abstractions listlengths 8 8 | train stringlengths 378 5.73k | test stringlengths 125 7.52k | source stringclasses 4
values | answer stringlengths 11 1.69k | num_tokens int64 490 4.08k |
|---|---|---|---|---|---|
[
"<note1>\n<description>Infer the output canvas shape by spotting when a one-dimensional signal is “unfolded” into a two-dimensional construction. A common rule is: set the output to a square whose side length equals the input row length, then embed the input row unchanged along the top edge to anchor all later geom... | [{"input": [[0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0], [0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0], [2, 0, 0,... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 1, 0, ... | arc 1 | ```
0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0
0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0
0 0 0 0 0 2 0 1 0 0 0 2 0 0 0 0 0
0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0 0
0 0 0 2 0 1 0 0 0 1 0 0 0 2 0 0 0
0 0 2 0 0 0 1 0 0 0 1 0 0 0 2 0 0
0 2 0 1 0 0 0 1 0 0 0 1 0 0 0 2 0
2 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 2
0 1 0 0 0 ... | 836 |
[
"<note1>\n<description>Start by identifying a single background color c_bg as the value that dominates the canvas, then treat every non-c_bg cell as candidate “ink.” This simplifies later steps because most transformations act only on ink while resetting everything else to c_bg. It works well when outputs look like... | [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7], [8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 7, 0, 7, 8, 8, 7, 7, 7], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 7, 0, 0, 0, 7, 8, 8, 7, 7, 7], [8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]... | [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 4, 1, 1, 1], [4, 1, 3, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 3, 3, 3, 4, 6, 6, 1], [4, 1, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 3, 1, 1, 4... | arc 2 | ```
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 1 3 3 3 3 3 3 3 3 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 1 3 1 1 1 1 1 1 3 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 1 3 1 1 1 1 1 1 3 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 ... | 2,961 |
[
"<note1>\n<description>When many objects exist, first isolate the “driver” object: a mostly uniform connected component that encloses a compact multicolor kernel. Extract the kernel as the minimal axis-aligned square patch of non-background cells embedded within the container. This works because the kernel usually ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 1, 5, 2, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0], [0, 2, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0]... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0... | arc 2 | ```
3 3 3 3 3 3 3 3 3 3 6 6
3 3 3 3 3 3 3 3 3 3 6 6
3 3 3 3 6 6 6 6 3 3 6 6
3 3 3 3 6 6 6 6 3 3 6 6
3 3 6 6 6 6 6 6 3 3 6 6
3 3 6 6 6 6 6 6 6 6 6 6
3 3 3 3 3 3 3 6 6 6 6 8
3 3 3 3 3 3 3 6 6 6 6 8
4 4 4 6 6 6 6 6 6 6 6 8
4 4 4 4 6 6 6 6 6 8 8 8
4 4 4 4 4 6 6 6 6 8 8 8
4 4 4 4 4 4 6 6 6 8 8 8
``` | 3,529 |
[
"<note1>\n<description>Start by separating background from foreground, then extract each foreground object as a connected region (typically using orthogonal adjacency). Treat each distinct color’s regions as separate candidates unless evidence suggests multi-color regions should be grouped. This object inventory is... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 8, 8, ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 0, 0, 0, 0], ... | barc_heavy | ```
4 0 0 0 0 9 0 0 0 0 0 0 0 0
4 0 0 0 0 9 0 0 0 0 0 0 0 0
4 0 0 0 0 9 0 0 0 0 0 0 0 0
4 0 0 0 0 9 0 0 0 0 0 0 0 0
4 0 0 0 0 9 0 9 0 0 0 0 0 0
4 0 0 0 0 0 9 9 9 0 0 0 0 0
4 0 0 0 0 9 9 9 9 9 0 0 0 0
4 0 0 0 0 0 9 9 9 0 0 0 0 0
4 0 4 0 0 0 0 9 0 0 0 0 0 0
0 4 4 4 0 0 0 0 0 0 0 0 0 0
4 4 4 4 4 0 0 0 0 0 0 0 0 0
0 4 4 4 ... | 3,030 |
["<note1>\n<description>When a grid contains one prominent multi-cell figure plus a few isolated col(...TRUNCATED) | "[{\"input\": [[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0,(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3(...TRUNCATED) | arc 1 | "```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0 0 3 0 0 0 0\n0 0 1 1 0 0 0 0 0 0 0 3 3 0 (...TRUNCATED) | 3,047 |
["<note1>\n<description>Start by identifying the background value and treating it as empty space; on(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 8], [0, 9, 9, 0, 7, 0, 7, 7, 0, 7, 0, 0], [0, 9, 9,(...TRUNCATED) | "[{\"input\": [[0, 6, 0, 9, 0, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 6, 0, 0], [5, 5, 5, 0, 0, 0, 0, 0, 6](...TRUNCATED) | barc_heavy | ```
6 9 5 4 2 8
``` | 948 |
["<note1>\n<description>Start by separating background from foreground and grouping contiguous foreg(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 0, 0, 0, 0, 0, 0], [6, 6, (...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0](...TRUNCATED) | barc_heavy | "```\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 1 1 0 0 0 0 0 0\n0 1 1 0 0 0 0 0 0\(...TRUNCATED) | 1,132 |
["<note1>\n<description>Start by partitioning the grid into connected components of non-background c(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 4, 0, 0, 0, 0, 0, 0], [0, 4, 8, 4, 0, 0, 0,(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 2, 2, 0, 0, 0, 0, 0], [0, 3, 3, 2, 0, 0, 0, 0, 0](...TRUNCATED) | arc 1 | "```\n0 0 0 0 0 0 0 0 0\n0 2 3 3 0 0 0 0 0\n0 2 2 3 0 0 0 0 0\n0 2 3 3 0 0 0 0 0\n0 0 0 0 0 1 1 1 0\(...TRUNCATED) | 1,702 |
["<note1>\n<description>Look for a uniform “divider” feature (often a full-length line in a uniq(...TRUNCATED) | "[{\"input\": [[4, 4, 4, 4, 1, 0, 0, 0, 0], [0, 4, 0, 4, 1, 4, 0, 0, 0], [4, 0, 0, 0, 1, 0, 4, 0, 0](...TRUNCATED) | "[{\"input\": [[0, 0, 4, 0, 1, 0, 0, 4, 0], [4, 0, 4, 4, 1, 4, 4, 0, 4], [0, 0, 0, 4, 1, 4, 4, 0, 4](...TRUNCATED) | arc 1 | ```
0 0 8 0
8 8 8 8
8 8 0 8
8 8 8 0
8 8 8 8
8 8 0 8
``` | 1,188 |
["<note1>\n<description>Start by inferring the background color as the most prevalent value, then se(...TRUNCATED) | "[{\"input\": [[6, 6, 6, 6, 6, 6, 6, 6], [9, 9, 9, 9, 6, 6, 6, 6], [9, 9, 9, 9, 6, 9, 9, 9], [0, 0, (...TRUNCATED) | "[{\"input\": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0], [6, 6(...TRUNCATED) | arc 2 | "```\n6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0 0 0 0\n6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6(...TRUNCATED) | 3,606 |
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