task_name
stringclasses
6 values
strategy_id
stringclasses
20 values
input_text
stringlengths
6
26
reasoning_trace
stringlengths
11
152
linear_equation_solving
linear_equation_solving:subtract-then-divide
2x+2=-8
2x+2=-8 ; 2x=-10 ; x=-5
base_conversion
base_conversion:repeated-division
n=222,base=16
DIV:222/16=13,r:14 ; DIV:13/16=0,r:13 ; OUT:DE
base_conversion
base_conversion:repeated-division
n=71,base=8
DIV:71/8=8,r:7 ; DIV:8/8=1,r:0 ; DIV:1/8=0,r:1 ; OUT:107
linear_equation_solving
linear_equation_solving:inverse-ops
3x+0=3
3x+0=3 ; x=(3-0)/3 ; x=3/3 ; x=1
linear_equation_solving
linear_equation_solving:inverse-ops
4x-32=-60
4x-32=-60 ; x=(-60--32)/4 ; x=-28/4 ; x=-7
linear_equation_solving
linear_equation_solving:subtract-then-divide
3x+27=54
3x+27=54 ; 3x=27 ; x=9
multidigit_addition
multidigit_addition:rounding-decomposition
730+986
round:730+986=1716 ; adjust:1716-0=1716 ; sum=1716
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(0,4) ; G=(1,5)
D:(1,4) ; R:(1,5)
list_summation
list_summation:left-to-right
5, 9, 4, 0
5+9=14 ; 14+4=18 ; 18+0=18
list_summation
list_summation:right-to-left
6, 0, 8, 6
8+6=14 ; 0+14=14 ; 6+14=20
linear_equation_solving
linear_equation_solving:inverse-ops
4x+0=12
4x+0=12 ; x=(12-0)/4 ; x=12/4 ; x=3
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(0,3) ; G=(4,5)
R:(0,4) ; D:(1,4) ; R:(1,5) ; D:(2,5) ; D:(3,5) ; D:(4,5)
multidigit_addition
multidigit_addition:right-to-left-carry
415+902
d2:5+2+0=7→w7,c0 ; d1:1+0+0=1→w1,c0 ; d0:4+9+0=13→w3,c1 ; sum=1317
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(0,3) ; G=(4,4)
D:(1,3) ; D:(2,3) ; D:(3,3) ; D:(4,3) ; R:(4,4)
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(2,2) ; G=(4,4)
R:(2,3) ; R:(2,4) ; D:(3,4) ; D:(4,4)
base_conversion
base_conversion:via-binary
n=158,base=2
BINLEN:8 ; CHUNK:0:1 ; CHUNK:1:0 ; CHUNK:2:0 ; CHUNK:3:1 ; CHUNK:4:1 ; CHUNK:5:1 ; CHUNK:6:1 ; CHUNK:7:0 ; OUT:10011110
list_summation
list_summation:left-to-right
9, 3, 7, 8
9+3=12 ; 12+7=19 ; 19+8=27
linear_equation_solving
linear_equation_solving:divide-then-subtract
2x+14=22
2x+14=22 ; x+7=11 ; x=11-7 ; x=4
base_conversion
base_conversion:repeated-division
n=254,base=16
DIV:254/16=15,r:14 ; DIV:15/16=0,r:15 ; OUT:FE
base_conversion
base_conversion:via-binary
n=99,base=4
BINLEN:7 ; CHUNK:0:1 ; CHUNK:1:2 ; CHUNK:2:0 ; CHUNK:3:3 ; OUT:1203
linear_equation_solving
linear_equation_solving:divide-then-subtract
5x+20=25
5x+20=25 ; x+4=5 ; x=5-4 ; x=1
list_summation
list_summation:right-to-left
6, 7, 4, 5
4+5=9 ; 7+9=16 ; 6+16=22
multidigit_addition
multidigit_addition:rounding-decomposition
929+796
round:930+796=1726 ; adjust:1726-1=1725 ; sum=1725
multidigit_addition
multidigit_addition:left-to-right-partials
578+481
p100:500+400=900 ; p10:70+80=150 ; p1:8+1=9 ; sum=900+150+9=1059
list_summation
list_summation:right-to-left
6, 3, 7, 3
7+3=10 ; 3+10=13 ; 6+13=19
list_summation
list_summation:right-to-left
3, 3, 0, 6
0+6=6 ; 3+6=9 ; 3+9=12
sorting_algorithms
sorting_algorithms:heap-sort
6, 7, 4, 0, 2
[7,6,4,0,2] ; [2,6,4,0,7] ; [6,2,4,0,7] ; [0,2,4,6,7] ; [4,2,0,6,7] ; [0,2,4,6,7] ; [2,0,4,6,7] ; [0,2,4,6,7]
linear_equation_solving
linear_equation_solving:subtract-then-divide
4x-20=16
4x-20=16 ; 4x=36 ; x=9
sorting_algorithms
sorting_algorithms:bubble-sort
0, 4, 6, 3, 7
[0,4,3,6,7] ; [0,3,4,6,7]
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)
base_conversion
base_conversion:repeated-division
n=127,base=16
DIV:127/16=7,r:15 ; DIV:7/16=0,r:7 ; OUT:7F
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(2,2) ; G=(3,3)
D:(3,2) ; R:(3,3)
linear_equation_solving
linear_equation_solving:inverse-ops
8x-40=-64
8x-40=-64 ; x=(-64--40)/8 ; x=-24/8 ; x=-3
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(3,2) ; G=(4,5)
R:(3,3) ; D:(4,3) ; R:(4,4) ; R:(4,5)
list_summation
list_summation:left-to-right
6, 2, 5, 2
6+2=8 ; 8+5=13 ; 13+2=15
base_conversion
base_conversion:via-binary
n=217,base=2
BINLEN:8 ; CHUNK:0:1 ; CHUNK:1:1 ; CHUNK:2:0 ; CHUNK:3:1 ; CHUNK:4:1 ; CHUNK:5:0 ; CHUNK:6:0 ; CHUNK:7:1 ; OUT:11011001
list_summation
list_summation:left-to-right
9, 9, 5, 0
9+9=18 ; 18+5=23 ; 23+0=23
base_conversion
base_conversion:decomposition
n=148,base=16
TERM:9*16^1=144 ; TERM:4*16^0=4 ; OUT:94
base_conversion
base_conversion:via-binary
n=74,base=8
BINLEN:7 ; CHUNK:0:1 ; CHUNK:1:1 ; CHUNK:2:2 ; OUT:112
list_summation
list_summation:right-to-left
7, 6, 8, 5
8+5=13 ; 6+13=19 ; 7+19=26
linear_equation_solving
linear_equation_solving:subtract-then-divide
8x+64=40
8x+64=40 ; 8x=-24 ; x=-3
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(4,4) ; G=(5,5)
R:(4,5) ; D:(5,5)
sorting_algorithms
sorting_algorithms:insertion-sort
2, 4, 7, 5, 0
[2,4,7,5,0] ; [2,4,7,5,0] ; [2,4,5,7,0] ; [0,2,4,5,7]
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(1,3) ; G=(4,5)
R:(1,4) ; R:(1,5) ; D:(2,5) ; D:(3,5) ; D:(4,5)
linear_equation_solving
linear_equation_solving:divide-then-subtract
7x-35=-56
7x-35=-56 ; x+-5=-8 ; x=-8--5 ; x=-3
linear_equation_solving
linear_equation_solving:subtract-then-divide
4x+12=36
4x+12=36 ; 4x=24 ; x=6
list_summation
list_summation:right-to-left
1, 5, 6, 8
6+8=14 ; 5+14=19 ; 1+19=20
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(0,0) ; G=(2,3)
R:(0,1) ; R:(0,2) ; R:(0,3) ; D:(1,3) ; D:(2,3)
list_summation
list_summation:right-to-left
5, 5, 0, 6
0+6=6 ; 5+6=11 ; 5+11=16
list_summation
list_summation:left-to-right
4, 7, 2, 1
4+7=11 ; 11+2=13 ; 13+1=14
list_summation
list_summation:right-to-left
4, 5, 4, 1
4+1=5 ; 5+5=10 ; 4+10=14
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(2,1) ; G=(5,5)
R:(2,2) ; R:(2,3) ; R:(2,4) ; R:(2,5) ; D:(3,5) ; D:(4,5) ; D:(5,5)
multidigit_addition
multidigit_addition:right-to-left-carry
531+510
d2:1+0+0=1→w1,c0 ; d1:3+1+0=4→w4,c0 ; d0:5+5+0=10→w0,c1 ; sum=1041
list_summation
list_summation:pairwise
4, 1, 2, 7
4+1=5 ; 2+7=9 ; 5+9=14
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(0,1) ; G=(3,2)
R:(0,2) ; D:(1,2) ; D:(2,2) ; D:(3,2)
linear_equation_solving
linear_equation_solving:inverse-ops
9x-54=-18
9x-54=-18 ; x=(-18--54)/9 ; x=36/9 ; x=4
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(1,3) ; G=(2,5)
R:(1,4) ; D:(2,4) ; R:(2,5)
linear_equation_solving
linear_equation_solving:inverse-ops
9x+36=36
9x+36=36 ; x=(36-36)/9 ; x=0/9 ; x=0
sorting_algorithms
sorting_algorithms:merge-sort
4, 9, 8, 3, 2
[4,9,3,8,2] ; [3,4,8,9,2] ; [2,3,4,8,9]
multidigit_addition
multidigit_addition:right-to-left-carry
979+351
d2:9+1+0=10→w0,c1 ; d1:7+5+1=13→w3,c1 ; d0:9+3+1=13→w3,c1 ; sum=1330
linear_equation_solving
linear_equation_solving:inverse-ops
9x-54=-108
9x-54=-108 ; x=(-108--54)/9 ; x=-54/9 ; x=-6
list_summation
list_summation:left-to-right
8, 5, 8, 6
8+5=13 ; 13+8=21 ; 21+6=27
linear_equation_solving
linear_equation_solving:subtract-then-divide
3x+6=33
3x+6=33 ; 3x=27 ; x=9
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(3,4) ; G=(4,5)
R:(3,5) ; D:(4,5)
linear_equation_solving
linear_equation_solving:divide-then-subtract
5x-5=-30
5x-5=-30 ; x+-1=-6 ; x=-6--1 ; x=-5
multidigit_addition
multidigit_addition:rounding-decomposition
999+576
round:1000+576=1576 ; adjust:1576-1=1575 ; sum=1575
list_summation
list_summation:right-to-left
2, 6, 3, 4
3+4=7 ; 6+7=13 ; 2+13=15
linear_equation_solving
linear_equation_solving:divide-then-subtract
2x-14=-20
2x-14=-20 ; x+-7=-10 ; x=-10--7 ; x=-3
multidigit_addition
multidigit_addition:right-to-left-carry
819+540
d2:9+0+0=9→w9,c0 ; d1:1+4+0=5→w5,c0 ; d0:8+5+0=13→w3,c1 ; sum=1359
linear_equation_solving
linear_equation_solving:subtract-then-divide
5x+35=20
5x+35=20 ; 5x=-15 ; x=-3
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(4,1) ; G=(5,4)
R:(4,2) ; R:(4,3) ; R:(4,4) ; D:(5,4)
multidigit_addition
multidigit_addition:rounding-decomposition
810+361
round:810+361=1171 ; adjust:1171-0=1171 ; sum=1171
list_summation
list_summation:right-to-left
4, 9, 1, 6
1+6=7 ; 9+7=16 ; 4+16=20
base_conversion
base_conversion:decomposition
n=140,base=8
TERM:2*8^2=128 ; TERM:1*8^1=8 ; TERM:4*8^0=4 ; OUT:214
sorting_algorithms
sorting_algorithms:heap-sort
5, 6, 3, 0, 1
[6,5,3,0,1] ; [1,5,3,0,6] ; [5,1,3,0,6] ; [0,1,3,5,6] ; [3,1,0,5,6] ; [0,1,3,5,6] ; [1,0,3,5,6] ; [0,1,3,5,6]
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(2,4) ; G=(3,5)
D:(3,4) ; R:(3,5)
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(1,4) ; G=(2,5)
R:(1,5) ; D:(2,5)
list_summation
list_summation:right-to-left
8, 0, 0, 6
0+6=6 ; 0+6=6 ; 8+6=14
linear_equation_solving
linear_equation_solving:divide-then-subtract
6x+36=60
6x+36=60 ; x+6=10 ; x=10-6 ; x=4
sorting_algorithms
sorting_algorithms:merge-sort
9, 4, 3, 1, 7
[4,9,3,1,7] ; [4,9,1,3,7] ; [1,3,4,9,7] ; [1,3,4,7,9]
list_summation
list_summation:pairwise
2, 6, 1, 2
2+6=8 ; 1+2=3 ; 8+3=11
sorting_algorithms
sorting_algorithms:selection-sort
8, 6, 3, 4, 0
[0,6,3,4,8] ; [0,3,6,4,8] ; [0,3,4,6,8] ; [0,3,4,6,8]
base_conversion
base_conversion:repeated-division
n=137,base=8
DIV:137/8=17,r:1 ; DIV:17/8=2,r:1 ; DIV:2/8=0,r:2 ; OUT:211
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(4,4) ; G=(5,5)
R:(4,5) ; D:(5,5)
linear_equation_solving
linear_equation_solving:inverse-ops
2x-8=-12
2x-8=-12 ; x=(-12--8)/2 ; x=-4/2 ; x=-2
multidigit_addition
multidigit_addition:left-to-right-partials
103+683
p100:100+600=700 ; p10:0+80=80 ; p1:3+3=6 ; sum=700+80+6=786
list_summation
list_summation:right-to-left
0, 8, 8, 5
8+5=13 ; 8+13=21 ; 0+21=21
multidigit_addition
multidigit_addition:left-to-right-partials
146+259
p100:100+200=300 ; p10:40+50=90 ; p1:6+9=15 ; sum=300+90+15=405
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(4,1) ; G=(5,5)
R:(4,2) ; R:(4,3) ; R:(4,4) ; R:(4,5) ; D:(5,5)
sorting_algorithms
sorting_algorithms:merge-sort
8, 7, 4, 9, 5
[7,8,4,9,5] ; [4,7,8,9,5] ; [4,5,7,8,9]
sorting_algorithms
sorting_algorithms:heap-sort
6, 9, 4, 0, 2
[9,6,4,0,2] ; [2,6,4,0,9] ; [6,2,4,0,9] ; [0,2,4,6,9] ; [4,2,0,6,9] ; [0,2,4,6,9] ; [2,0,4,6,9] ; [0,2,4,6,9]
sorting_algorithms
sorting_algorithms:merge-sort
7, 9, 4, 2, 1
[7,9,2,4,1] ; [2,4,7,9,1] ; [1,2,4,7,9]
list_summation
list_summation:right-to-left
4, 5, 3, 3
3+3=6 ; 5+6=11 ; 4+11=15
base_conversion
base_conversion:via-binary
n=125,base=8
BINLEN:7 ; CHUNK:0:1 ; CHUNK:1:7 ; CHUNK:2:5 ; OUT:175
base_conversion
base_conversion:via-binary
n=244,base=2
BINLEN:8 ; CHUNK:0:1 ; CHUNK:1:1 ; CHUNK:2:1 ; CHUNK:3:1 ; CHUNK:4:0 ; CHUNK:5:1 ; CHUNK:6:0 ; CHUNK:7:0 ; OUT:11110100
multidigit_addition
multidigit_addition:right-to-left-carry
764+555
d2:4+5+0=9→w9,c0 ; d1:6+5+0=11→w1,c1 ; d0:7+5+1=13→w3,c1 ; sum=1319
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(2,0) ; G=(3,3)
R:(2,1) ; R:(2,2) ; R:(2,3) ; D:(3,3)
base_conversion
base_conversion:decomposition
n=19,base=16
TERM:1*16^1=16 ; TERM:3*16^0=3 ; OUT:13
list_summation
list_summation:pairwise
6, 4, 9, 3
6+4=10 ; 9+3=12 ; 10+12=22
sorting_algorithms
sorting_algorithms:merge-sort
9, 1, 2, 6, 4
[1,9,2,6,4] ; [1,2,6,9,4] ; [1,2,4,6,9]