task_name
stringclasses
6 values
strategy_id
stringclasses
20 values
input_text
stringlengths
6
26
reasoning_trace
stringlengths
11
152
sorting_algorithms
sorting_algorithms:insertion-sort
2, 4, 6, 8, 0
[2,4,6,8,0] ; [2,4,6,8,0] ; [2,4,6,8,0] ; [0,2,4,6,8]
sorting_algorithms
sorting_algorithms:heap-sort
1, 8, 9, 6, 5
[9,8,1,6,5] ; [5,8,1,6,9] ; [8,5,1,6,9] ; [8,6,1,5,9] ; [5,6,1,8,9] ; [6,5,1,8,9] ; [1,5,6,8,9] ; [5,1,6,8,9] ; [1,5,6,8,9]
linear_equation_solving
linear_equation_solving:divide-then-subtract
9x-54=-81
9x-54=-81 ; x+-6=-9 ; x=-9--6 ; x=-3
linear_equation_solving
linear_equation_solving:inverse-ops
4x-12=8
4x-12=8 ; x=(8--12)/4 ; x=20/4 ; x=5
linear_equation_solving
linear_equation_solving:divide-then-subtract
4x+4=28
4x+4=28 ; x+1=7 ; x=7-1 ; x=6
multidigit_addition
multidigit_addition:rounding-decomposition
600+489
round:600+489=1089 ; adjust:1089-0=1089 ; sum=1089
sorting_algorithms
sorting_algorithms:insertion-sort
3, 2, 5, 0, 7
[2,3,5,0,7] ; [2,3,5,0,7] ; [0,2,3,5,7] ; [0,2,3,5,7]
sorting_algorithms
sorting_algorithms:insertion-sort
9, 1, 2, 0, 4
[1,9,2,0,4] ; [1,2,9,0,4] ; [0,1,2,9,4] ; [0,1,2,4,9]
base_conversion
base_conversion:via-binary
n=50,base=2
BINLEN:6 ; CHUNK:0:1 ; CHUNK:1:1 ; CHUNK:2:0 ; CHUNK:3:0 ; CHUNK:4:1 ; CHUNK:5:0 ; OUT:110010
sorting_algorithms
sorting_algorithms:bubble-sort
0, 8, 9, 5, 7
[0,8,5,9,7] ; [0,8,5,7,9] ; [0,5,8,7,9] ; [0,5,7,8,9]
sorting_algorithms
sorting_algorithms:bubble-sort
0, 5, 2, 9, 4
[0,2,5,9,4] ; [0,2,5,4,9] ; [0,2,4,5,9]
sorting_algorithms
sorting_algorithms:insertion-sort
7, 1, 3, 2, 0
[1,7,3,2,0] ; [1,3,7,2,0] ; [1,2,3,7,0] ; [0,1,2,3,7]
base_conversion
base_conversion:via-binary
n=51,base=8
BINLEN:6 ; CHUNK:0:6 ; CHUNK:1:3 ; OUT:63
linear_equation_solving
linear_equation_solving:inverse-ops
7x+49=42
7x+49=42 ; x=(42-49)/7 ; x=-7/7 ; x=-1
base_conversion
base_conversion:decomposition
n=25,base=4
TERM:1*4^2=16 ; TERM:2*4^1=8 ; TERM:1*4^0=1 ; OUT:121
sorting_algorithms
sorting_algorithms:bubble-sort
7, 9, 5, 3, 2
[7,5,9,3,2] ; [7,5,3,9,2] ; [7,5,3,2,9] ; [5,7,3,2,9] ; [5,3,7,2,9] ; [5,3,2,7,9] ; [3,5,2,7,9] ; [3,2,5,7,9] ; [2,3,5,7,9]
sorting_algorithms
sorting_algorithms:selection-sort
2, 6, 9, 7, 0
[0,6,9,7,2] ; [0,2,9,7,6] ; [0,2,6,7,9] ; [0,2,6,7,9]
list_summation
list_summation:right-to-left
9, 4, 1, 6
1+6=7 ; 4+7=11 ; 9+11=20
multidigit_addition
multidigit_addition:right-to-left-carry
718+824
d2:8+4+0=12→w2,c1 ; d1:1+2+1=4→w4,c0 ; d0:7+8+0=15→w5,c1 ; sum=1542
multidigit_addition
multidigit_addition:right-to-left-carry
134+533
d2:4+3+0=7→w7,c0 ; d1:3+3+0=6→w6,c0 ; d0:1+5+0=6→w6,c0 ; sum=667
multidigit_addition
multidigit_addition:rounding-decomposition
162+234
round:170+234=404 ; adjust:404-8=396 ; sum=396
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(3,0) ; G=(4,1)
D:(4,0) ; R:(4,1)
base_conversion
base_conversion:repeated-division
n=87,base=16
DIV:87/16=5,r:7 ; DIV:5/16=0,r:5 ; OUT:57
sorting_algorithms
sorting_algorithms:insertion-sort
2, 7, 3, 8, 1
[2,7,3,8,1] ; [2,3,7,8,1] ; [2,3,7,8,1] ; [1,2,3,7,8]
list_summation
list_summation:right-to-left
6, 6, 6, 0
6+0=6 ; 6+6=12 ; 6+12=18
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(4,1) ; G=(5,5)
D:(5,1) ; R:(5,2) ; R:(5,3) ; R:(5,4) ; R:(5,5)
sorting_algorithms
sorting_algorithms:insertion-sort
1, 8, 3, 7, 5
[1,8,3,7,5] ; [1,3,8,7,5] ; [1,3,7,8,5] ; [1,3,5,7,8]
list_summation
list_summation:left-to-right
3, 7, 5, 3
3+7=10 ; 10+5=15 ; 15+3=18
linear_equation_solving
linear_equation_solving:subtract-then-divide
4x+0=12
4x+0=12 ; 4x=12 ; x=3
linear_equation_solving
linear_equation_solving:subtract-then-divide
6x+54=48
6x+54=48 ; 6x=-6 ; x=-1
linear_equation_solving
linear_equation_solving:divide-then-subtract
6x-6=24
6x-6=24 ; x+-1=4 ; x=4--1 ; x=5
base_conversion
base_conversion:via-binary
n=16,base=16
BINLEN:5 ; CHUNK:0:1 ; CHUNK:1:0 ; OUT:10
base_conversion
base_conversion:via-binary
n=93,base=2
BINLEN:7 ; CHUNK:0:1 ; CHUNK:1:0 ; CHUNK:2:1 ; CHUNK:3:1 ; CHUNK:4:1 ; CHUNK:5:0 ; CHUNK:6:1 ; OUT:1011101
list_summation
list_summation:left-to-right
2, 6, 4, 8
2+6=8 ; 8+4=12 ; 12+8=20
list_summation
list_summation:left-to-right
0, 3, 8, 9
0+3=3 ; 3+8=11 ; 11+9=20
linear_equation_solving
linear_equation_solving:divide-then-subtract
3x+0=21
3x+0=21 ; x+0=7 ; x=7-0 ; x=7
base_conversion
base_conversion:via-binary
n=255,base=2
BINLEN:8 ; CHUNK:0:1 ; CHUNK:1:1 ; CHUNK:2:1 ; CHUNK:3:1 ; CHUNK:4:1 ; CHUNK:5:1 ; CHUNK:6:1 ; CHUNK:7:1 ; OUT:11111111
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(1,3) ; G=(2,5)
R:(1,4) ; R:(1,5) ; D:(2,5)
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(2,4) ; G=(5,5)
R:(2,5) ; D:(3,5) ; D:(4,5) ; D:(5,5)
base_conversion
base_conversion:decomposition
n=200,base=16
TERM:12*16^1=192 ; TERM:8*16^0=8 ; OUT:C8
multidigit_addition
multidigit_addition:left-to-right-partials
271+120
p100:200+100=300 ; p10:70+20=90 ; p1:1+0=1 ; sum=300+90+1=391
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(0,2) ; G=(3,5)
R:(0,3) ; R:(0,4) ; R:(0,5) ; D:(1,5) ; D:(2,5) ; D:(3,5)
multidigit_addition
multidigit_addition:right-to-left-carry
939+240
d2:9+0+0=9→w9,c0 ; d1:3+4+0=7→w7,c0 ; d0:9+2+0=11→w1,c1 ; sum=1179
sorting_algorithms
sorting_algorithms:bubble-sort
3, 8, 2, 1, 9
[3,2,8,1,9] ; [3,2,1,8,9] ; [2,3,1,8,9] ; [2,1,3,8,9] ; [1,2,3,8,9]
linear_equation_solving
linear_equation_solving:subtract-then-divide
8x-24=-56
8x-24=-56 ; 8x=-32 ; x=-4
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(0,4) ; G=(3,5)
R:(0,5) ; D:(1,5) ; D:(2,5) ; D:(3,5)
multidigit_addition
multidigit_addition:left-to-right-partials
803+386
p100:800+300=1100 ; p10:0+80=80 ; p1:3+6=9 ; sum=1100+80+9=1189
base_conversion
base_conversion:repeated-division
n=55,base=2
DIV:55/2=27,r:1 ; DIV:27/2=13,r:1 ; DIV:13/2=6,r:1 ; DIV:6/2=3,r:0 ; DIV:3/2=1,r:1 ; DIV:1/2=0,r:1 ; OUT:110111
multidigit_addition
multidigit_addition:rounding-decomposition
967+584
round:970+584=1554 ; adjust:1554-3=1551 ; sum=1551
multidigit_addition
multidigit_addition:right-to-left-carry
633+585
d2:3+5+0=8→w8,c0 ; d1:3+8+0=11→w1,c1 ; d0:6+5+1=12→w2,c1 ; sum=1218
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(3,3) ; G=(4,4)
R:(3,4) ; D:(4,4)
linear_equation_solving
linear_equation_solving:subtract-then-divide
8x-8=-40
8x-8=-40 ; 8x=-32 ; x=-4
list_summation
list_summation:pairwise
8, 3, 9, 0
8+3=11 ; 9+0=9 ; 11+9=20
multidigit_addition
multidigit_addition:left-to-right-partials
122+836
p100:100+800=900 ; p10:20+30=50 ; p1:2+6=8 ; sum=900+50+8=958
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(0,2) ; G=(2,4)
R:(0,3) ; R:(0,4) ; D:(1,4) ; D:(2,4)
linear_equation_solving
linear_equation_solving:divide-then-subtract
2x-12=4
2x-12=4 ; x+-6=2 ; x=2--6 ; x=8
list_summation
list_summation:right-to-left
0, 0, 1, 3
1+3=4 ; 0+4=4 ; 0+4=4
sorting_algorithms
sorting_algorithms:selection-sort
8, 5, 0, 4, 2
[0,5,8,4,2] ; [0,2,8,4,5] ; [0,2,4,8,5] ; [0,2,4,5,8]
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(0,3) ; G=(2,5)
R:(0,4) ; D:(1,4) ; R:(1,5) ; D:(2,5)
list_summation
list_summation:right-to-left
1, 6, 3, 2
3+2=5 ; 6+5=11 ; 1+11=12
linear_equation_solving
linear_equation_solving:subtract-then-divide
6x-24=30
6x-24=30 ; 6x=54 ; x=9
multidigit_addition
multidigit_addition:left-to-right-partials
728+847
p100:700+800=1500 ; p10:20+40=60 ; p1:8+7=15 ; sum=1500+60+15=1575
sorting_algorithms
sorting_algorithms:heap-sort
9, 7, 3, 1, 6
[6,7,3,1,9] ; [7,6,3,1,9] ; [1,6,3,7,9] ; [6,1,3,7,9] ; [3,1,6,7,9] ; [1,3,6,7,9]
linear_equation_solving
linear_equation_solving:inverse-ops
6x+48=36
6x+48=36 ; x=(36-48)/6 ; x=-12/6 ; x=-2
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(0,3) ; G=(3,5)
R:(0,4) ; D:(1,4) ; R:(1,5) ; D:(2,5) ; D:(3,5)
list_summation
list_summation:pairwise
3, 7, 7, 7
3+7=10 ; 7+7=14 ; 10+14=24
linear_equation_solving
linear_equation_solving:subtract-then-divide
7x-7=-28
7x-7=-28 ; 7x=-21 ; x=-3
base_conversion
base_conversion:repeated-division
n=65,base=2
DIV:65/2=32,r:1 ; DIV:32/2=16,r:0 ; DIV:16/2=8,r:0 ; DIV:8/2=4,r:0 ; DIV:4/2=2,r:0 ; DIV:2/2=1,r:0 ; DIV:1/2=0,r:1 ; OUT:1000001
multidigit_addition
multidigit_addition:rounding-decomposition
239+394
round:240+394=634 ; adjust:634-1=633 ; sum=633
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(0,2) ; G=(3,3)
D:(1,2) ; D:(2,2) ; D:(3,2) ; R:(3,3)
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(2,1) ; G=(4,2)
R:(2,2) ; D:(3,2) ; D:(4,2)
linear_equation_solving
linear_equation_solving:inverse-ops
6x+18=-36
6x+18=-36 ; x=(-36-18)/6 ; x=-54/6 ; x=-9
list_summation
list_summation:pairwise
3, 0, 0, 5
3+0=3 ; 0+5=5 ; 3+5=8
multidigit_addition
multidigit_addition:right-to-left-carry
750+701
d2:0+1+0=1→w1,c0 ; d1:5+0+0=5→w5,c0 ; d0:7+7+0=14→w4,c1 ; sum=1451
list_summation
list_summation:pairwise
5, 6, 0, 8
5+6=11 ; 0+8=8 ; 11+8=19
base_conversion
base_conversion:via-binary
n=129,base=8
BINLEN:8 ; CHUNK:0:2 ; CHUNK:1:0 ; CHUNK:2:1 ; OUT:201
sorting_algorithms
sorting_algorithms:selection-sort
2, 8, 1, 4, 9
[1,8,2,4,9] ; [1,2,8,4,9] ; [1,2,4,8,9] ; [1,2,4,8,9]
sorting_algorithms
sorting_algorithms:heap-sort
3, 8, 6, 7, 4
[8,3,6,7,4] ; [8,7,6,3,4] ; [4,7,6,3,8] ; [7,4,6,3,8] ; [3,4,6,7,8] ; [6,4,3,7,8] ; [3,4,6,7,8] ; [4,3,6,7,8] ; [3,4,6,7,8]
list_summation
list_summation:right-to-left
3, 7, 7, 7
7+7=14 ; 7+14=21 ; 3+21=24
base_conversion
base_conversion:via-binary
n=41,base=4
BINLEN:6 ; CHUNK:0:2 ; CHUNK:1:2 ; CHUNK:2:1 ; OUT:221
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(0,2) ; G=(3,5)
D:(1,2) ; D:(2,2) ; D:(3,2) ; R:(3,3) ; R:(3,4) ; R:(3,5)
linear_equation_solving
linear_equation_solving:inverse-ops
3x-21=6
3x-21=6 ; x=(6--21)/3 ; x=27/3 ; x=9
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(3,0) ; G=(4,2)
R:(3,1) ; R:(3,2) ; D:(4,2)
base_conversion
base_conversion:decomposition
n=43,base=8
TERM:5*8^1=40 ; TERM:3*8^0=3 ; OUT:53
linear_equation_solving
linear_equation_solving:subtract-then-divide
5x-30=5
5x-30=5 ; 5x=35 ; x=7
linear_equation_solving
linear_equation_solving:inverse-ops
2x-8=-4
2x-8=-4 ; x=(-4--8)/2 ; x=4/2 ; x=2
multidigit_addition
multidigit_addition:left-to-right-partials
249+773
p100:200+700=900 ; p10:40+70=110 ; p1:9+3=12 ; sum=900+110+12=1022
multidigit_addition
multidigit_addition:rounding-decomposition
213+442
round:220+442=662 ; adjust:662-7=655 ; sum=655
multidigit_addition
multidigit_addition:right-to-left-carry
799+558
d2:9+8+0=17→w7,c1 ; d1:9+5+1=15→w5,c1 ; d0:7+5+1=13→w3,c1 ; sum=1357
list_summation
list_summation:left-to-right
4, 2, 9, 4
4+2=6 ; 6+9=15 ; 15+4=19
multidigit_addition
multidigit_addition:left-to-right-partials
333+213
p100:300+200=500 ; p10:30+10=40 ; p1:3+3=6 ; sum=500+40+6=546
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(1,2) ; G=(5,5)
R:(1,3) ; D:(2,3) ; R:(2,4) ; D:(3,4) ; R:(3,5) ; D:(4,5) ; D:(5,5)
multidigit_addition
multidigit_addition:left-to-right-partials
191+576
p100:100+500=600 ; p10:90+70=160 ; p1:1+6=7 ; sum=600+160+7=767
sorting_algorithms
sorting_algorithms:heap-sort
1, 9, 0, 4, 7
[9,1,0,4,7] ; [9,7,0,4,1] ; [1,7,0,4,9] ; [7,1,0,4,9] ; [7,4,0,1,9] ; [1,4,0,7,9] ; [4,1,0,7,9] ; [0,1,4,7,9] ; [1,0,4,7,9] ; [0,1,4,7,9]
sorting_algorithms
sorting_algorithms:selection-sort
8, 4, 7, 9, 2
[2,4,7,9,8] ; [2,4,7,9,8] ; [2,4,7,9,8] ; [2,4,7,8,9]
list_summation
list_summation:pairwise
4, 3, 8, 5
4+3=7 ; 8+5=13 ; 7+13=20
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(4,1) ; G=(5,4)
D:(5,1) ; R:(5,2) ; R:(5,3) ; R:(5,4)
sorting_algorithms
sorting_algorithms:insertion-sort
8, 7, 0, 6, 2
[7,8,0,6,2] ; [0,7,8,6,2] ; [0,6,7,8,2] ; [0,2,6,7,8]
sorting_algorithms
sorting_algorithms:selection-sort
6, 8, 9, 0, 4
[0,8,9,6,4] ; [0,4,9,6,8] ; [0,4,6,9,8] ; [0,4,6,8,9]
base_conversion
base_conversion:decomposition
n=10,base=4
TERM:2*4^1=8 ; TERM:2*4^0=2 ; OUT:22