task_name stringclasses 6
values | strategy_id stringclasses 20
values | input_text stringlengths 6 26 | reasoning_trace stringlengths 11 152 |
|---|---|---|---|
multidigit_addition | multidigit_addition:right-to-left-carry | 299+223 | d2:9+3+0=12→w2,c1 ; d1:9+2+1=12→w2,c1 ; d0:2+2+1=5→w5,c0 ; sum=522 |
grid_pathfinding | grid_pathfinding:right-first | grid=6 ; S=(2,4) ; G=(4,5) | R:(2,5) ; D:(3,5) ; D:(4,5) |
sorting_algorithms | sorting_algorithms:heap-sort | 3, 0, 5, 1, 9 | [3,9,5,1,0] ; [9,3,5,1,0] ; [0,3,5,1,9] ; [5,3,0,1,9] ; [1,3,0,5,9] ; [3,1,0,5,9] ; [0,1,3,5,9] ; [1,0,3,5,9] ; [0,1,3,5,9] |
linear_equation_solving | linear_equation_solving:inverse-ops | 6x-36=-18 | 6x-36=-18 ; x=(-18--36)/6 ; x=18/6 ; x=3 |
base_conversion | base_conversion:repeated-division | n=104,base=8 | DIV:104/8=13,r:0 ; DIV:13/8=1,r:5 ; DIV:1/8=0,r:1 ; OUT:150 |
grid_pathfinding | grid_pathfinding:alternating | grid=6 ; S=(2,0) ; G=(5,5) | R:(2,1) ; D:(3,1) ; R:(3,2) ; D:(4,2) ; R:(4,3) ; D:(5,3) ; R:(5,4) ; R:(5,5) |
list_summation | list_summation:right-to-left | 3, 9, 4, 6 | 4+6=10 ; 9+10=19 ; 3+19=22 |
linear_equation_solving | linear_equation_solving:divide-then-subtract | 4x+12=24 | 4x+12=24 ; x+3=6 ; x=6-3 ; x=3 |
list_summation | list_summation:right-to-left | 2, 7, 3, 5 | 3+5=8 ; 7+8=15 ; 2+15=17 |
base_conversion | base_conversion:decomposition | n=208,base=8 | TERM:3*8^2=192 ; TERM:2*8^1=16 ; TERM:0*8^0=0 ; OUT:320 |
base_conversion | base_conversion:via-binary | n=173,base=2 | BINLEN:8 ; CHUNK:0:1 ; CHUNK:1:0 ; CHUNK:2:1 ; CHUNK:3:0 ; CHUNK:4:1 ; CHUNK:5:1 ; CHUNK:6:0 ; CHUNK:7:1 ; OUT:10101101 |
linear_equation_solving | linear_equation_solving:divide-then-subtract | 7x+63=0 | 7x+63=0 ; x+9=0 ; x=0-9 ; x=-9 |
base_conversion | base_conversion:via-binary | n=162,base=2 | BINLEN:8 ; CHUNK:0:1 ; CHUNK:1:0 ; CHUNK:2:1 ; CHUNK:3:0 ; CHUNK:4:0 ; CHUNK:5:0 ; CHUNK:6:1 ; CHUNK:7:0 ; OUT:10100010 |
linear_equation_solving | linear_equation_solving:inverse-ops | 7x+42=14 | 7x+42=14 ; x=(14-42)/7 ; x=-28/7 ; x=-4 |
sorting_algorithms | sorting_algorithms:selection-sort | 1, 2, 3, 0, 8 | [0,2,3,1,8] ; [0,1,3,2,8] ; [0,1,2,3,8] ; [0,1,2,3,8] |
base_conversion | base_conversion:decomposition | n=22,base=16 | TERM:1*16^1=16 ; TERM:6*16^0=6 ; OUT:16 |
grid_pathfinding | grid_pathfinding:alternating | grid=6 ; S=(2,3) ; G=(3,4) | R:(2,4) ; D:(3,4) |
linear_equation_solving | linear_equation_solving:subtract-then-divide | 4x-20=-52 | 4x-20=-52 ; 4x=-32 ; x=-8 |
sorting_algorithms | sorting_algorithms:heap-sort | 1, 7, 6, 0, 9 | [1,9,6,0,7] ; [9,1,6,0,7] ; [9,7,6,0,1] ; [1,7,6,0,9] ; [7,1,6,0,9] ; [0,1,6,7,9] ; [6,1,0,7,9] ; [0,1,6,7,9] ; [1,0,6,7,9] ; [0,1,6,7,9] |
base_conversion | base_conversion:repeated-division | n=244,base=2 | DIV:244/2=122,r:0 ; DIV:122/2=61,r:0 ; DIV:61/2=30,r:1 ; DIV:30/2=15,r:0 ; DIV:15/2=7,r:1 ; DIV:7/2=3,r:1 ; DIV:3/2=1,r:1 ; DIV:1/2=0,r:1 ; OUT:11110100 |
list_summation | list_summation:pairwise | 6, 6, 3, 6 | 6+6=12 ; 3+6=9 ; 12+9=21 |
grid_pathfinding | grid_pathfinding:down-first | grid=6 ; S=(3,1) ; G=(4,3) | D:(4,1) ; R:(4,2) ; R:(4,3) |
sorting_algorithms | sorting_algorithms:merge-sort | 0, 5, 6, 1, 2 | [0,5,1,6,2] ; [0,1,5,6,2] ; [0,1,2,5,6] |
sorting_algorithms | sorting_algorithms:selection-sort | 9, 4, 8, 5, 6 | [4,9,8,5,6] ; [4,5,8,9,6] ; [4,5,6,9,8] ; [4,5,6,8,9] |
list_summation | list_summation:pairwise | 7, 0, 6, 1 | 7+0=7 ; 6+1=7 ; 7+7=14 |
base_conversion | base_conversion:via-binary | n=88,base=16 | BINLEN:7 ; CHUNK:0:5 ; CHUNK:1:8 ; OUT:58 |
sorting_algorithms | sorting_algorithms:merge-sort | 6, 1, 9, 4, 3 | [1,6,9,4,3] ; [1,6,4,9,3] ; [1,4,6,9,3] ; [1,3,4,6,9] |
multidigit_addition | multidigit_addition:left-to-right-partials | 560+584 | p100:500+500=1000 ; p10:60+80=140 ; p1:0+4=4 ; sum=1000+140+4=1144 |
sorting_algorithms | sorting_algorithms:selection-sort | 9, 6, 2, 5, 8 | [2,6,9,5,8] ; [2,5,9,6,8] ; [2,5,6,9,8] ; [2,5,6,8,9] |
grid_pathfinding | grid_pathfinding:down-first | grid=6 ; S=(1,0) ; G=(5,1) | D:(2,0) ; D:(3,0) ; D:(4,0) ; D:(5,0) ; R:(5,1) |
sorting_algorithms | sorting_algorithms:insertion-sort | 3, 4, 8, 5, 2 | [3,4,8,5,2] ; [3,4,8,5,2] ; [3,4,5,8,2] ; [2,3,4,5,8] |
base_conversion | base_conversion:repeated-division | n=22,base=8 | DIV:22/8=2,r:6 ; DIV:2/8=0,r:2 ; OUT:26 |
multidigit_addition | multidigit_addition:left-to-right-partials | 566+310 | p100:500+300=800 ; p10:60+10=70 ; p1:6+0=6 ; sum=800+70+6=876 |
linear_equation_solving | linear_equation_solving:subtract-then-divide | 7x-42=21 | 7x-42=21 ; 7x=63 ; x=9 |
base_conversion | base_conversion:via-binary | n=74,base=4 | BINLEN:7 ; CHUNK:0:1 ; CHUNK:1:0 ; CHUNK:2:2 ; CHUNK:3:2 ; OUT:1022 |
multidigit_addition | multidigit_addition:rounding-decomposition | 982+485 | round:990+485=1475 ; adjust:1475-8=1467 ; sum=1467 |
linear_equation_solving | linear_equation_solving:inverse-ops | 4x-4=32 | 4x-4=32 ; x=(32--4)/4 ; x=36/4 ; x=9 |
list_summation | list_summation:right-to-left | 4, 2, 6, 7 | 6+7=13 ; 2+13=15 ; 4+15=19 |
list_summation | list_summation:right-to-left | 8, 0, 7, 3 | 7+3=10 ; 0+10=10 ; 8+10=18 |
sorting_algorithms | sorting_algorithms:bubble-sort | 5, 7, 4, 3, 2 | [5,4,7,3,2] ; [5,4,3,7,2] ; [5,4,3,2,7] ; [4,5,3,2,7] ; [4,3,5,2,7] ; [4,3,2,5,7] ; [3,4,2,5,7] ; [3,2,4,5,7] ; [2,3,4,5,7] |
sorting_algorithms | sorting_algorithms:bubble-sort | 3, 1, 9, 5, 8 | [1,3,9,5,8] ; [1,3,5,9,8] ; [1,3,5,8,9] |
list_summation | list_summation:left-to-right | 9, 1, 7, 6 | 9+1=10 ; 10+7=17 ; 17+6=23 |
grid_pathfinding | grid_pathfinding:alternating | grid=6 ; S=(3,4) ; G=(5,5) | R:(3,5) ; D:(4,5) ; D:(5,5) |
base_conversion | base_conversion:decomposition | n=168,base=4 | TERM:2*4^3=128 ; TERM:2*4^2=32 ; TERM:2*4^1=8 ; TERM:0*4^0=0 ; OUT:2220 |
multidigit_addition | multidigit_addition:right-to-left-carry | 116+174 | d2:6+4+0=10→w0,c1 ; d1:1+7+1=9→w9,c0 ; d0:1+1+0=2→w2,c0 ; sum=290 |
base_conversion | base_conversion:decomposition | n=57,base=8 | TERM:7*8^1=56 ; TERM:1*8^0=1 ; OUT:71 |
sorting_algorithms | sorting_algorithms:selection-sort | 8, 0, 2, 1, 7 | [0,8,2,1,7] ; [0,1,2,8,7] ; [0,1,2,8,7] ; [0,1,2,7,8] |
list_summation | list_summation:left-to-right | 4, 3, 9, 7 | 4+3=7 ; 7+9=16 ; 16+7=23 |
linear_equation_solving | linear_equation_solving:divide-then-subtract | 4x-24=0 | 4x-24=0 ; x+-6=0 ; x=0--6 ; x=6 |
base_conversion | base_conversion:decomposition | n=159,base=8 | TERM:2*8^2=128 ; TERM:3*8^1=24 ; TERM:7*8^0=7 ; OUT:237 |
multidigit_addition | multidigit_addition:left-to-right-partials | 618+914 | p100:600+900=1500 ; p10:10+10=20 ; p1:8+4=12 ; sum=1500+20+12=1532 |
base_conversion | base_conversion:repeated-division | n=77,base=2 | DIV:77/2=38,r:1 ; DIV:38/2=19,r:0 ; DIV:19/2=9,r:1 ; DIV:9/2=4,r:1 ; DIV:4/2=2,r:0 ; DIV:2/2=1,r:0 ; DIV:1/2=0,r:1 ; OUT:1001101 |
grid_pathfinding | grid_pathfinding:down-first | grid=6 ; S=(2,1) ; G=(5,5) | D:(3,1) ; D:(4,1) ; D:(5,1) ; R:(5,2) ; R:(5,3) ; R:(5,4) ; R:(5,5) |
list_summation | list_summation:left-to-right | 2, 9, 8, 0 | 2+9=11 ; 11+8=19 ; 19+0=19 |
list_summation | list_summation:left-to-right | 4, 0, 0, 6 | 4+0=4 ; 4+0=4 ; 4+6=10 |
list_summation | list_summation:pairwise | 9, 1, 2, 0 | 9+1=10 ; 2+0=2 ; 10+2=12 |
multidigit_addition | multidigit_addition:left-to-right-partials | 539+636 | p100:500+600=1100 ; p10:30+30=60 ; p1:9+6=15 ; sum=1100+60+15=1175 |
sorting_algorithms | sorting_algorithms:bubble-sort | 5, 7, 3, 9, 1 | [5,3,7,9,1] ; [5,3,7,1,9] ; [3,5,7,1,9] ; [3,5,1,7,9] ; [3,1,5,7,9] ; [1,3,5,7,9] |
linear_equation_solving | linear_equation_solving:divide-then-subtract | 5x+5=-35 | 5x+5=-35 ; x+1=-7 ; x=-7-1 ; x=-8 |
grid_pathfinding | grid_pathfinding:right-first | grid=6 ; S=(4,3) ; G=(5,5) | R:(4,4) ; R:(4,5) ; D:(5,5) |
sorting_algorithms | sorting_algorithms:merge-sort | 8, 7, 1, 4, 5 | [7,8,1,4,5] ; [1,4,7,8,5] ; [1,4,5,7,8] |
multidigit_addition | multidigit_addition:rounding-decomposition | 794+817 | round:800+817=1617 ; adjust:1617-6=1611 ; sum=1611 |
sorting_algorithms | sorting_algorithms:selection-sort | 4, 6, 0, 9, 7 | [0,6,4,9,7] ; [0,4,6,9,7] ; [0,4,6,9,7] ; [0,4,6,7,9] |
list_summation | list_summation:pairwise | 3, 9, 5, 6 | 3+9=12 ; 5+6=11 ; 12+11=23 |
base_conversion | base_conversion:repeated-division | n=51,base=8 | DIV:51/8=6,r:3 ; DIV:6/8=0,r:6 ; OUT:63 |
list_summation | list_summation:pairwise | 1, 0, 2, 2 | 1+0=1 ; 2+2=4 ; 1+4=5 |
list_summation | list_summation:left-to-right | 3, 3, 9, 8 | 3+3=6 ; 6+9=15 ; 15+8=23 |
base_conversion | base_conversion:decomposition | n=175,base=16 | TERM:10*16^1=160 ; TERM:15*16^0=15 ; OUT:AF |
linear_equation_solving | linear_equation_solving:subtract-then-divide | 8x-56=-88 | 8x-56=-88 ; 8x=-32 ; x=-4 |
grid_pathfinding | grid_pathfinding:down-first | grid=6 ; S=(3,0) ; G=(5,2) | D:(4,0) ; D:(5,0) ; R:(5,1) ; R:(5,2) |
sorting_algorithms | sorting_algorithms:insertion-sort | 0, 7, 1, 8, 4 | [0,7,1,8,4] ; [0,1,7,8,4] ; [0,1,7,8,4] ; [0,1,4,7,8] |
grid_pathfinding | grid_pathfinding:right-first | grid=6 ; S=(2,3) ; G=(5,4) | R:(2,4) ; D:(3,4) ; D:(4,4) ; D:(5,4) |
base_conversion | base_conversion:repeated-division | n=37,base=8 | DIV:37/8=4,r:5 ; DIV:4/8=0,r:4 ; OUT:45 |
base_conversion | base_conversion:via-binary | n=11,base=4 | BINLEN:4 ; CHUNK:0:2 ; CHUNK:1:3 ; OUT:23 |
linear_equation_solving | linear_equation_solving:subtract-then-divide | 8x+8=56 | 8x+8=56 ; 8x=48 ; x=6 |
list_summation | list_summation:left-to-right | 6, 2, 7, 1 | 6+2=8 ; 8+7=15 ; 15+1=16 |
base_conversion | base_conversion:decomposition | n=232,base=2 | TERM:1*2^7=128 ; TERM:1*2^6=64 ; TERM:1*2^5=32 ; TERM:0*2^4=0 ; TERM:1*2^3=8 ; TERM:0*2^2=0 ; TERM:0*2^1=0 ; TERM:0*2^0=0 ; OUT:11101000 |
sorting_algorithms | sorting_algorithms:insertion-sort | 7, 9, 3, 8, 5 | [7,9,3,8,5] ; [3,7,9,8,5] ; [3,7,8,9,5] ; [3,5,7,8,9] |
base_conversion | base_conversion:repeated-division | n=143,base=4 | DIV:143/4=35,r:3 ; DIV:35/4=8,r:3 ; DIV:8/4=2,r:0 ; DIV:2/4=0,r:2 ; OUT:2033 |
base_conversion | base_conversion:decomposition | n=145,base=8 | TERM:2*8^2=128 ; TERM:2*8^1=16 ; TERM:1*8^0=1 ; OUT:221 |
sorting_algorithms | sorting_algorithms:insertion-sort | 9, 5, 2, 7, 0 | [5,9,2,7,0] ; [2,5,9,7,0] ; [2,5,7,9,0] ; [0,2,5,7,9] |
grid_pathfinding | grid_pathfinding:right-first | grid=6 ; S=(3,3) ; G=(4,5) | R:(3,4) ; R:(3,5) ; D:(4,5) |
multidigit_addition | multidigit_addition:rounding-decomposition | 445+640 | round:450+640=1090 ; adjust:1090-5=1085 ; sum=1085 |
base_conversion | base_conversion:repeated-division | n=100,base=8 | DIV:100/8=12,r:4 ; DIV:12/8=1,r:4 ; DIV:1/8=0,r:1 ; OUT:144 |
multidigit_addition | multidigit_addition:left-to-right-partials | 142+899 | p100:100+800=900 ; p10:40+90=130 ; p1:2+9=11 ; sum=900+130+11=1041 |
sorting_algorithms | sorting_algorithms:selection-sort | 1, 5, 3, 8, 7 | [1,5,3,8,7] ; [1,3,5,8,7] ; [1,3,5,8,7] ; [1,3,5,7,8] |
sorting_algorithms | sorting_algorithms:heap-sort | 0, 9, 7, 4, 8 | [9,0,7,4,8] ; [9,8,7,4,0] ; [0,8,7,4,9] ; [8,0,7,4,9] ; [8,4,7,0,9] ; [0,4,7,8,9] ; [7,4,0,8,9] ; [0,4,7,8,9] ; [4,0,7,8,9] ; [0,4,7,8,9] |
multidigit_addition | multidigit_addition:left-to-right-partials | 558+487 | p100:500+400=900 ; p10:50+80=130 ; p1:8+7=15 ; sum=900+130+15=1045 |
linear_equation_solving | linear_equation_solving:subtract-then-divide | 5x+25=60 | 5x+25=60 ; 5x=35 ; x=7 |
grid_pathfinding | grid_pathfinding:alternating | grid=6 ; S=(2,1) ; G=(3,2) | R:(2,2) ; D:(3,2) |
multidigit_addition | multidigit_addition:rounding-decomposition | 955+532 | round:960+532=1492 ; adjust:1492-5=1487 ; sum=1487 |
sorting_algorithms | sorting_algorithms:insertion-sort | 6, 4, 5, 7, 1 | [4,6,5,7,1] ; [4,5,6,7,1] ; [4,5,6,7,1] ; [1,4,5,6,7] |
sorting_algorithms | sorting_algorithms:bubble-sort | 9, 2, 5, 0, 1 | [2,9,5,0,1] ; [2,5,9,0,1] ; [2,5,0,9,1] ; [2,5,0,1,9] ; [2,0,5,1,9] ; [2,0,1,5,9] ; [0,2,1,5,9] ; [0,1,2,5,9] |
multidigit_addition | multidigit_addition:right-to-left-carry | 530+352 | d2:0+2+0=2→w2,c0 ; d1:3+5+0=8→w8,c0 ; d0:5+3+0=8→w8,c0 ; sum=882 |
list_summation | list_summation:left-to-right | 3, 5, 7, 7 | 3+5=8 ; 8+7=15 ; 15+7=22 |
base_conversion | base_conversion:repeated-division | n=118,base=2 | DIV:118/2=59,r:0 ; DIV:59/2=29,r:1 ; DIV:29/2=14,r:1 ; DIV:14/2=7,r:0 ; DIV:7/2=3,r:1 ; DIV:3/2=1,r:1 ; DIV:1/2=0,r:1 ; OUT:1110110 |
multidigit_addition | multidigit_addition:rounding-decomposition | 739+398 | round:740+398=1138 ; adjust:1138-1=1137 ; sum=1137 |
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) |
multidigit_addition | multidigit_addition:right-to-left-carry | 862+632 | d2:2+2+0=4→w4,c0 ; d1:6+3+0=9→w9,c0 ; d0:8+6+0=14→w4,c1 ; sum=1494 |
grid_pathfinding | grid_pathfinding:right-first | grid=6 ; S=(4,2) ; G=(5,4) | R:(4,3) ; R:(4,4) ; D:(5,4) |
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