15', '15-14=1'] Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,48 unequal: No Solution Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,48 unequal: No Solution Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,48 unequal: No Solution Moving to Node #0,3,4 Current State: 48:[53, 1], Operations: ['96-14=82', '82-81=1'] Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,48 unequal: No Solution Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,48 unequal: No Solution Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,48 unequal: No Solution Moving to Node #0,4,2 Current State: 48:[15, 39], Operations: ['96-81=15', '53-14=39'] Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,48 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,48 unequal: No Solution Moving to Node #0,4,1 Current State: 48:[53, 29], Operations: ['96-81=15', '14+15=29'] Exploring Operation: 53*29=1537, Resulting Numbers: [1537] 1537,48 unequal: No Solution Exploring Operation: 53+29=82, Resulting Numbers: [82] 82,48 unequal: No Solution Exploring Operation: 53-29=24, Resulting Numbers: [24] 24,48 unequal: No Solution Moving to Node #0,4,3 Current State: 48:[14, 38], Operations: ['96-81=15', '53-15=38'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 14*38=532, Resulting Numbers: [532] 532,48 unequal: No Solution Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,48 unequal: No Solution Moving to Node #0,4,4 Current State: 48:[15, 67], Operations: ['96-81=15', '53+14=67'] Exploring Operation: 67-15=52, Resulting Numbers: [52] 52,48 unequal: No Solution Exploring Operation: 15*67=1005, Resulting Numbers: [1005] 1005,48 unequal: No Solution Exploring Operation: 15+67=82, Resulting Numbers: [82] 82,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[14, 68], Operations: ['81-53=28', '96-28=68'] Exploring Operation: 14+68=82, Resulting Numbers: [82] 82,48 unequal: No Solution Exploring Operation: 14*68=952, Resulting Numbers: [952] 952,48 unequal: No Solution Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[28, 82], Operations: ['81-53=28', '96-14=82'] Exploring Operation: 28*82=2296, Resulting Numbers: [2296] 2296,48 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 28+82=110, Resulting Numbers: [110] 110,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[81, 29], Operations: ['96-14=82', '82-53=29'] Exploring Operation: 81*29=2349, Resulting Numbers: [2349] 2349,48 unequal: No Solution Exploring Operation: 81+29=110, Resulting Numbers: [110] 110,48 unequal: No Solution Exploring Operation: 81-29=52, Resulting Numbers: [52] 52,48 unequal: No Solution Moving to Node #0,3,0 Current State: 48:[82, 28], Operations: ['96-14=82', '81-53=28'] Exploring Operation: 82+28=110, Resulting Numbers: [110] 110,48 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 82*28=2296, Resulting Numbers: [2296] 2296,48 unequal: No Solution Moving to Node #0,1,3 Current State: 48:[96, 2], Operations: ['81-53=28', '28/14=2'] Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,48 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,48 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,48 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[81, 53, 14, 96], Operations: [] Exploring Operation: 81-53=28, Resulting Numbers: [14, 96, 28] Generated Node #0,1: 48:[14, 96, 28] Operation: 81-53=28 Moving to Node #0,1 Current State: 48:[14, 96, 28], Operations: ['81-53=28'] Exploring Operation: 28/14=2, Resulting Numbers: [96, 2] Generated Node #0,1,3: 48:[96, 2] Operation: 28/14=2 Moving to Node #0,1,3 Current State: 48:[96, 2], Operations: ['81-53=28', '28/14=2'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.913194
hs_5
sum_heuristic
[ 30, 27, 70, 10 ]
31
[ "70-30=40", "40/10=4", "27+4=31" ]
Current State: 31:[30, 27, 70, 10], Operations: [] Exploring Operation: 70-30=40, Resulting Numbers: [27, 10, 40] Generated Node #2: [27, 10, 40] from Operation: 70-30=40 Current State: 31:[27, 10, 40], Operations: ['70-30=40'] Exploring Operation: 40/10=4, Resulting Numbers: [27, 4] Generated Node #3: [27, 4] from Operation: 40/10=4 Current State: 31:[27, 4], Operations: ['70-30=40', '40/10=4'] Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[30, 27, 70, 10], Operations: [] Exploring Operation: 70-30=40, Resulting Numbers: [27, 10, 40] Generated Node #0,0: 31:[27, 10, 40] Operation: 70-30=40 Exploring Operation: 70/10=7, Resulting Numbers: [30, 27, 7] Generated Node #0,1: 31:[30, 27, 7] Operation: 70/10=7 Exploring Operation: 70-27=43, Resulting Numbers: [30, 10, 43] Generated Node #0,2: 31:[30, 10, 43] Operation: 70-27=43 Moving to Node #0,1 Current State: 31:[30, 27, 7], Operations: ['70/10=7'] Exploring Operation: 30+7=37, Resulting Numbers: [27, 37] Generated Node #0,1,0: 31:[27, 37] Operation: 30+7=37 Exploring Operation: 27+7=34, Resulting Numbers: [30, 34] Generated Node #0,1,1: 31:[30, 34] Operation: 27+7=34 Exploring Operation: 30-7=23, Resulting Numbers: [27, 23] Generated Node #0,1,2: 31:[27, 23] Operation: 30-7=23 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[30, 34], Operations: ['70/10=7', '27+7=34'] Exploring Operation: 34-30=4, Resulting Numbers: [4] 4,31 unequal: No Solution Exploring Operation: 30+34=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 30*34=1020, Resulting Numbers: [1020] 1020,31 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:[27, 37], Operations: ['70/10=7', '30+7=37'] Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,31 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[27, 23], Operations: ['70/10=7', '30-7=23'] Exploring Operation: 27*23=621, Resulting Numbers: [621] 621,31 unequal: No Solution Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,31 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: 31:[27, 10, 40], Operations: ['70-30=40'] Exploring Operation: 40-10=30, Resulting Numbers: [27, 30] Generated Node #0,0,0: 31:[27, 30] Operation: 40-10=30 Exploring Operation: 27+10=37, Resulting Numbers: [40, 37] Generated Node #0,0,1: 31:[40, 37] Operation: 27+10=37 Exploring Operation: 27-10=17, Resulting Numbers: [40, 17] Generated Node #0,0,2: 31:[40, 17] Operation: 27-10=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[27, 30], Operations: ['70-30=40', '40-10=30'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,31 unequal: No Solution Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,31 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:[40, 37], Operations: ['70-30=40', '27+10=37'] Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,31 unequal: No Solution Exploring Operation: 40*37=1480, Resulting Numbers: [1480] 1480,31 unequal: No Solution Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[40, 17], Operations: ['70-30=40', '27-10=17'] Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 40+17=57, Resulting Numbers: [57] 57,31 unequal: No Solution Exploring Operation: 40*17=680, Resulting Numbers: [680] 680,31 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:[30, 10, 43], Operations: ['70-27=43'] Exploring Operation: 43-10=33, Resulting Numbers: [30, 33] Generated Node #0,2,0: 31:[30, 33] Operation: 43-10=33 Exploring Operation: 30-10=20, Resulting Numbers: [43, 20] Generated Node #0,2,1: 31:[43, 20] Operation: 30-10=20 Exploring Operation: 30+10=40, Resulting Numbers: [43, 40] Generated Node #0,2,2: 31:[43, 40] Operation: 30+10=40 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[30, 33], Operations: ['70-27=43', '43-10=33'] Exploring Operation: 30*33=990, Resulting Numbers: [990] 990,31 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 30+33=63, Resulting Numbers: [63] 63,31 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:[43, 40], Operations: ['70-27=43', '30+10=40'] Exploring Operation: 43*40=1720, Resulting Numbers: [1720] 1720,31 unequal: No Solution Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,31 unequal: No Solution Exploring Operation: 43-40=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 #0,2,1 Current State: 31:[43, 20], Operations: ['70-27=43', '30-10=20'] Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,31 unequal: No Solution Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,31 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,31 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
[ 51, 8, 45, 98 ]
84
[ "51+8=59", "45+98=143", "143-59=84" ]
Current State: 84:[51, 8, 45, 98], Operations: [] Exploring Operation: 51+8=59, Resulting Numbers: [45, 98, 59] Generated Node #2: [45, 98, 59] from Operation: 51+8=59 Current State: 84:[45, 98, 59], Operations: ['51+8=59'] Exploring Operation: 45+98=143, Resulting Numbers: [59, 143] Generated Node #3: [59, 143] from Operation: 45+98=143 Current State: 84:[59, 143], Operations: ['51+8=59', '45+98=143'] Exploring Operation: 143-59=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[51, 8, 45, 98], Operations: [] Exploring Operation: 51-8=43, Resulting Numbers: [45, 98, 43] Generated Node #0,0: 84:[45, 98, 43] Operation: 51-8=43 Exploring Operation: 98-8=90, Resulting Numbers: [51, 45, 90] Generated Node #0,1: 84:[51, 45, 90] Operation: 98-8=90 Exploring Operation: 98-51=47, Resulting Numbers: [8, 45, 47] Generated Node #0,2: 84:[8, 45, 47] Operation: 98-51=47 Exploring Operation: 51-45=6, Resulting Numbers: [8, 98, 6] Generated Node #0,3: 84:[8, 98, 6] Operation: 51-45=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[8, 45, 47], Operations: ['98-51=47'] Exploring Operation: 45-8=37, Resulting Numbers: [47, 37] Generated Node #0,2,0: 84:[47, 37] Operation: 45-8=37 Exploring Operation: 45+47=92, Resulting Numbers: [8, 92] Generated Node #0,2,1: 84:[8, 92] Operation: 45+47=92 Exploring Operation: 47-8=39, Resulting Numbers: [45, 39] Generated Node #0,2,2: 84:[45, 39] Operation: 47-8=39 Exploring Operation: 47-45=2, Resulting Numbers: [8, 2] Generated Node #0,2,3: 84:[8, 2] Operation: 47-45=2 Moving to Node #0,2,3 Current State: 84:[8, 2], Operations: ['98-51=47', '47-45=2'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,84 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[45, 39], Operations: ['98-51=47', '47-8=39'] Exploring Operation: 45+39=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[51, 8, 45, 98], Operations: [] Exploring Operation: 98-51=47, Resulting Numbers: [8, 45, 47] Generated Node #0,2: 84:[8, 45, 47] Operation: 98-51=47 Moving to Node #0,2 Current State: 84:[8, 45, 47], Operations: ['98-51=47'] Exploring Operation: 47-8=39, Resulting Numbers: [45, 39] Generated Node #0,2,2: 84:[45, 39] Operation: 47-8=39 Moving to Node #0,2,2 Current State: 84:[45, 39], Operations: ['98-51=47', '47-8=39'] Exploring Operation: 45+39=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 95, 44, 60, 35 ]
26
[ "95-44=51", "60-35=25", "51-25=26" ]
Current State: 26:[95, 44, 60, 35], Operations: [] Exploring Operation: 95-44=51, Resulting Numbers: [60, 35, 51] Generated Node #2: [60, 35, 51] from Operation: 95-44=51 Current State: 26:[60, 35, 51], Operations: ['95-44=51'] Exploring Operation: 60-35=25, Resulting Numbers: [51, 25] Generated Node #3: [51, 25] from Operation: 60-35=25 Current State: 26:[51, 25], Operations: ['95-44=51', '60-35=25'] Exploring Operation: 51-25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[95, 44, 60, 35], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [44, 60, 60] Generated Node #0,0: 26:[44, 60, 60] Operation: 95-35=60 Exploring Operation: 60-44=16, Resulting Numbers: [95, 35, 16] Generated Node #0,1: 26:[95, 35, 16] Operation: 60-44=16 Exploring Operation: 95-60=35, Resulting Numbers: [44, 35, 35] Generated Node #0,2: 26:[44, 35, 35] Operation: 95-60=35 Exploring Operation: 60-35=25, Resulting Numbers: [95, 44, 25] Generated Node #0,3: 26:[95, 44, 25] Operation: 60-35=25 Exploring Operation: 95-44=51, Resulting Numbers: [60, 35, 51] Generated Node #0,4: 26:[60, 35, 51] Operation: 95-44=51 Moving to Node #0,2 Current State: 26:[44, 35, 35], Operations: ['95-60=35'] Exploring Operation: 44-35=9, Resulting Numbers: [35, 9] Generated Node #0,2,0: 26:[35, 9] Operation: 44-35=9 Exploring Operation: 44-35=9, Resulting Numbers: [35, 9] Generated Node #0,2,1: 26:[35, 9] Operation: 44-35=9 Exploring Operation: 35/35=1, Resulting Numbers: [44, 1] Generated Node #0,2,2: 26:[44, 1] Operation: 35/35=1 Exploring Operation: 44+35=79, Resulting Numbers: [35, 79] Generated Node #0,2,3: 26:[35, 79] Operation: 44+35=79 Exploring Operation: 35-35=0, Resulting Numbers: [44, 0] Generated Node #0,2,4: 26:[44, 0] Operation: 35-35=0 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[35, 9], Operations: ['95-60=35', '44-35=9'] Exploring Operation: 35+9=44, Resulting Numbers: [44] 44,26 unequal: No Solution Exploring Operation: 35*9=315, Resulting Numbers: [315] 315,26 unequal: No Solution Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[95, 44, 60, 35], Operations: [] Exploring Operation: 95-60=35, Resulting Numbers: [44, 35, 35] Generated Node #0,2: 26:[44, 35, 35] Operation: 95-60=35 Moving to Node #0,2 Current State: 26:[44, 35, 35], Operations: ['95-60=35'] Exploring Operation: 44-35=9, Resulting Numbers: [35, 9] Generated Node #0,2,0: 26:[35, 9] Operation: 44-35=9 Moving to Node #0,2,0 Current State: 26:[35, 9], Operations: ['95-60=35', '44-35=9'] Exploring Operation: 35-9=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 36, 34, 96, 82 ]
84
[ "36+34=70", "96-82=14", "70+14=84" ]
Current State: 84:[36, 34, 96, 82], Operations: [] Exploring Operation: 36+34=70, Resulting Numbers: [96, 82, 70] Generated Node #2: [96, 82, 70] from Operation: 36+34=70 Current State: 84:[96, 82, 70], Operations: ['36+34=70'] Exploring Operation: 96-82=14, Resulting Numbers: [70, 14] Generated Node #3: [70, 14] from Operation: 96-82=14 Current State: 84:[70, 14], Operations: ['36+34=70', '96-82=14'] Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[36, 34, 96, 82], Operations: [] Exploring Operation: 96-82=14, Resulting Numbers: [36, 34, 14] Generated Node #0,0: 84:[36, 34, 14] Operation: 96-82=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[36, 34, 14], Operations: ['96-82=14'] Exploring Operation: 36-34=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 84:[14, 2] Operation: 36-34=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 84:[14, 2], Operations: ['96-82=14', '36-34=2'] Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 9, 29, 11, 64 ]
66
[ "29-11=18", "18/9=2", "64+2=66" ]
Current State: 66:[9, 29, 11, 64], Operations: [] Exploring Operation: 29-11=18, Resulting Numbers: [9, 64, 18] Generated Node #2: [9, 64, 18] from Operation: 29-11=18 Current State: 66:[9, 64, 18], Operations: ['29-11=18'] Exploring Operation: 18/9=2, Resulting Numbers: [64, 2] Generated Node #3: [64, 2] from Operation: 18/9=2 Current State: 66:[64, 2], Operations: ['29-11=18', '18/9=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[9, 29, 11, 64], Operations: [] Exploring Operation: 29-9=20, Resulting Numbers: [11, 64, 20] Generated Node #0,0: 66:[11, 64, 20] Operation: 29-9=20 Moving to Node #0,0 Current State: 66:[11, 64, 20], Operations: ['29-9=20'] Exploring Operation: 11+20=31, Resulting Numbers: [64, 31] Generated Node #0,0,0: 66:[64, 31] Operation: 11+20=31 Moving to Node #0,0,0 Current State: 66:[64, 31], Operations: ['29-9=20', '11+20=31'] Exploring Operation: 64-31=33, Resulting Numbers: [33] 33,66 unequal: No Solution No solution found.
0
hs_1
mult_heuristic