Remove the lone anchor pixel and place the two blocks so they occupy the same contiguous area (they will be adjacent). The final grid will contain only the background plus the two intact 2×2 blocks arranged next to one another.</description>\\n<example>After deciding which block is nearer to the anchor, remove the lone pixel and position the two 2×2 blocks side-by-side (for example, one to the left and one to the right of the anchor’s former location) so they form a single contiguous region.</example>\\n</note5>\",\n \"<note1>\\n<description>Scan the grid for small, contiguous non-background color clusters and treat each as an atomic object to move. Represent each object by its bounding box (top, left, height, width) so you can compare positions reliably.</description>\\n<example>Imagine a grid with three distinct colored blobs: a 1×1 pixel, a 2×2 square, and another 2×2 square. For each blob compute its bounding box (for example, the 1×1 box would be (r,c,1,1) and the 2×2 boxes would be (r,c,2,2)). These boxes give you a compact description to reason about where things are and how they can be moved.</example>\\n</note1>\\n\\n<note2>\\n<description>Identify the anchor object — the one with the smallest bounding-box area (the single pixel). That single pixel is the pivot that determines the translation direction for the larger blocks. Use its coordinates as the reference point for moving other objects.</description>\\n<example>If the three bounding boxes are sizes 1, 2 and 2, the 1×1 object is the anchor. Its top-left corner (r,c) becomes the reference: the other objects will be translated relative to that coordinate rather than to the grid center or to one another.</example>\\n</note2>\\n\\n<note3>\\n<description>Compute the translation vector by aligning the anchor's bounding box with the target bounding box: the vector is (target_top − anchor_top, target_left − anchor_left). Apply that same vector to every pixel of the anchor and every other object so the whole group moves together.</description>\\n<example>Suppose the anchor's box top-left is (r,c) and you want it to align with a target box at (r',c'). The translation is (r'−r, c'−c). Move every pixel of the anchor by that offset, and then move every other object by the same offset so the whole set translates as one unit.</example>\\n</note3>\\n\\n<note4>\\n<description>Preserve each object's internal layout and color when translating: do not rotate, reflect, or reshape objects — only shift them. This keeps the relative arrangement of pixels inside each object unchanged after the move.</description>\\n<example>If a 2×2 block has a different color in its top-left cell, after translation that cell will remain top-left inside the moved block and retain its color. Apply the same preservation rule for every object so shapes remain identical except for their position.</example>\\n</note4>\\n\\n<note5>\\n<description>Decide target alignment rules and watch for collisions: in these tasks the anchor is usually moved to touch the nearest non-background object (or to a specific edge) rather than to the grid center. If an object would overlap another, re-evaluate the target alignment so overlaps are avoided.</description>\\n<example>If the anchor is at the top and there is a non-background object below it, consider moving the anchor down so it touches that object (or the nearest object). If a direct translation would cause two objects to occupy the same cell, adjust the alignment rule (for example, move the anchor to the nearest available row/column) to prevent overlap while keeping the translation consistent.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for small, uniform objects (same color and same size) that occur exactly twice in each training input. Treat each such repeated object as a single movable unit rather than many independent pixels.</description>\\n<example>Imagine a grid with two identical 2×2 red squares. Because they are identical and identical in size, you can represent each square by its top-left coordinate and handle them as two blocks to be moved together, rather than moving individual pixels.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the vertical center of each object by averaging its top and bottom row indices (center = (top+bottom)/2). This gives a single vertical position that captures the block's vertical placement.</description>\\n<example>If a 2×2 square occupies rows 3–4, its vertical center is (3+4)/2 = 3.5. If another square occupies rows 7–8, its vertical center is 7.5; these two centers tell you how far apart the blocks are vertically.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide the direction of movement by comparing those vertical centers: the block with the smaller center will be moved upward and the block with the larger center downward. Do not change the horizontal positions of the blocks.</description>\\n<example>If one block's center is 3.5 and the other's is 7.5, move the block at 3.5 up and the block at 7.5 down so they end up closer vertically.</example>\\n</note3>\\n\\n<note4>\\n<description>Move each block as a rigid unit: keep its width and height and translate every pixel by the same row offset. When a block reaches the top or bottom, stop there — do not let it extend outside the grid.</description>\\n<example>A 2×2 block at rows 3–4 moved up by one becomes rows 2–3; if it had already been at row 0 it would remain at row 0. Apply the same row offset to every pixel of that block.</example>\\n</note4>\\n\\n<note5>\\n<description>After moving, check that the blocks remain distinct and that no other pixels were altered. The transformation should preserve colors and shapes while only relocating the two identical blocks toward each other.</description>\\n<example>After translation, verify each block still occupies the same number of rows and columns and that the intervening rows between them are now reduced; ensure no stray pixels of other colors were moved or changed.</example>\\n</note5>\",\n \"<note1>\\n<description>Look first for a single isolated pixel of a color that stands out from the other colored pixels. This lone pixel usually acts as an anchor or marker that signals where something should be placed.</description>\\n<example>Imagine a grid with three colored clusters and one blue pixel alone. That solitary blue pixel is likely the marker: it is different in count and placement and often tells you where to look for a relocation rule.</example>\\n</note1>\\n\\n<note2>\\n<description>Identify the two distinct multi-cell blocks (shapes) that appear more than once and are not the marker. These repeated blocks are the objects to be moved or repositioned.</description>\\n<example>For instance, if you see two identical 2×2 red squares and one isolated green pixel, treat the two red squares as the objects to relocate. Ignore the green pixel when deciding which shapes to move.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide the direction by comparing the marker’s row and column with the target blocks’ rows and columns: the block whose row is nearest to the marker’s row and whose column is nearest to the marker’s column should be moved toward the marker. In other words, choose the block that is closest in both row and column to the marker.</description>\\n<example>If the marker sits above and to the right of one block and below and to the left of another, the block that is closest in both directions (the one nearer in row and nearer in column) is the one to move. This gives a single unambiguous choice when there are two candidates.</example>\\n</note3>\\n\\n<note4>\\n<description>Move the chosen block by translating it horizontally toward the marker so that the block’s leftmost column becomes immediately to the right of the marker. Preserve the block’s internal pixel arrangement and color; only shift its horizontal position.</description>\\n<example>If the marker is at column 5 and the block’s left edge is at column 2, shift the block right until its left edge is at column 6 so it sits directly to the right of the marker. Do not change the block’s height or color.</example>\\n</note4>\\n\\n<note5>\\n<description>After placing the block, clear any cells that the block occupied before (set them to background). The marker and the other unchanged block remain in place, so the result shows the moved block adjacent to the marker and the rest of the scene unchanged.</description>\\n<example>Following the move, the former block’s old cells become background zeros while the block now occupies the new column(s) immediately to the marker’s right. The marker stays as it was, and the other block stays where it was.</example>\\n</note5>\",\n \"<note1>\\n<description>Start by isolating the colored objects: treat each contiguous group of non-background pixels as an object and compute its bounding box (min/max row and column). This gives a compact representation of each object's shape and position. Knowing the bounding box is the first step to comparing objects and deciding how they should move.</description>\\n<example>Imagine a grid with three colored blobs. For each blob record its top, bottom, left and right coordinates; these four numbers summarize the object's size and location. Working with these boxes (not individual pixels) makes it easy to compare where objects sit and whether they can be shifted without overlapping.</example>\\n</note1>\\n\\n<note2>\\n<description>Look for a fixed vertical offset between objects: compute the vertical gaps between each object's top row and the next object's top row. If those gaps are consistent across examples, that gap is the target vertical distance to use when stacking objects. A consistent gap means you can treat stacking as a uniform shift rather than a case-by-case change.</description>\\n<example>For instance, if one object sits at row 2 and the next at row 6, the gap is 4 rows. If another object sits at row 10, place it at row 14 (same 4-row gap) so the vertical alignment is preserved. Recognizing this pattern reduces the problem to moving objects by the same vertical step.</example>\\n</note2>\\n\\n<note3>\\n<description>Preserve each object's horizontal placement and internal arrangement: when you shift an object vertically, do not change its left/right column indices or the internal pattern of colors inside its bounding box. Only the top row of each object should be adjusted to match the vertical gap. This keeps shapes and relative colors intact while aligning them vertically.</description>\\n<example>Suppose a 2×2 blue square has its top-left at column 5; after shifting it down by the computed gap, keep its top-left at column 5 and its two rows still blue. You are only changing the vertical coordinate of the whole object, not its columns or orientation.</example>\\n</note3>\\n\\n<note4>\\n<description>Handle collisions by stacking in a consistent order: choose a rule (for example, the smallest bounding-box area placed first) and apply that same ordering to every example. If two objects would overlap after shifting, the one with the smaller bounding-box area should be placed in the lower slot so the larger object is stacked above. Using a single deterministic rule avoids ambiguity.</description>\\n<example>If a 2×2 object (area 4) and a 2×4 object (area 8) are both shifted down, place the 2×2 in the lower row and the 2×4 above it; do this consistently across all examples so the final arrangement is unambiguous.</example>\\n</note4>\\n\\n<note5>\\n<description>After applying the vertical shift and stacking rule, verify that all original colored pixels are accounted for and that the grid size and background remain unchanged. This final check ensures you did not accidentally rotate, mirror, or recolor any object. If something looks off, re-check the measured vertical gaps and the chosen stacking order.</description>\\n<example>After shifting objects down by the computed gap and stacking them according to the chosen order, count pixels and confirm each colored pixel from the input appears in the output in the same color but at the new vertical position. If counts or colors don't match, revisit your gap measurement or stacking order.</example>\\n</note5>\",\n \"<note1>\\n<description>Locate the colored objects and summarize each by its bounding box (top row, left column, width, height). This gives a compact representation of each object's shape and position that you can compare across examples.</description>\\n<example>Imagine three colored blocks: a 2×2 square, a 1×2 horizontal pair, and a lone pixel. For each, record the bounding box (e.g., top-left coordinate and size). That summary makes it easy to see which objects are identical in shape and where they sit on the grid.</example>\\n</note1>\\n\\n<note2>\\n<description>Check which objects share the same bounding-box dimensions and orientation. Objects that match exactly (same size and shape) are likely related and should be treated as a group for the transformation.</description>\\n<example>If two objects both have a 2×2 bounding box and are axis-aligned, mark them as the same class. A single pixel or a 1×2 pair will form a different class and should be handled differently.</example>\\n</note2>\\n\\n<note3>\\n<description>Find the unique singleton (the object that is different from the matched pair). The transformation usually keeps the matched pair(s) and relocates the singleton in a consistent way relative to them.</description>\\n<example>When two 2×2 squares exist and one lone pixel remains, identify that lone pixel as the element to move. The rest of the rule is about where to place that lone pixel relative to the 2×2 squares.</example>\\n</note3>\\n\\n<note4>\\n<description>Decide on a consistent anchor for the singleton: the top-left of the topmost 2×2 square or the top-left of the leftmost 2×2 square. Use that anchor to compute the new coordinates by moving the singleton a fixed offset (typically one cell right and one cell down).</description>\\n<example>If the two 2×2 squares are stacked, use the topmost 2×2's top-left as the anchor; then place the lone pixel one row below and one column to the right of that anchor. If the squares are side-by-side, use the leftmost 2×2's top-left and apply the same offset.</example>\\n</note4>\\n\\n<note5>\\n<description>Apply the move and verify: keep the matched objects in place and ensure the lone pixel lands on a background cell (no overlaps). If a direct placement would collide, check whether the examples use an alternate consistent offset (e.g., down instead of right) or whether the singleton is only moved when there is exactly one such object.</description>\\n<example>After placing the lone pixel according to the anchor+offset rule, confirm it is on a zero cell and that the two 2×2 squares remain unchanged. If the examples ever show a different offset in a similar situation, adopt that alternate rule consistently across the grid.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for compact, contiguous multi-cell shapes (the same color touching orthogonally). These are the objects that matter: they are the only non-zero pixels in each example and determine the transformation.</description>\\n<example>Imagine a grid with a single 2×2 blue block, a single 2×2 red block and a lone isolated green pixel. Treat the blue and red blocks as the objects (two objects) and the green pixel as a marker to be handled separately.</example>\\n</note1>\\n\\n<note2>\\n<description>Decide which of the multi-cell objects to move by checking which one is isolated from the others (has no same-colored neighbors). The isolated multi-cell object is the one that will be relocated.</description>\\n<example>If the red 2×2 block is adjacent to the blue 2×2 block, the red block is not isolated. If the blue 2×2 is alone, then the blue block is the isolated object to move.</example>\\n</note2>\\n\\n<note3>\\n<description>When moving an object, preserve its exact shape and orientation: copy the cells into the same relative positions within the destination. Do not rotate or flip unless the examples explicitly show such a change.</description>\\n<example>A 2×2 block that occupies rows r..r+1 and columns c..c+1 should appear again as rows r..r+1 and columns c..c+1 in the destination; only its coordinates change, not its internal pattern.</example>\\n</note3>\\n\\n<note4>\\n<description>Compute the destination by translating the isolated object by a fixed offset equal to the distance between the two multi-cell objects. Use the geometric midpoint of the two objects' bounding boxes (or the vector between their bounding-box centers) to choose the offset direction and magnitude.</description>\\n<example>If one object is near the top and the other near the bottom, the midpoint will be toward the center; if one is left and the other right, the midpoint will be toward the middle. Move the isolated object by that midpoint-derived translation so it ends up between the two objects.</example>\\n</note4>\\n\\n<note5>\\n<description>After placing the moved object, clear its original cells and leave the other multi-cell object(s) in place. The final scene should contain the two original multi-cell objects (one moved) and the original marker pixel(s) unchanged.</description>\\n<example>After translating the isolated block, set its former cells back to background and verify that the other block still occupies its original position and that any isolated single-color pixel remains where it was.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for small, uniform 2×2 color blocks that are the only non-background pixels. These blocks are easy to detect because they occupy exactly four cells of the same color and form a perfect square.</description>\\n<example>Imagine a grid with three isolated 2×2 blocks of colors A, B, and C. Because each block is exactly four adjacent same-colored cells in a 2×2 arrangement, you can identify them reliably by scanning for those exact 2×2 patterns rather than single pixels.</example>\\n</note1>\\n<note2>\\n<description>Compute the bounding box of each 2×2 block and note its top-left cell (row, column). The bounding box gives a single anchor for each object and simplifies later placement decisions.</description>\\n<example>For a 2×2 block whose four cells occupy rows 3–4 and columns 5–6, the bounding box is rows 3–4, cols 5–6 and the top-left anchor is (3,5). Use that anchor when you consider where to place or move the block.</example>\\n</note2>\\n<note3>\\n<description>Find the isolated single-cell color (a lone pixel of a different color) and treat it as a marker. Its position relative to the 2×2 blocks is the key clue about where those blocks should be moved.</description>\\n<example>If you see one pixel of color X at (7,10) while the 2×2 blocks are elsewhere, that lone pixel is not part of any block and its coordinates are the natural reference point for relocating the blocks.</example>\\n</note3>\\n<note4>\\n<description>Translate each 2×2 block by the vector from the marker to the block’s top-left anchor (or by the marker’s coordinates minus the block’s anchor). This preserves the block’s orientation and moves it so the block’s top-left sits at the marker’s coordinates.</description>\\n<example>Suppose a block’s top-left is at (2,8) and the marker is at (6,12); the translation vector is (4,4) and the new top-left becomes (6,12). Apply that same translation to every 2×2 block so their top-left coordinates match the marker.</example>\\n</note4>\\n<note5>\\n<description>After moving blocks, verify they remain inside the grid and do not overlap (use the original anchors as a reference to detect overlap). If overlap occurs, choose a consistent rule (for example, keep the one that matches the marker’s side or the one with the smaller original row index) to resolve collisions.</description>\\n<example>If two blocks would overlap after translation, pick the block that originally had the smaller top-left row (or the one that originally sat on the same side as the marker) and keep that placement; the other block can be shifted slightly to avoid overlap while preserving the marker-anchor alignment.</example>\\n</note5>\",\n \"<note1>\\n<description>Look first for a single, isolated non‑zero pixel that is not part of any contiguous colored region; this isolated pixel usually signals a marker or pivot. Treat it as a special location rather than a color to be copied.</description>\\n<example>Imagine a grid with three colored blocks and one solitary pixel somewhere else. That solitary pixel is likely acting as a reference point (a marker) and should not be moved; instead it indicates where a copy or placement will be anchored.</example>\\n</note1>\\n\\n<note2>\\n<description>Find the two contiguous two‑cell blocks of the same color (they form 2×2 squares or two adjacent cells). These two blocks are the objects that will be compared and moved. Record their top‑left corners and the vector between them (the displacement).</description>\\n<example>If you see two 2×2 blocks at (row 1,col 4) and (row 5,col 8), note their top‑left coordinates and the displacement (row difference, column difference). That displacement will be used to reposition the other block.</example>\\n</note2>\\n\\n<note3>\\n<description>Use the displacement from one 2×2 block to the marker as the translation vector to move the other 2×2 block. Compute the vector from the 2×2 block’s top‑left to the marker, then add that vector to the other 2×2 block’s top‑left to get its new anchor.</description>\\n<example>Suppose the first 2×2 is at (1,4) and the marker is at (5,7). The vector is (4,3); applying that to the second 2×2 at (5,8) gives a new anchor at (9,11), so the second 2×2 should be placed so its top‑left is at (9,11).</example>\\n</note3>\\n\\n<note4>\\n<description>When you move the block, keep its internal pattern and color exactly the same; do not rotate or reflect it. If the new top‑left falls off the grid, slide the block horizontally and vertically as far as possible (wrap or clip) until it fits.</description>\\n<example>If a 2×2 block would be placed with top‑left at (10,14) in a 12×12 grid, slide it down and left until it fits inside the grid; the relative arrangement of the two cells inside the block must remain identical.</example>\\n</note4>\\n\\n<note5>\\n<description>After placing the moved block, clear the original block’s cells and the marker cell (they become background). The final scene should contain the two 2×2 blocks in the new positions and the original isolated pixel removed.</description>\\n<example>Once the second 2×2 block is in place, set its former cells and the single marker cell back to the background color; the grid then shows only the two relocated 2×2 blocks and the rest is background.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for small, identical non-background objects and treat them as units to move. When a color appears as a compact block (same size and shape), consider that whole block as one object rather than individual pixels.</description>\\n<example>Imagine a 2×2 red square and a single isolated blue pixel. If the transformation moves the red square as a unit but leaves the blue pixel alone, then the red square is the object to follow. Identifying that block first simplifies where to look for a partner.</example>\\n</note1>\\n\\n<note2>\\n<description>Find the partner by matching size and color: the partner is the other non-background object with the same shape and color. Partners are usually symmetric in the examples (same dimensions, same color, same orientation).</description>\\n<example>If you see a 2×2 green block and another 2×2 green block elsewhere, those two are likely partners. If instead you see a 2×2 and a single pixel of a different color, they are not partners and should be treated separately.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide the vertical alignment rule: the partner is placed directly above the object so their vertical midpoints coincide. In other words, move the partner so its top row equals the object's top row (or equivalently, so their row indices are equal).</description>\\n<example>Suppose an object occupies rows 8–9 and a partner occupies rows 10–11. To align vertically, move the partner up so it occupies rows 8–9 instead of 10–11. The horizontal positions are preserved by this rule.</example>\\n</note3>\\n\\n<note4>\\n<description>Do not alter the partner's horizontal position or orientation; only translate it vertically. The partner should remain in the same column range and with the same shape and color.</description>\\n<example>If a 2×2 block sits at columns 5–6 and you move it up to rows 8–9, keep it at columns 5–6. You should not rotate, reflect, or shift it left/right—only move it up/down to the aligned rows.</example>\\n</note4>\\n\\n<note5>\\n<description>Use a consistent tie-breaker if multiple candidates exist: prefer the partner that is not adjacent to the object (or the one that is farther down). After placing the partner, the object usually disappears (is replaced by background), so confirm that the partner now occupies the object's original rows.</description>\\n<example>When there are two identical blocks, choose the one that is not immediately above or below the target block and move it up so it shares the target's rows. If you then check the grid, the original object should be background and the partner should occupy the same rows as the object.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for compact, uniform 2×2 patches: these are the atomic units that are moved. A 2×2 patch is four adjacent cells in a square arrangement and is the smallest nontrivial object in many ARC tasks.</description>\\n<example>Imagine a grid with a 2×2 red square and a single blue pixel elsewhere. Treat the red square as a single object (top-left corner at (r,c)) rather than four separate pixels when deciding how to move it.</example>\\n</note1>\\n\\n<note2>\\n<description>Identify the lone single-color pixel (the \\\"anchor\\\") and record its coordinates. That isolated pixel often supplies the horizontal offset (the column) that determines where the 2×2 block should be placed.</description>\\n<example>If there is one green pixel at column 7, note that column 7 as the candidate horizontal anchor; later you will try placing the 2×2 block so its columns align with that column (e.g., top-left at (r,7) or (r,7+2)).</example>\\n</note2>\\n\\n<note3>\\n<description>Try placing the 2×2 block immediately to the right of the anchor (shift horizontally by two cells). The top-left target column is the anchor’s column plus two, and the top-left row stays the same as the block’s original row.</description>\\n<example>With a 2×2 block originally at (r,c) and an anchor at column 7, the new top-left would be (r, c+2). If c+2 is outside the grid, the block cannot be placed that way.</example>\\n</note3>\\n\\n<note4>\\n<description>If the rightward placement is impossible (would go off-grid or overlap), try the other diagonal direction: move the 2×2 block directly below the anchor (shift vertically by two rows). Use the anchor’s row as the new top-left row and the same column as the block’s original column.</description>\\n<example>If the anchor sits at row 5 and the block’s top row is 3, move the block so its top-left becomes (5, c). If that would overlap existing colored pixels, prefer the direction that fits the grid and avoids conflicts.</example>\\n</note4>\\n\\n<note5>\\n<description>Apply the chosen placement consistently: copy the 2×2 block’s color and shape to the new coordinates, remove the original 2×2 block, and leave the anchor and any other unrelated pixels unchanged. If both placements are blocked, use the examples to infer a consistent tie-break (e.g., prefer the direction that stays inside the grid).</description>\\n<example>If both horizontal and vertical placements would collide, choose the one that fits entirely inside the grid; then paste the 2×2 block into that location, clear the original block, and keep the anchor pixel exactly where it was.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for a single, isolated pixel of a color that does not belong to a compact shape; this pixel often serves as a marker that indicates where a nearby object should be moved. When one color appears only as a single isolated pixel while another color appears as a multi-cell block, the isolated pixel is a natural anchor for the transformation.</description>\\n<example>Imagine a grid with a 2×2 red block and a single blue pixel far from it. The blue pixel is isolated (no blue neighbors), while red forms a contiguous block, so the blue pixel is a likely marker that will be used to locate the red block.</example>\\n</note1>\\n\\n<note2>\\n<description>Find the bounding box of the multi-cell object (the smallest rectangle that contains every cell of that color) and compute its center (the midpoint of the box). The center is the natural reference point for moving the object because it preserves the object's orientation and symmetry.</description>\\n<example>If a color occupies cells (r1,c1) through (r2,c2), the box center is ((r1+r2)/2, (c1+c2)/2). For a 2×2 square the center is the midpoint between the top-left and bottom-right corners and is the natural pivot to move the whole square.</example>\\n</note2>\\n\\n<note3>\\n<description>Translate the entire multi-cell object so that its bounding-box center coincides with the marker pixel's coordinates. This keeps the object's shape and orientation intact while relocating it to the marker's position.</description>\\n<example>Suppose the object's center is at (r_obj,c_obj) and the marker is at (r_m, c_m). Move every cell of the object by (r_m - r_obj, c_m - c_obj) so that the object's center becomes (r_m, c_m).</example>\\n</note3>\\n\\n<note4>\\n<description>After translation, check that the object fits entirely inside the grid and that its cells are still the same color; if the object would go outside the grid, the intended transformation is simply the translation that places the object's center at the marker's coordinates (no resizing or recoloring).</description>\\n<example>If a 2×2 block is translated toward the marker but would extend beyond the right edge, accept the translation that centers the block on the marker and do not attempt to crop or change the block's size.</example>\\n</note4>\\n\\n<note5>\\n<description>Do not alter other isolated pixels or unrelated colors — only the multi-cell object should be moved. The marker pixel itself may be removed or left as a background pixel after the object is relocated; everything else stays the same.</description>\\n<example>If there are several isolated single-color pixels elsewhere in the grid, leave them unchanged; only the object whose bounding-box center matches the marker's coordinates should be relocated, and its original position should be cleared.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the single isolated pixel that is not part of any contiguous colored block; that pixel usually serves as a marker and does not move. Its color is important because it signals a spatial relationship between the two blocks.</description>\\n<example>Imagine a grid with one lone red pixel somewhere and two colored 2×2 blocks elsewhere. Treat the lone red pixel as a marker: it is likely used to compare positions of the two blocks rather than being moved itself. First mark that pixel and record its row and column relative to the blocks.</example>\\n</note1>\\n\\n<note2>\\n<description>Find the two 2×2 blocks and note their bounding boxes and centers. Use the center (or the average of the four corners) of each block as the representative coordinate for that block so you can compare them with the marker and with each other.</description>\\n<example>For a 2×2 block occupying rows r..r+1 and cols c..c+1, the center is (r+0.5, c+0.5). If you have two such blocks, compute their centers and compare those center coordinates to the marker’s coordinates to see how they align.</example>\\n</note2>\\n\\n<note3>\\n<description>Compare the marker’s position to the two block centers and decide which axis is dominant: if the marker’s column is closer to one block’s center than the other, that block is the “left” block; if its row is closer, that block is the “top” block. This gives you a binary choice (left vs right, top vs bottom) that determines the block to move.</description>\\n<example>Suppose the marker is nearer in column to the left block than to the right block, then treat the left block as the one to move. If instead the marker is nearer in row to the top block, treat the top block as the one to move. Use whichever axis (row or column) the marker is closest to as the selection criterion.</example>\\n</note3>\\n\\n<note4>\\n<description>Translate the chosen block so that its center (or its bounding box) lies directly on the marker’s row and column. The block is moved intact (no rotation or color change) and placed so the marker sits on the same row and column as the block’s representative coordinate.</description>\\n<example>If you decide to move the left block and the marker is at (r,c), shift the 2×2 block so its center is at (r,c). The block will occupy the four cells that correspond to that shifted center (for a 2×2 block this is a 2×2 square centered at (r,c)).</example>\\n</note4>\\n\\n<note5>\\n<description>After placing the moved block, clear the original block’s cells and leave the marker unchanged; the marker then sits on the moved block’s location. This produces a single 2×2 block whose center coincides with the marker’s coordinates.</description>\\n<example>Once the chosen block has been translated to the marker’s row/column, set all original cells of that block to background (zero) and keep the lone pixel as-is. The final grid should show the moved block at the marker’s position and the other block in its original place (if it wasn’t moved).</example>\\n</note5>\",\n \"<note1>\\n<description>Look for repeated, identical small shapes (same color, same bounding box). When a color appears as multiple disconnected components with the same size and orientation, those components are likely the objects to be moved together.</description>\\n<example>Imagine a grid with three identical 2×2 green squares scattered around. Treat each 2×2 green area as one object: record its top-left coordinate and size. If two of those objects share the same color and size, they are good candidates for the same operation.</example>\\n</note1>\\n\\n<note2>\\n<description>Decide which two components form the pair by color and size. Prefer the color that appears exactly twice in the same small shape; ignore singletons or colors that occur only once.</description>\\n<example>Suppose blue appears twice as identical 2×2 blocks and red appears only once. Select the two blue blocks as the pair to move, while leaving the single red block unchanged.</example>\\n</note2>\\n\\n<note3>\\n<description>Compute the midpoint between the two components' bounding boxes. For axis-aligned squares, take the average of the two top-left coordinates (or the two centers) to get the target top-left corner; this gives a single, symmetric placement.</description>\\n<example>If one 2×2 block is at (r,c) and the other at (r+2,c+2), the midpoint top-left is (r+1, c+1) and the midpoint center is (r+1.5, c+1.5). Use the top-left integer coordinate as the new placement for both blocks.</example>\\n</note3>\\n\\n<note4>\\n<description>Translate both components so their bounding boxes are centered on that midpoint and preserve their original orientation and colors. Do not rotate or change the block sizes—only shift them.</description>\\n<example>Two 2×2 blocks at (r,c) and (r+2,c+2) both become centered on (r+1,c+1) after translation, so each occupies the cells (r+1..r+2,c+1..c+2). Verify that both blocks are identical and unchanged except for position.</example>\\n</note4>\\n\\n<note5>\\n<description>After moving, check that the moved components are now adjacent (or symmetrically placed) and that all other colors remain unchanged. If a midpoint falls on a cell already occupied by another non-background color, prefer an integer midpoint that keeps the pair aligned and symmetric without overlapping.</description>\\n<example>If the midpoint is at a half-cell coordinate, shift the blocks by one column or row so the midpoint becomes an integer while both blocks remain centered on the same integer top-left. Confirm that no other colored pixels were altered and that the pair’s orientation and colors are preserved.</example>\\n</note5>\",\n \"<note1>\\n<description>Isolate the meaningful objects by finding connected non-background pixels and computing each object's bounding box (min/max row and column). This gives you the object's size and the exact coordinates needed to reason about movement or placement.</description>\\n<example>Imagine a grid with a 2×2 red square, a 2×2 blue square and a single isolated green pixel. Compute each object's bounding box: the red/blue boxes are 2×2 and the green is 1×1. Treat the single green pixel as a 1×1 object so you can compare sizes and positions consistently.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare the bounding boxes of the two multi-cell objects to determine their relative placement (which one is above, below, left of or right of the other). The examples use a clear vertical ordering (one object sits above the other) rather than left/right.</description>\\n<example>If the red square's top row is smaller than the blue square's top row, the red square is above the blue square. If they are at the same row, use their leftmost columns to decide left vs right; otherwise they are not in the same vertical pair and won't be the ones moved.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide which object to move by a simple size rule: choose the object with the larger bounding-box area (or, if areas equal, the one that is above the other). The chosen object is the one that will be relocated.</description>\\n<example>Given a 2×2 (area 4) object and a 2×2 (area 4) object, they tie; then choose the one whose top row is smaller (the one above). If the areas differ, pick the larger area object regardless of vertical order.</example>\\n</note3>\\n\\n<note4>\\n<description>When you move the chosen object, keep its exact pixel pattern and color; slide it vertically down until its bottom row reaches the same row as the other object's top row (i.e., place it directly above that object). Do not rotate or change its shape.</description>\\n<example>If the chosen object is two rows above the target and the target's top row is row 8, move the chosen object down by two rows so its bottom row becomes 8 and its top row becomes 6. After moving, the two objects share the same top/bottom row and are stacked vertically.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate the result by checking that the moved object still occupies the same columns and that the two objects no longer overlap or touch; if they do, re-evaluate which object was chosen or whether the vertical alignment should be adjusted. This avoids accidental overwriting or shifting.</description>\\n<example>After placing the moved object so its bottom equals the other object's top, compare their column ranges: they should be the same columns. If one pixel from the moved object would land on a non-background cell, try the other candidate object or a different vertical offset until both objects are cleanly stacked without overlap.</example>\\n</note5>\",\n \"<note1>\\n<description>Identify the active colors by frequency and shape: look for colors that form a compact cluster (an L, a 2×2 square, or a 1×2 pair) rather than isolated single pixels. These compact clusters are the objects that are moved or rearranged in the transformation.</description>\\n<example>Imagine a grid with one isolated red pixel, one 2×2 green square, and one 1×2 blue pair. The red single pixel is unlikely to be the moved object; the green square and the blue pair are the likely candidates because they form clear clusters.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the minimal bounding rectangle for each candidate cluster and record its height and width. The bounding box captures the object's shape and size and is the unit that gets translated as a whole.</description>\\n<example>If a candidate occupies cells at (r,c),(r+1,c),(r+1,c+1),(r+2,c+1) the minimal rectangle spans rows r..r+2 and cols c..c+1, so its height is 3 and width is 2. That rectangle is the thing you will move.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a single consistent translation vector across examples: determine how the bounding box is shifted between input and output. Often the translation is the same (e.g., move by a fixed number of rows and columns) rather than a rotation or reflection.</description>\\n<example>Suppose in every example the top-left of the bounding box ends up shifted down and to the right by the same offset; then the rule is “translate the bounding box by that fixed offset” rather than changing its orientation or color.</example>\\n</note3>\\n\\n<note4>\\n<description>When you translate, copy the entire bounding rectangle exactly (same colors and internal arrangement) and do not rotate or flip it. Preserve the object's internal pattern so the transformed block looks like the original moved intact.</description>\\n<example>If the bounding box is a 2×2 block of color A, after translation it should still be a 2×2 block of A in the same orientation, just placed at the new coordinates.</example>\\n</note4>\\n\\n<note5>\\n<description>Verify the translation is applied to the correct cluster and handle overlaps by checking examples: the moved cluster typically does not overwrite other colors, and the original cluster is cleared. Use the training pairs to confirm which cluster is moved and whether any other color is also affected.</description>\\n<example>If the training outputs show the moved block appearing in a new location without changing other colors, then after applying the same translation to the test input, you should expect the original cluster to be cleared and the new cluster to appear at the translated position without altering other pixels.</example>\\n</note5>\"\n]","isConversational":false},"train":{"kind":"string","value":"[{\"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, 0], [0, 0, 0, 0, 0, 0, 3, 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, 2, 2, 0], [0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 4, 4, 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]], \"output\": [[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, 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, 2, 2, 0], [0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 4, 4, 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]]}, {\"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, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0], [0, 0, 0, 0, 0, 0, 3, 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, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 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]], \"output\": [[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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0], [0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 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]]}, {\"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, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 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]], \"output\": [[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, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 4], [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]]}]"},"test":{"kind":"string","value":"[{\"input\": [[0, 0, 0, 0, 0, 3, 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, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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, 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, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0]], \"output\": [[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, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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, 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, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0]]}]"},"source":{"kind":"string","value":"barc_heavy"},"prompt":{"kind":"string","value":"You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectangular matrix of integers between 0 and 9 (inclusive). Each number corresponds to a color. 0 is black. Your task is to determine the transformation rule from examples and find out the answer, involving determining the size of the output grid for the test and correctly filling each cell of the grid with the appropriate color or number. The transformation only needs to be unambiguous and applicable to the example inputs and the test input. It doesn't need to work for all possible inputs. Observe the examples carefully, imagine the grid visually, and try to find the pattern. Please output your answer within a code block (```), formatted as a grid of numbers. \n\n# Examples\n## Example 1\nInput:\n```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0\n0 0 0 0 0 0 4 4 0 0 0 0 0 0 2 2 0\n0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0\n0 0 0 0 0 0 4 4 0 0 0 0 0 0 2 2 0\n0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\n## Example 2\nInput:\n```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 4 4 0\n0 0 0 0 0 0 0 0 0 0 0 0 4 4 0\n0 0 0 0 0 0 3 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 2 2 0 0 0 0 0 0 0 0 0 0\n0 0 0 2 2 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 2 2 0 0 0 0 0 0 0 4 4 0\n0 0 0 2 2 0 0 0 0 0 0 0 4 4 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\n## Example 3\nInput:\n```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 3 0 0 0 0 0 0 0 0 0 4 4\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4\n0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 2 2 0 4 4\n0 0 0 0 0 0 0 0 0 0 0 2 2 0 4 4\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\n# Test Problem:\n```\n0 0 0 0 0 3 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 2 2 0 0 0 0 0 0 0\n0 0 0 0 0 2 2 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 4 4 0\n0 0 0 0 0 0 0 0 0 0 0 4 4 0\n```"},"answer":{"kind":"string","value":"```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 2 2 0 0 0 0 0 0 0\n0 0 0 0 0 2 2 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 4 4 0\n0 0 0 0 0 0 0 0 0 0 0 4 4 0\n```"},"num_tokens":{"kind":"number","value":3030,"string":"3,030"}}},{"rowIdx":97,"cells":{"abstraction_prompt":{"kind":"string","value":"<|im_start|>user\nDeveloper: # ARC HINT GENERATOR\n\n## Role & Goal\nYou are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted hint that helps the user discover the core transformation principle for themselves without revealing the answer.\n\nBegin with a concise checklist (3-7 bullets) of what you will do; keep items conceptual, not implementation-level.\n\n---\n\n## Hint Generation Strategy\n1. **Compare** the input and output grids for each example. Identify the shared transformation pattern that allows the input grid to be converted into the output grid.\n2. **Identify the Core Principle**: Review the problem description and ground-truth solution to fully discern the key transformation rule. Break it down into its essential operations (e.g., object completion, pattern repetition, symmetry, gravity), paying close attention to properties such as object count, shapes, colors, sizes, symmetry, repetition, relative positioning, and broader grid-level patterns.\n3. **Craft a Targeted Hint**: Generate a hint that guides the user toward the core insight needed to solve the problem. The hint should assist the user during their attempt without revealing the solution.\n4. Structure each note using the template below:\n - **Description** (up to 3 sentences): Explain the concept, when and why it applies, and why it is effective. Include any relevant general formula or principle in its most general form.\n - **Example** (up to 6 sentences): Present a worked example covering all aspects of the description, using a simplified yet representative scenario (not necessarily from the current problem).\n - Optionally, include **Heuristics** or **Pitfalls** in the note where relevant.\n - Focus on methodologies and core principles over specific calculations or problem details.\n - Ensure each hint applies broadly—at least 80% of analogous problems.\n\nAfter generating a hint, verify that no specifics of the solution are revealed, and that the hint remains at the level of guiding the approach.\n\n### Output Format\nProduce a **sequence of 5** notes in the structure:\n<note1>\n<description>...</description>\n<example>...</example>\n</note1>\n<note2>\n<description>...</description>\n<example>...</example>\n</note2>\n...\n\n### Design Guidelines\n- Clarity: Use precise language and correct sentence structure.\n- Atomicity: Each note addresses one recognizable sub-problem.\n- Self-containment: All information needed to understand the idea and its application is within the note.\n- Generalizability: Avoid problem-specific details or variables.\n- Transferability: Notes should apply across a class of problems.\n- Distinctness: Each note addresses a distinct principle.\n\n---\n\n## Guidelines\n- **Guide, Don't Solve**: Illuminate the approach, not the answer. Emphasize what to observe or consider.\n- **Specific yet Abstract**: Use concrete grid details (e.g., \"note the relationship between the blue and red pixels\") to ground abstract patterns (e.g., \"think about one color containing another\").\n\nValidate your generated hint: confirm it is self-contained, actionable, and nondirective. If any aspect is too revealing, revise before finalizing.\n\n---\n\n## Inputs\n### Problem Description\nA full ARC problem, including input/output pairs for training and testing.\n\nYou will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectangular matrix of integers between 0 and 9 (inclusive). Each number corresponds to a color. 0 is black. Your task is to determine the transformation rule from examples and find out the answer, involving determining the size of the output grid for the test and correctly filling each cell of the grid with the appropriate color or number. The transformation only needs to be unambiguous and applicable to the example inputs and the test input. It doesn't need to work for all possible inputs. Observe the examples carefully, imagine the grid visually, and try to find the pattern. Please output your answer within a code block (```), formatted as a grid of numbers. \n\n# Examples\n## Example 1\nInput:\n```\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n```\n\nOutput:\n```\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n```\n\n## Example 2\nInput:\n```\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 7 7 7 7 5 5 5 5\n5 5 7 7 7 7 5 5 5 5\n5 5 7 7 7 7 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n```\n\nOutput:\n```\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5\n5 5 5 7 7 7 7 5 5 5\n5 5 5 7 7 7 7 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n```\n\n## Example 3\nInput:\n```\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n```\n\nOutput:\n```\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n```\n\n# Test Problem:\n```\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n```\n\n---\n\n\n# Generated Hint<|im_end|>\n<|im_start|>assistant\n"},"abstraction_prompt_length":{"kind":"number","value":2174,"string":"2,174"},"generated_abstractions":{"kind":"list like","value":["<note1>\n<description>Look for the single non-background color that forms a compact, rectangular region. This color is usually the only one that changes from input to output and is treated as the object to transform.</description>\n<example>Imagine a mostly gray grid with a solid red rectangle somewhere inside. The red rectangle is the object: it is contiguous, has a rectangular bounding box, and appears only once. Identifying this object is the first step because the transformation targets it specifically.</example>\n</note1>\n\n<note2>\n<description>Measure the object's bounding box: record its height and width and the coordinates of its top-left corner. These four numbers (top row, left column, height, width) are the key parameters that determine how the object will be moved.</description>\n<example>If the object occupies rows 2..5 and columns 3..6, then its top row is 2, left column is 3, height is 4 and width is 4. Keep these four values — they will be used to compute the new placement.</example>\n</note2>\n\n<note3>\n<description>Compute the new top-left by adding the object's height and width to its current top-left: new_top = old_top + height, new_left = old_left + width. In other words, the object is shifted by (height, width) relative to its original corner.</description>\n<example>For an object at (2,3) with height 4 and width 4, the new top-left becomes (2+4, 3+4) = (6,7). This arithmetic is the core translation rule you should apply.</example>\n</note3>\n\n<note4>\n<description>Place the object at the computed top-left and keep its color and internal pattern exactly as before; do not resize or recolor it. If the new top-left would place the object outside the grid, the examples typically keep the object inside (so use the grid bounds as a constraint if needed).</description>\n<example>After computing (6,7) as the new top-left, paste the same 4×4 rectangle there unchanged. If that would push the rectangle off the grid, check the examples to see whether the intended placement is clipped or shifted back to fit.</example>\n</note4>\n\n<note5>\n<description>Finally, clear the original object's cells (set them to the background color) so the object appears only at its new location. This ensures the output shows the single, freshly placed object rather than overlapping copies.</description>\n<example>Once the rectangle is pasted at the new coordinates, set every cell that was part of the original rectangle back to the background color (e.g., gray). The result should be a single, clean copy of the object at its new position.</example>\n</note5>","<note1>\n<description>Look for the single compact region whose color differs from the background; treat that region as the object to be transformed. The transformation usually acts on this whole contiguous colored block rather than on individual pixels scattered across the grid.</description>\n<example>Imagine a mostly uniform grid with one solid square of a different color sitting in the middle. That solid square is the object you should focus on: record its color and its bounding box (top, bottom, left, right) before applying any move.</example>\n</note1>\n\n<note2>\n<description>Compute the object's bounding box and its height and width. The bounding box gives you the dimensions and exact placement (row range and column range) of the object so you can reason about how it might be moved or resized.</description>\n<example>If the colored pixels occupy rows 3–6 and columns 4–7, the bounding box is 4 rows by 4 columns. These numbers tell you the object is a compact block and that any transformation will preserve those dimensions (unless the examples suggest otherwise).</example>\n</note2>\n\n<note3>\n<description>Compare the object's topmost row across examples: if it is consistently higher in the output than in the input, the object has been translated upward. In other words, the object's vertical position changed while its shape and color stayed the same.</description>\n<example>If in the input the object's top row is at row 2 but in the output it is at row 0, the object moved up by two rows. That consistent upward shift across examples points to a vertical translation rather than a rotation or reflection.</example>\n</note3>\n\n<note4>\n<description>Decide whether the move preserves the object's width and height: if the colored pixels still form the same shape and occupy the same number of rows/columns in the output, the transformation is a pure translation (no resizing or rotation). This distinguishes translation from operations that alter shape.</description>\n<example>A 3×3 block that remains 3×3 after the transformation means the operation only changed its position, not its size or orientation. Confirm this by checking that the same number of colored pixels appear in the output and that they form the same contiguous rectangle.</example>\n</note4>\n\n<note5>\n<description>Apply the same kind of upward translation to the test input: translate the object up by the same amount seen in the training examples and keep it the same size and color. As a final check, ensure the object stays entirely inside the grid (if necessary, only translate as far as the grid boundary allows).</description>\n<example>Take the test object's bounding box, move its top row upward by the same offset you observed in the examples, and place the same-sized block at the new position. Verify that no pixels are lost or duplicated and that the object's color matches the original.</example>\n</note5>","<note1>\n<description>Look first for the single non-background color that forms a compact rectangular patch; that patch is the element being transformed. When only one such block exists, it is the natural candidate to track between input and output.</description>\n<example>Imagine a grid mostly filled with color A and a single contiguous rectangle of color B. Counting colors and inspecting connected components will quickly reveal B as the unique object to follow.</example>\n</note1>\n\n<note2>\n<description>Measure the object's bounding box: record its top row, bottom row, left column and right column (or equivalently its height and width). These four numbers fully describe the object's shape and position and are the basis for any translation or resizing operation.</description>\n<example>If the colored pixels occupy rows 2–4 and columns 5–8, then the bounding box is top=2, bottom=4, left=5, right=8 (height=3, width=4); those values let you refer to the object unambiguously.</example>\n</note2>\n\n<note3>\n<description>Check whether the object's bounding box is preserved in the output (same height and width). If so, the transformation is a rigid translation (no rotation, reflection, or resizing) and only the position changes.</description>\n<example>If the input box is 3×4 and the output box is also 3×4, then you should treat the object as a rigid block and focus on how its coordinates are altered rather than on changing its size.</example>\n</note3>\n\n<note4>\n<description>Compare the object's column indices (left and right) between input and output: they are moved together by the same horizontal offset. This means the object is translated horizontally by a constant amount in both examples.</description>\n<example>If the object's left column changes from 2 to 6 between input and output, then every pixel in that object shifts right by +4; the same offset applies to the right column.</example>\n</note4>\n\n<note5>\n<description>Use the training pairs to infer the offset and apply it to the test object: translate the object's bounding-box coordinates by that offset and place it inside the grid while keeping its color and shape. Verify the placement doesn't overlap the background and matches the examples' behavior.</description>\n<example>From the examples determine the consistent horizontal shift, then compute the new top/left by adding that shift to the original top/left; fill the new bounding-box with the object's color and leave all other cells unchanged.</example>\n</note5>","<note1>\n<description>First isolate the foreground object: find the color that forms a compact, multi-cell region distinct from the uniform background. Treat that region as a single entity to be transformed rather than as many independent pixels.</description>\n<example>Imagine a mostly blue grid with one contiguous red block. Mark every red cell as belonging to the same object and ignore stray single pixels of other colors; that red block is the thing you will move or resize.</example>\n</note1>\n\n<note2>\n<description>Compute the object’s bounding box and its width and height. Knowing these simple metrics tells you how large the object is and whether it is a square or rectangle.</description>\n<example>If the red block occupies rows 2–4 and columns 3–6, its bounding box spans height=3 and width=4. These numbers are what you will use to decide how to place or resize the object.</example>\n</note2>\n\n<note3>\n<description>Compare the object’s dimensions to the grid’s dimensions: the transformation is about making the object as large as it can be while staying inside the grid. This usually means expanding or re-centering the block so it fills more of the available space.</description>\n<example>On a 10×10 grid, a 3×4 block that sits near the edge can be moved or extended so that its bounding box becomes 4×4 (or even 6×6 if there is room), always keeping the block’s color and shape unchanged.</example>\n</note3>\n\n<note4>\n<description>Apply the chosen enlargement by copying the object’s color into new cells within the expanded bounding box, leaving the background untouched. The operation is a fill of the new box with the object’s color, not a rotation or recoloring.</description>\n<example>If you decide to expand a 3×3 green square into a 4×4 square, paint every cell in that 4×4 area green while keeping the rest of the grid as it was; the object’s color and shape are preserved, only its size increases.</example>\n</note4>\n\n<note5>\n<description>Be mindful of alignment and edge cases: the examples keep the object’s orientation and use the same color, and if the object already fills its natural size, the output may leave it unchanged. Always check the grid limits before filling new cells.</description>\n<example>If the red block is already 6×6 and there is no room to grow further, the output will show it in place. If it is smaller, the transformation will typically expand it so it is larger or centered, but never change its color or rotate it.</example>\n</note5>","<note1>\n<description>Locate the single non-background object by finding the color that differs from the dominant background. This object is usually contiguous and rectangular; identifying its bounding box (min/max row and column) gives you its height, width, and exact location.</description>\n<example>Imagine a grid filled with color A except for a contiguous block of color B. Count the contiguous B pixels and take the smallest and largest row and column indices that contain B — those four numbers define a rectangle (height = max_row - min_row + 1, width = max_col - min_col + 1).</example>\n</note1>\n\n<note2>\n<description>Decide the target placement by measuring the vertical distance from the top of the grid to the object's top edge and from the bottom edge to the grid bottom. The examples consistently choose the placement that is farther from the background edge (i.e., the side with the larger gap), so prefer the side with the greater vertical margin.</description>\n<example>If the object sits 2 rows from the top but 4 rows from the bottom, the bottom placement is chosen because 4 > 2. If it sits 5 rows from the top and 5 from the bottom, either side is acceptable but prefer the side that matches the examples' consistent tie-break.</example>\n</note2>\n\n<note3>\n<description>Keep the object's shape and color unchanged and do not rotate or resize it. The transformation is a translation (a shift) only; the object's internal pattern and dimensions remain identical after placement.</description>\n<example>A 3×4 colored rectangle should still be 3×4 after the move — only its row indices are changed while column indices are preserved. So copy the rectangle exactly and place it in the new vertical location.</example>\n</note3>\n\n<note4>\n<description>When translating, align the object so its columns remain the same (do not shift horizontally) and place it flush against the chosen background edge. This preserves the object's left/right alignment and keeps the grid background uniform around the object.</description>\n<example>If the object spans columns 3–6, keep those columns after moving; slide the whole rectangle vertically so its leftmost column lines up with the chosen background edge (top or bottom). The background cells immediately adjacent to the object will remain the background color.</example>\n</note4>\n\n<note5>\n<description>After placement, verify the object is fully inside the grid and that no other colored pixels were altered. If you accidentally rotated, mirrored, or changed the object's color, that will break the pattern seen in the examples — re-check alignment and preservation of color and shape.</description>\n<example>After moving the rectangle to the chosen side, scan the grid to ensure every cell that was the object color remains the same color and that the rectangle fits entirely inside the grid. If something looks off, re-evaluate which side was chosen and whether the object was translated rather than transformed.</example>\n</note5>","<note1>\n<description>First isolate the object by finding the smallest axis-aligned rectangle that contains every cell of the non-background color. This rectangle is defined by the minimum and maximum row and column indices of that color and summarizes the object's shape and size.</description>\n<example>Imagine a 3×4 block of blue pixels in a sea of gray. The bounding rectangle is exactly that 3×4 area (min row..max row, min col..max col). Working with that rectangle makes it easy to reason about where to move or resize the object without tracking individual pixels.</example>\n</note1>\n\n<note2>\n<description>Check whether the output preserves the rectangle's width and height exactly. If so, the transformation is a translation (a shift) rather than a resize, rotation, or reflection—so you can focus on changing position only.</description>\n<example>If the object in the input is 3 rows by 4 columns and the output shows the same 3×4 block of the same color, then you should treat the operation as a relocation of that block rather than as changing its shape or orientation.</example>\n</note2>\n\n<note3>\n<description>Look for a consistent vertical displacement: in the examples the rectangle is moved straight down by a fixed number of rows. Determine that offset by comparing the top row indices of the object in input and output across examples.</description>\n<example>For instance, if the input object starts at row 2 and the output object starts at row 5 in every training pair, that indicates a downward shift of 3 rows. Use that same offset when you move the object in the test case.</example>\n</note3>\n\n<note4>\n<description>When moving the rectangle, keep its internal pattern and color unchanged and fill any new background cells with the original background color. Do not alter the block's orientation, colors, or internal arrangement—only its position.</description>\n<example>If the rectangle contains a hollow center or a repeated motif, that motif should appear at the same relative coordinates inside the translated rectangle; the surrounding cells become the background color wherever the rectangle used to be.</example>\n</note4>\n\n<note5>\n<description>Use simple invariants to validate your result: the count of colored cells and the number of rows/columns in the rectangle should be unchanged after the move, and the background should remain uniform elsewhere. If those invariants are violated, re-check your bounding box or the assumed offset.</description>\n<example>After translating the rectangle down by the determined offset, count the colored pixels and confirm they match the original count; if they do, the transformation is consistent and likely correct. This check prevents accidental resizing or color mixing.</example>\n</note5>","<note1>\n<description>Isolate the object: find the single contiguous cluster of non-background cells and treat it as one unit. Knowing its color and the number of cells inside it simplifies reasoning about what can be done to it.</description>\n<example>Imagine a grid of background color A with a solid square of color B occupying some interior cells. Record the B-cluster as the object — its color and the count of B cells are the only attributes you need to consider next.</example>\n</note1>\n\n<note2>\n<description>Decide the object's bounding box and its size: compute the min/max row and column of the object to get width and height, and note whether those dimensions are equal. A square bounding box indicates a uniform filled square.</description>\n<example>If the object occupies rows 2–5 and columns 3–6, its bounding box is 4×4; if it occupies rows 3–4 and columns 6–7, its bounding box is 2×2. Use those dimensions to reason about how the object could be moved or resized.</example>\n</note2>\n\n<note3>\n<description>Look for a uniform translation that moves the object to a canonical corner or edge: try shifting the bounding box by a fixed vector (same row change and same column change) so the object ends up in a consistent corner (e.g., top-left). This is often a simple translation rather than rotation or reflection.</description>\n<example>Take a 3×3 object whose bounding box is at rows 6–8 and cols 4–6; moving it by (-2, -2) (i.e., subtract 2 from each row and each column) places its top-left at the grid origin, keeping the object's orientation and shape unchanged.</example>\n</note3>\n\n<note4>\n<description>Do not alter the object's shape or color when moving it: only translate (or possibly resize uniformly) the cluster so it fits the grid while preserving its internal pattern. The transformation should keep the object's internal arrangement intact.</description>\n<example>If the object is a filled 2×3 rectangle, after translation it should still be a 2×3 rectangle of the same color; you should not rotate, mirror, or change pixel values inside the object.</example>\n</note4>\n\n<note5>\n<description>Validate by checking consistency across examples and handling edge cases: ensure the translated object fits entirely inside the grid, that the background elsewhere remains unchanged, and that the same operation explains every example. If the object touches the grid edge, a different uniform shift may be needed.</description>\n<example>If multiple training examples show the same color-cluster moved to the same corner, the same translation vector should work for the test case; if a cluster is already touching an edge, try a different constant offset so the object still fits without clipping.</example>\n</note5>","<note1>\n<description>Spot the object: look for a contiguous cluster of cells that are not the dominant background color. Treat that cluster as a single object whose pixels all share the same color and form a clear boundary.</description>\n<example>Imagine a mostly blue grid with a compact red block; the red block is the object. Counting and grouping same-colored pixels will show that red forms a single connected component while blue fills the rest.</example>\n</note1>\n\n<note2>\n<description>Compute the object's bounding box: record the smallest and largest row and column indices that contain the object's pixels. This gives the object's height (rows) and width (columns) and the top-left corner (min row, min col).</description>\n<example>If the red block occupies rows 2–4 and columns 5–8, its bounding box is 3 rows by 4 columns and its top-left corner is (row 2, column 5). Those four numbers summarize the object's placement and size.</example>\n</note2>\n\n<note3>\n<description>Translate the object to the top-left: keep the object's shape and color unchanged but move every pixel so its top-left coordinate becomes (0,0). In other words, subtract the bounding-box top-left from each pixel's coordinates.</description>\n<example>A 2×4 block with top-left (r,c) becomes a 2×4 block at (0,0) after this shift; every red pixel's row and column are reduced by r and c respectively, preserving the block's internal pattern.</example>\n</note3>\n\n<note4>\n<description>Preserve background and relative layout: do not change the background color or any other colored regions outside the moved object. Only the object's pixels are relocated; the rest of the grid remains exactly as it was.</description>\n<example>If the grid had a different color elsewhere, that color stays where it is after the move. The moved object simply occupies the top-left area while other colored pixels keep their original positions.</example>\n</note4>\n\n<note5>\n<description>Watch for edge cases: ensure the object is a single solid color and connected (no holes or multiple separate pieces). If the bounding box is empty or contains only background, no translation is needed; otherwise apply the translation as described.</description>\n<example>If the red cluster is disconnected into two islands, you would need to decide whether to treat them as one object or separately—but in typical problems the object is a single contiguous rectangle. If the bounding box is empty, the object is already at the top-left and you leave it unchanged.</example>\n</note5>","<note1>\n<description>First, identify the background and the single non-background object: the background is the color that fills most of the grid, and the object is the contiguous patch of a different color. Treat that patch as a single unit to be transformed.</description>\n<example>Imagine a grid mostly filled with color A and a 2×3 rectangle of color B somewhere inside. Mark the B region as the object and ignore isolated stray pixels of other colors; focus on that rectangle as the element to move or resize.</example>\n</note1>\n\n<note2>\n<description>Compute the object’s bounding box and record its height and width. These two numbers (h, w) are the key invariants that determine how the object will be changed in the output.</description>\n<example>If the object occupies rows 3–4 and columns 6–8, its bounding box spans height 2 and width 3. Record h=2 and w=3 — these values will be used to decide the next step.</example>\n</note2>\n\n<note3>\n<description>Look for a simple geometric transformation: the object is often turned into a square whose side length equals its width (or equivalently, its height). In other words, swap height and width to produce a square of side equal to the original dimension.</description>\n<example>For a rectangle 2 rows by 3 columns, a natural square to make is 3×3 (use the original width as the square side). For a 4×2 rectangle, use a 2×2 square (use the original height).</example>\n</note3>\n\n<note4>\n<description>Decide the anchor for the new square: the examples consistently place the square so that the original bounding-box top-left corner becomes the new square’s top-left. That keeps the object anchored at the same relative position inside the grid.</description>\n<example>If the original box top-left is at (r,c), the new square should also start at (r,c). The square may extend outside the original box in other directions, but it always begins at that same corner.</example>\n</note4>\n\n<note5>\n<description>Recolor the square with the object’s original color and leave all other cells unchanged. Verify that the new square has exactly the side length you computed and that only that square differs from the input.</description>\n<example>After creating a 3×3 square at the original top-left, fill it with the object’s color and check the rest of the grid remains identical to the input. This confirms you applied the intended geometric and color transformation.</example>\n</note5>","<note1>\n<description>First isolate the object: find the contiguous region of a color that is different from the dominant background. Treat that region as the single unit to be transformed, not as many independent pixels.</description>\n<example>Imagine a mostly-blue grid with a single contiguous red rectangle. Mark every red pixel and compute the minimal bounding rectangle that contains them — that rectangle is the object you will move. If there are multiple disconnected red patches, consider each patch separately or treat them as one object if they are the same color.</example>\n</note1>\n\n<note2>\n<description>Compute the object's bounding box and record its top-left coordinates (row and column) and its width and height. These four numbers summarize the object's placement and size and are the only attributes you need to reproduce the object in the output.</description>\n<example>If the red rectangle occupies rows 4..7 and columns 6..9, then its top-left is (4,6), width = 4 and height = 4. Use those four numbers to describe the object's position and size before any movement.</example>\n</note2>\n\n<note3>\n<description>Look for a consistent horizontal translation across examples: the object's column index is being shifted by a fixed offset while its row index stays the same. That offset is constant for all examples — find it by comparing the object's column in the input and output.</description>\n<example>If in every training pair the object appears one column to the right in the output, then the rule is a horizontal shift by +1. Once you know that offset, apply it to the object's top-left column to compute its new left edge.</example>\n</note3>\n\n<note4>\n<description>Do not alter the object's internal pattern or color: the transformation preserves the object's shape and the background remains unchanged. Only the object's position changes; its pixels keep their relative arrangement and color.</description>\n<example>A 2×3 green block should remain a 2×3 green block after the move — it should not be stretched, rotated, mirrored, or recolored. Verify that the new bounding box contains the same number of pixels of the same color as the original box.</example>\n</note4>\n\n<note5>\n<description>Reconstruct the output by placing the unchanged object at its new top-left (original row + unchanged column + the computed offset) and filling every other cell with the original background color. This produces the minimal, consistent transformation across examples.</description>\n<example>With a known offset and bounding box, copy the object's pixels into the new top-left and leave all other cells as background. If you find a different, smaller object in the examples, apply the same procedure to it separately.</example>\n</note5>","<note1>\n<description>Isolate the object by finding the smallest rectangle that contains every non-background cell. This bounding box (its top, bottom, left and right coordinates) is the primary unit of transformation because the rule operates on the whole object, not on individual pixels.</description>\n<example>Imagine a grid mostly filled with one color and a compact cluster of another color. Draw the tightest rectangle around that cluster — that rectangle's boundaries are what you will move or resize in the transformation.</example>\n</note1>\n\n<note2>\n<description>Compare the bounding-box height and width between input and output to see if the object was scaled. If both dimensions are multiplied by the same integer factor, the object was uniformly scaled; if only one dimension changed, the object was stretched or compressed.</description>\n<example>If an object's bounding box is 4×4 in the input and the output shows a 4×4 block that is 8×8, the object was scaled by a factor of two. If one side doubled while the other stayed the same, the object was stretched.</example>\n</note2>\n\n<note3>\n<description>Check how the scaled bounding box is anchored in the grid. The rule may shift the object so its bounding box touches a specific edge (for example, the top or bottom) rather than preserving its original vertical placement.</description>\n<example>When the object becomes larger, the examples often reposition the object so the top of its bounding box aligns with the grid's top edge; in other cases the bottom may be anchored instead. Determining which edge is used tells you how much to translate the box.</example>\n</note3>\n\n<note4>\n<description>Ensure the object's color and internal pattern are preserved during the transformation. The operation is a geometric change (move, scale) rather than a recoloring or pattern alteration.</description>\n<example>If the object is a solid square of color X, the output should still be a square of color X (possibly larger or moved), with no new colors or internal changes introduced.</example>\n</note4>\n\n<note5>\n<description>Use simple heuristics to pick the right scale factor and anchor: count contiguous rows/columns of the object in the input, and compare the output bounding-box height/width to that count; also look for the same anchor in all training outputs to confirm the intended placement rule.</description>\n<example>For instance, if the object occupies 4 contiguous rows in the input and the output object occupies 8 contiguous rows, a factor of two is suggested. If every training output places the object's top at row 0, then the top-anchor rule is consistent and should be applied to the test case.</example>\n</note5>","<note1>\n<description>Isolate the object: find the color that differs from the uniform background and treat its connected component as the object to transform. Working with the object's bounding box (min/max row and column) simplifies the rest of the reasoning.</description>\n<example>Imagine a 12×12 grid of background color with a single 3×4 block of another color. Record the block's top row, bottom row, left column and right column. Those four numbers summarize the object's position and size for further steps.</example>\n</note1>\n\n<note2>\n<description>Compute the object's vertical span (the number of rows it occupies) and the grid height. Use the vertical span to decide how many rows to preserve from the top of the grid for the object.</description>\n<example>If the grid has 12 rows and the object occupies 4 rows, then the top portion of the grid that will contain the object is the first 4 rows. If the object were 2 rows tall on a 12-row grid, you would consider the top 2 rows for placement.</example>\n</note2>\n\n<note3>\n<description>Reposition the object so its top row aligns with the computed top portion (i.e., place the object so its top edge sits at the same row index as the top portion). Do not change the object's width or color — only move it vertically.</description>\n<example>For a 4×3 object on a 12-row grid, slide the object upward so its top row is the first row of the grid; the object will occupy rows 1–4 and columns 2–4 (keeping the same width).</example>\n</note3>\n\n<note4>\n<description>Keep the object's horizontal alignment unchanged: do not shift left or right unless the examples show a horizontal movement. Maintain the object's internal pattern and color exactly when placing it in the new top position.</description>\n<example>If the object originally started at column 3 and spans 3 columns, after moving it vertically you should still start at column 3 and keep the same 3-column width; only the row indices change.</example>\n</note4>\n\n<note5>\n<description>Validate the result: after repositioning, the object should occupy exactly the computed top rows and the same columns as before, and every other cell should remain the original background color. If something else changed, reconsider the rule (e.g., width change or horizontal shift).</description>\n<example>After placing the object at the top rows, scan the grid: the object's color should appear in the same columns but on the first few rows, and the rest of the grid should be unchanged. If a row below the object or a neighboring column differs, you likely misapplied the vertical-placement rule.</example>\n</note5>","<note1>\n<description>Isolate the object to transform: identify the single contiguous region that is not the background color. Treat that region as the unit to move rather than changing many scattered cells.</description>\n<example>Imagine a 12×12 grid where most cells are color A and one compact block of color B sits somewhere inside. Mark all B cells and note their bounding box (top, bottom, left, right). That bounding box is the object you will relocate.</example>\n</note1>\n\n<note2>\n<description>Use the object's bounding box to define its size and shape: record width and height (and whether it is square or rectangular). The transformation preserves these dimensions and the pattern inside the box.</description>\n<example>If the B pixels form a 4×4 filled rectangle, note width=4, height=4. You will keep that 4×4 block intact when you move it—no stretching or reshaping is needed.</example>\n</note2>\n\n<note3>\n<description>Look for a single consistent translation vector across examples: check how the object's top-left corner moves from input to output and express that as (Δrow, Δcol). The same vector should apply to every training case.</description>\n<example>For several training pairs, compute the difference (output_top_left_row − input_top_left_row) and (output_top_left_col − input_top_left_col). If both differences are the same for each example, that difference is the translation to use.</example>\n</note3>\n\n<note4>\n<description>Apply the translation while preserving the object's internal color and orientation: copy the whole bounding-box pattern and place it at the new coordinates, leaving the background unchanged. Do not rotate or recolor the object.</description>\n<example>Take the 4×4 block you identified, shift it by the computed vector, and paste it into the grid. The block's internal pattern (every cell still color B) remains identical except for its position.</example>\n</note4>\n\n<note5>\n<description>Validate by checking invariants: the object should remain contiguous, its color unchanged, and the background should be unchanged except for the moved object. If anything else changes, re-check your bounding-box and translation vector.</description>\n<example>After moving the block, count B cells and confirm the same number appears in the new location; ensure no other cells were altered. If counts or shape differ, you likely misidentified the object or used the wrong translation.</example>\n</note5>","<note1>\n<description>Identify the target object by its color and shape: find the contiguous region of a non-background color and compute its bounding box (top, bottom, left, right). This gives you the object's width, height and its original position relative to the grid edges. Working with these four coordinates makes the transformation easy to express and apply.</description>\n<example>Imagine a 7×7 grid with a single 4×3 rectangle of color A. Its bounding box is top=1, bottom=4, left=2, right=5; width=4 and height=3. If you need to move or resize that object later, these numbers let you compute where the new box should be placed.</example>\n</note1>\n\n<note2>\n<description>Look for a horizontal translation: many tasks move the object toward the left edge by shifting its columns left by the same offset for every row. In other words, subtract a fixed horizontal offset from each column index while keeping the object's height and row indices unchanged. This keeps the object's shape and color identical but changes its left–right placement.</description>\n<example>For example, a 3×3 square at columns 4–6 can be shifted so it occupies columns 1–3 by subtracting 3 from every column index (columns 4→1, 5→2, 6→3). The 3 rows remain the same, only the columns have been translated.</example>\n</note2>\n\n<note3>\n<description>When the object reaches the left edge, do not wrap or reflect it: keep the object's left edge at the grid's leftmost column and keep its rows fixed. The transformation is a rigid translation until the left edge is at 0, after which the object is anchored there. This preserves vertical alignment while anchoring horizontally.</description>\n<example>If a 2×4 rectangle ends up with its left column at 0 after shifting, it will occupy columns 0–3 (not columns 0–3 and then wrap around). Its top and bottom rows remain unchanged from before the shift.</example>\n</note3>\n\n<note4>\n<description>Handle overlapping with the background by replacing background cells with the object's color; do not erase the object's pixels. If the shifted object would write into background cells, those cells become the object color; if the object already occupied those cells, they stay the object color. This is a fill/overlay operation rather than a deletion.</description>\n<example>Suppose a blue rectangle is moved so it covers some black cells; those black cells become blue. If the rectangle already covered those cells before, they remain blue. The operation is \"paint the object's color into any cell it covers.\"</example>\n</note4>\n\n<note5>\n<description>Apply the same horizontal offset to every row and preserve the object's color and internal pattern. Treat each row independently when shifting: shift each row by the same column-offset, then write the row back with the object color where appropriate. This ensures the object keeps its shape and color after the transformation.</description>\n<example>A 1×6 horizontal stripe can be moved by subtracting 3 from each of its 6 column indices; every row of that stripe is translated the same way and then written back with the stripe's color. Doing this for every row produces the same horizontal translation across the object.</example>\n</note5>","<note1>\n<description>Find the object by color: locate the color that forms a compact contiguous region (often the only non-background color). Treat that region as a single entity to be transformed rather than many separate pixels.</description>\n<example>Imagine a grid of black with a 4×4 red square somewhere inside. Mark all red pixels as one object; ignore isolated single pixels of other colors when deciding which shape to move.</example>\n</note1>\n\n<note2>\n<description>Compute the object's bounding box and its center: the bounding box gives the object's width and height; the center is the midpoint of that box (use integer or half-integer depending on whether the box is odd or even in size).</description>\n<example>For a 4×4 square the bounding box spans 4 rows and 4 columns, so its center is at the midpoint of that span (e.g., (row_center = (top+bottom)/2, col_center = (left+right)/2)).</example>\n</note2>\n\n<note3>\n<description>Translate the entire object so its center aligns with the grid center (use the same centering rule for even-sized boxes). This produces a single, symmetric placement of the object in the grid.</description>\n<example>If the grid is 10×10 and the object's center is at (r0,c0), move the object so its center becomes (5,5) by shifting each pixel by (5 − r0, 5 − c0) while keeping the object's shape and orientation unchanged.</example>\n</note3>\n\n<note4>\n<description>Keep the object's size, orientation, and color unchanged; only translate it. Do not resize, rotate, or recolor the object when applying the rule.</description>\n<example>If the object is a 4×4 filled block, after translation it should still be a 4×4 block in the same orientation and with the same color, just in a new location.</example>\n</note4>\n\n<note5>\n<description>Handle multiple examples by applying the same centering rule consistently (preserve orientation and color), and watch for edge cases such as even-sized boxes or multiple colored objects—examples usually show a single compact object to move.</description>\n<example>If you see two identical objects in different positions, try centering each on the grid center; if the examples always show one clear object, focus on that object and do not split or merge it.</example>\n</note5>","<note1>\n<description>Look for a single, compact colored region that stands out from the uniform background. When one color forms a contiguous rectangular block, that block is usually the object to transform.</description>\n<example>Imagine a mostly gray grid with a solid blue rectangle somewhere inside. Count and compare colors: the blue pixels form a compact block while gray fills most of the grid; that blue block is the likely object to manipulate.</example>\n</note1>\n\n<note2>\n<description>Compute the object’s bounding box: record its minimum and maximum row and column indices. The bounding box gives the block’s height and width and its top-left corner (min row, min column).</description>\n<example>If the colored pixels occupy rows 3..6 and columns 2..5, then the bounding box is rows 3–6 (height 4) and columns 2–5 (width 4), with top-left at (row 3, column 2).</example>\n</note2>\n\n<note3>\n<description>Translate the whole block by the same offset in both directions so the bounding-box top-left moves to the grid origin (row 0, column 0). This is a pure translation: every pixel inside the box is moved by the same (row_offset, col_offset).</description>\n<example>With a bounding box at (3,2), subtract 3 from every row index and 2 from every column index so the block’s top-left lands at (0,0); the relative pattern and colors remain unchanged, only its position does.</example>\n</note3>\n\n<note4>\n<description>After translation, check that the object fits entirely inside the grid and that no other colored pixels are introduced. The transformation preserves color and shape, so the translated block should be a contiguous rectangle of the same color.</description>\n<example>If the translated block would extend outside the grid, the examples usually keep it fully inside; if everything fits, the translated rectangle will match the original block’s color and size exactly.</example>\n</note4>\n\n<note5>\n<description>When you apply the translation, leave every other cell unchanged. The correct operation is a rigid translation of the detected object, not a rotation, reflection, or recoloring of other areas.</description>\n<example>Take the original grid, move only the bounding-box pixels by the computed offset, and copy the rest of the grid unchanged; the resulting grid will show the object in a new location while the background remains identical.</example>\n</note5>"],"string":"[\n \"<note1>\\n<description>Look for the single non-background color that forms a compact, rectangular region. This color is usually the only one that changes from input to output and is treated as the object to transform.</description>\\n<example>Imagine a mostly gray grid with a solid red rectangle somewhere inside. The red rectangle is the object: it is contiguous, has a rectangular bounding box, and appears only once. Identifying this object is the first step because the transformation targets it specifically.</example>\\n</note1>\\n\\n<note2>\\n<description>Measure the object's bounding box: record its height and width and the coordinates of its top-left corner. These four numbers (top row, left column, height, width) are the key parameters that determine how the object will be moved.</description>\\n<example>If the object occupies rows 2..5 and columns 3..6, then its top row is 2, left column is 3, height is 4 and width is 4. Keep these four values — they will be used to compute the new placement.</example>\\n</note2>\\n\\n<note3>\\n<description>Compute the new top-left by adding the object's height and width to its current top-left: new_top = old_top + height, new_left = old_left + width. In other words, the object is shifted by (height, width) relative to its original corner.</description>\\n<example>For an object at (2,3) with height 4 and width 4, the new top-left becomes (2+4, 3+4) = (6,7). This arithmetic is the core translation rule you should apply.</example>\\n</note3>\\n\\n<note4>\\n<description>Place the object at the computed top-left and keep its color and internal pattern exactly as before; do not resize or recolor it. If the new top-left would place the object outside the grid, the examples typically keep the object inside (so use the grid bounds as a constraint if needed).</description>\\n<example>After computing (6,7) as the new top-left, paste the same 4×4 rectangle there unchanged. If that would push the rectangle off the grid, check the examples to see whether the intended placement is clipped or shifted back to fit.</example>\\n</note4>\\n\\n<note5>\\n<description>Finally, clear the original object's cells (set them to the background color) so the object appears only at its new location. This ensures the output shows the single, freshly placed object rather than overlapping copies.</description>\\n<example>Once the rectangle is pasted at the new coordinates, set every cell that was part of the original rectangle back to the background color (e.g., gray). The result should be a single, clean copy of the object at its new position.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the single compact region whose color differs from the background; treat that region as the object to be transformed. The transformation usually acts on this whole contiguous colored block rather than on individual pixels scattered across the grid.</description>\\n<example>Imagine a mostly uniform grid with one solid square of a different color sitting in the middle. That solid square is the object you should focus on: record its color and its bounding box (top, bottom, left, right) before applying any move.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object's bounding box and its height and width. The bounding box gives you the dimensions and exact placement (row range and column range) of the object so you can reason about how it might be moved or resized.</description>\\n<example>If the colored pixels occupy rows 3–6 and columns 4–7, the bounding box is 4 rows by 4 columns. These numbers tell you the object is a compact block and that any transformation will preserve those dimensions (unless the examples suggest otherwise).</example>\\n</note2>\\n\\n<note3>\\n<description>Compare the object's topmost row across examples: if it is consistently higher in the output than in the input, the object has been translated upward. In other words, the object's vertical position changed while its shape and color stayed the same.</description>\\n<example>If in the input the object's top row is at row 2 but in the output it is at row 0, the object moved up by two rows. That consistent upward shift across examples points to a vertical translation rather than a rotation or reflection.</example>\\n</note3>\\n\\n<note4>\\n<description>Decide whether the move preserves the object's width and height: if the colored pixels still form the same shape and occupy the same number of rows/columns in the output, the transformation is a pure translation (no resizing or rotation). This distinguishes translation from operations that alter shape.</description>\\n<example>A 3×3 block that remains 3×3 after the transformation means the operation only changed its position, not its size or orientation. Confirm this by checking that the same number of colored pixels appear in the output and that they form the same contiguous rectangle.</example>\\n</note4>\\n\\n<note5>\\n<description>Apply the same kind of upward translation to the test input: translate the object up by the same amount seen in the training examples and keep it the same size and color. As a final check, ensure the object stays entirely inside the grid (if necessary, only translate as far as the grid boundary allows).</description>\\n<example>Take the test object's bounding box, move its top row upward by the same offset you observed in the examples, and place the same-sized block at the new position. Verify that no pixels are lost or duplicated and that the object's color matches the original.</example>\\n</note5>\",\n \"<note1>\\n<description>Look first for the single non-background color that forms a compact rectangular patch; that patch is the element being transformed. When only one such block exists, it is the natural candidate to track between input and output.</description>\\n<example>Imagine a grid mostly filled with color A and a single contiguous rectangle of color B. Counting colors and inspecting connected components will quickly reveal B as the unique object to follow.</example>\\n</note1>\\n\\n<note2>\\n<description>Measure the object's bounding box: record its top row, bottom row, left column and right column (or equivalently its height and width). These four numbers fully describe the object's shape and position and are the basis for any translation or resizing operation.</description>\\n<example>If the colored pixels occupy rows 2–4 and columns 5–8, then the bounding box is top=2, bottom=4, left=5, right=8 (height=3, width=4); those values let you refer to the object unambiguously.</example>\\n</note2>\\n\\n<note3>\\n<description>Check whether the object's bounding box is preserved in the output (same height and width). If so, the transformation is a rigid translation (no rotation, reflection, or resizing) and only the position changes.</description>\\n<example>If the input box is 3×4 and the output box is also 3×4, then you should treat the object as a rigid block and focus on how its coordinates are altered rather than on changing its size.</example>\\n</note3>\\n\\n<note4>\\n<description>Compare the object's column indices (left and right) between input and output: they are moved together by the same horizontal offset. This means the object is translated horizontally by a constant amount in both examples.</description>\\n<example>If the object's left column changes from 2 to 6 between input and output, then every pixel in that object shifts right by +4; the same offset applies to the right column.</example>\\n</note4>\\n\\n<note5>\\n<description>Use the training pairs to infer the offset and apply it to the test object: translate the object's bounding-box coordinates by that offset and place it inside the grid while keeping its color and shape. Verify the placement doesn't overlap the background and matches the examples' behavior.</description>\\n<example>From the examples determine the consistent horizontal shift, then compute the new top/left by adding that shift to the original top/left; fill the new bounding-box with the object's color and leave all other cells unchanged.</example>\\n</note5>\",\n \"<note1>\\n<description>First isolate the foreground object: find the color that forms a compact, multi-cell region distinct from the uniform background. Treat that region as a single entity to be transformed rather than as many independent pixels.</description>\\n<example>Imagine a mostly blue grid with one contiguous red block. Mark every red cell as belonging to the same object and ignore stray single pixels of other colors; that red block is the thing you will move or resize.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object’s bounding box and its width and height. Knowing these simple metrics tells you how large the object is and whether it is a square or rectangle.</description>\\n<example>If the red block occupies rows 2–4 and columns 3–6, its bounding box spans height=3 and width=4. These numbers are what you will use to decide how to place or resize the object.</example>\\n</note2>\\n\\n<note3>\\n<description>Compare the object’s dimensions to the grid’s dimensions: the transformation is about making the object as large as it can be while staying inside the grid. This usually means expanding or re-centering the block so it fills more of the available space.</description>\\n<example>On a 10×10 grid, a 3×4 block that sits near the edge can be moved or extended so that its bounding box becomes 4×4 (or even 6×6 if there is room), always keeping the block’s color and shape unchanged.</example>\\n</note3>\\n\\n<note4>\\n<description>Apply the chosen enlargement by copying the object’s color into new cells within the expanded bounding box, leaving the background untouched. The operation is a fill of the new box with the object’s color, not a rotation or recoloring.</description>\\n<example>If you decide to expand a 3×3 green square into a 4×4 square, paint every cell in that 4×4 area green while keeping the rest of the grid as it was; the object’s color and shape are preserved, only its size increases.</example>\\n</note4>\\n\\n<note5>\\n<description>Be mindful of alignment and edge cases: the examples keep the object’s orientation and use the same color, and if the object already fills its natural size, the output may leave it unchanged. Always check the grid limits before filling new cells.</description>\\n<example>If the red block is already 6×6 and there is no room to grow further, the output will show it in place. If it is smaller, the transformation will typically expand it so it is larger or centered, but never change its color or rotate it.</example>\\n</note5>\",\n \"<note1>\\n<description>Locate the single non-background object by finding the color that differs from the dominant background. This object is usually contiguous and rectangular; identifying its bounding box (min/max row and column) gives you its height, width, and exact location.</description>\\n<example>Imagine a grid filled with color A except for a contiguous block of color B. Count the contiguous B pixels and take the smallest and largest row and column indices that contain B — those four numbers define a rectangle (height = max_row - min_row + 1, width = max_col - min_col + 1).</example>\\n</note1>\\n\\n<note2>\\n<description>Decide the target placement by measuring the vertical distance from the top of the grid to the object's top edge and from the bottom edge to the grid bottom. The examples consistently choose the placement that is farther from the background edge (i.e., the side with the larger gap), so prefer the side with the greater vertical margin.</description>\\n<example>If the object sits 2 rows from the top but 4 rows from the bottom, the bottom placement is chosen because 4 > 2. If it sits 5 rows from the top and 5 from the bottom, either side is acceptable but prefer the side that matches the examples' consistent tie-break.</example>\\n</note2>\\n\\n<note3>\\n<description>Keep the object's shape and color unchanged and do not rotate or resize it. The transformation is a translation (a shift) only; the object's internal pattern and dimensions remain identical after placement.</description>\\n<example>A 3×4 colored rectangle should still be 3×4 after the move — only its row indices are changed while column indices are preserved. So copy the rectangle exactly and place it in the new vertical location.</example>\\n</note3>\\n\\n<note4>\\n<description>When translating, align the object so its columns remain the same (do not shift horizontally) and place it flush against the chosen background edge. This preserves the object's left/right alignment and keeps the grid background uniform around the object.</description>\\n<example>If the object spans columns 3–6, keep those columns after moving; slide the whole rectangle vertically so its leftmost column lines up with the chosen background edge (top or bottom). The background cells immediately adjacent to the object will remain the background color.</example>\\n</note4>\\n\\n<note5>\\n<description>After placement, verify the object is fully inside the grid and that no other colored pixels were altered. If you accidentally rotated, mirrored, or changed the object's color, that will break the pattern seen in the examples — re-check alignment and preservation of color and shape.</description>\\n<example>After moving the rectangle to the chosen side, scan the grid to ensure every cell that was the object color remains the same color and that the rectangle fits entirely inside the grid. If something looks off, re-evaluate which side was chosen and whether the object was translated rather than transformed.</example>\\n</note5>\",\n \"<note1>\\n<description>First isolate the object by finding the smallest axis-aligned rectangle that contains every cell of the non-background color. This rectangle is defined by the minimum and maximum row and column indices of that color and summarizes the object's shape and size.</description>\\n<example>Imagine a 3×4 block of blue pixels in a sea of gray. The bounding rectangle is exactly that 3×4 area (min row..max row, min col..max col). Working with that rectangle makes it easy to reason about where to move or resize the object without tracking individual pixels.</example>\\n</note1>\\n\\n<note2>\\n<description>Check whether the output preserves the rectangle's width and height exactly. If so, the transformation is a translation (a shift) rather than a resize, rotation, or reflection—so you can focus on changing position only.</description>\\n<example>If the object in the input is 3 rows by 4 columns and the output shows the same 3×4 block of the same color, then you should treat the operation as a relocation of that block rather than as changing its shape or orientation.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a consistent vertical displacement: in the examples the rectangle is moved straight down by a fixed number of rows. Determine that offset by comparing the top row indices of the object in input and output across examples.</description>\\n<example>For instance, if the input object starts at row 2 and the output object starts at row 5 in every training pair, that indicates a downward shift of 3 rows. Use that same offset when you move the object in the test case.</example>\\n</note3>\\n\\n<note4>\\n<description>When moving the rectangle, keep its internal pattern and color unchanged and fill any new background cells with the original background color. Do not alter the block's orientation, colors, or internal arrangement—only its position.</description>\\n<example>If the rectangle contains a hollow center or a repeated motif, that motif should appear at the same relative coordinates inside the translated rectangle; the surrounding cells become the background color wherever the rectangle used to be.</example>\\n</note4>\\n\\n<note5>\\n<description>Use simple invariants to validate your result: the count of colored cells and the number of rows/columns in the rectangle should be unchanged after the move, and the background should remain uniform elsewhere. If those invariants are violated, re-check your bounding box or the assumed offset.</description>\\n<example>After translating the rectangle down by the determined offset, count the colored pixels and confirm they match the original count; if they do, the transformation is consistent and likely correct. This check prevents accidental resizing or color mixing.</example>\\n</note5>\",\n \"<note1>\\n<description>Isolate the object: find the single contiguous cluster of non-background cells and treat it as one unit. Knowing its color and the number of cells inside it simplifies reasoning about what can be done to it.</description>\\n<example>Imagine a grid of background color A with a solid square of color B occupying some interior cells. Record the B-cluster as the object — its color and the count of B cells are the only attributes you need to consider next.</example>\\n</note1>\\n\\n<note2>\\n<description>Decide the object's bounding box and its size: compute the min/max row and column of the object to get width and height, and note whether those dimensions are equal. A square bounding box indicates a uniform filled square.</description>\\n<example>If the object occupies rows 2–5 and columns 3–6, its bounding box is 4×4; if it occupies rows 3–4 and columns 6–7, its bounding box is 2×2. Use those dimensions to reason about how the object could be moved or resized.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a uniform translation that moves the object to a canonical corner or edge: try shifting the bounding box by a fixed vector (same row change and same column change) so the object ends up in a consistent corner (e.g., top-left). This is often a simple translation rather than rotation or reflection.</description>\\n<example>Take a 3×3 object whose bounding box is at rows 6–8 and cols 4–6; moving it by (-2, -2) (i.e., subtract 2 from each row and each column) places its top-left at the grid origin, keeping the object's orientation and shape unchanged.</example>\\n</note3>\\n\\n<note4>\\n<description>Do not alter the object's shape or color when moving it: only translate (or possibly resize uniformly) the cluster so it fits the grid while preserving its internal pattern. The transformation should keep the object's internal arrangement intact.</description>\\n<example>If the object is a filled 2×3 rectangle, after translation it should still be a 2×3 rectangle of the same color; you should not rotate, mirror, or change pixel values inside the object.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate by checking consistency across examples and handling edge cases: ensure the translated object fits entirely inside the grid, that the background elsewhere remains unchanged, and that the same operation explains every example. If the object touches the grid edge, a different uniform shift may be needed.</description>\\n<example>If multiple training examples show the same color-cluster moved to the same corner, the same translation vector should work for the test case; if a cluster is already touching an edge, try a different constant offset so the object still fits without clipping.</example>\\n</note5>\",\n \"<note1>\\n<description>Spot the object: look for a contiguous cluster of cells that are not the dominant background color. Treat that cluster as a single object whose pixels all share the same color and form a clear boundary.</description>\\n<example>Imagine a mostly blue grid with a compact red block; the red block is the object. Counting and grouping same-colored pixels will show that red forms a single connected component while blue fills the rest.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object's bounding box: record the smallest and largest row and column indices that contain the object's pixels. This gives the object's height (rows) and width (columns) and the top-left corner (min row, min col).</description>\\n<example>If the red block occupies rows 2–4 and columns 5–8, its bounding box is 3 rows by 4 columns and its top-left corner is (row 2, column 5). Those four numbers summarize the object's placement and size.</example>\\n</note2>\\n\\n<note3>\\n<description>Translate the object to the top-left: keep the object's shape and color unchanged but move every pixel so its top-left coordinate becomes (0,0). In other words, subtract the bounding-box top-left from each pixel's coordinates.</description>\\n<example>A 2×4 block with top-left (r,c) becomes a 2×4 block at (0,0) after this shift; every red pixel's row and column are reduced by r and c respectively, preserving the block's internal pattern.</example>\\n</note3>\\n\\n<note4>\\n<description>Preserve background and relative layout: do not change the background color or any other colored regions outside the moved object. Only the object's pixels are relocated; the rest of the grid remains exactly as it was.</description>\\n<example>If the grid had a different color elsewhere, that color stays where it is after the move. The moved object simply occupies the top-left area while other colored pixels keep their original positions.</example>\\n</note4>\\n\\n<note5>\\n<description>Watch for edge cases: ensure the object is a single solid color and connected (no holes or multiple separate pieces). If the bounding box is empty or contains only background, no translation is needed; otherwise apply the translation as described.</description>\\n<example>If the red cluster is disconnected into two islands, you would need to decide whether to treat them as one object or separately—but in typical problems the object is a single contiguous rectangle. If the bounding box is empty, the object is already at the top-left and you leave it unchanged.</example>\\n</note5>\",\n \"<note1>\\n<description>First, identify the background and the single non-background object: the background is the color that fills most of the grid, and the object is the contiguous patch of a different color. Treat that patch as a single unit to be transformed.</description>\\n<example>Imagine a grid mostly filled with color A and a 2×3 rectangle of color B somewhere inside. Mark the B region as the object and ignore isolated stray pixels of other colors; focus on that rectangle as the element to move or resize.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object’s bounding box and record its height and width. These two numbers (h, w) are the key invariants that determine how the object will be changed in the output.</description>\\n<example>If the object occupies rows 3–4 and columns 6–8, its bounding box spans height 2 and width 3. Record h=2 and w=3 — these values will be used to decide the next step.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a simple geometric transformation: the object is often turned into a square whose side length equals its width (or equivalently, its height). In other words, swap height and width to produce a square of side equal to the original dimension.</description>\\n<example>For a rectangle 2 rows by 3 columns, a natural square to make is 3×3 (use the original width as the square side). For a 4×2 rectangle, use a 2×2 square (use the original height).</example>\\n</note3>\\n\\n<note4>\\n<description>Decide the anchor for the new square: the examples consistently place the square so that the original bounding-box top-left corner becomes the new square’s top-left. That keeps the object anchored at the same relative position inside the grid.</description>\\n<example>If the original box top-left is at (r,c), the new square should also start at (r,c). The square may extend outside the original box in other directions, but it always begins at that same corner.</example>\\n</note4>\\n\\n<note5>\\n<description>Recolor the square with the object’s original color and leave all other cells unchanged. Verify that the new square has exactly the side length you computed and that only that square differs from the input.</description>\\n<example>After creating a 3×3 square at the original top-left, fill it with the object’s color and check the rest of the grid remains identical to the input. This confirms you applied the intended geometric and color transformation.</example>\\n</note5>\",\n \"<note1>\\n<description>First isolate the object: find the contiguous region of a color that is different from the dominant background. Treat that region as the single unit to be transformed, not as many independent pixels.</description>\\n<example>Imagine a mostly-blue grid with a single contiguous red rectangle. Mark every red pixel and compute the minimal bounding rectangle that contains them — that rectangle is the object you will move. If there are multiple disconnected red patches, consider each patch separately or treat them as one object if they are the same color.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object's bounding box and record its top-left coordinates (row and column) and its width and height. These four numbers summarize the object's placement and size and are the only attributes you need to reproduce the object in the output.</description>\\n<example>If the red rectangle occupies rows 4..7 and columns 6..9, then its top-left is (4,6), width = 4 and height = 4. Use those four numbers to describe the object's position and size before any movement.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a consistent horizontal translation across examples: the object's column index is being shifted by a fixed offset while its row index stays the same. That offset is constant for all examples — find it by comparing the object's column in the input and output.</description>\\n<example>If in every training pair the object appears one column to the right in the output, then the rule is a horizontal shift by +1. Once you know that offset, apply it to the object's top-left column to compute its new left edge.</example>\\n</note3>\\n\\n<note4>\\n<description>Do not alter the object's internal pattern or color: the transformation preserves the object's shape and the background remains unchanged. Only the object's position changes; its pixels keep their relative arrangement and color.</description>\\n<example>A 2×3 green block should remain a 2×3 green block after the move — it should not be stretched, rotated, mirrored, or recolored. Verify that the new bounding box contains the same number of pixels of the same color as the original box.</example>\\n</note4>\\n\\n<note5>\\n<description>Reconstruct the output by placing the unchanged object at its new top-left (original row + unchanged column + the computed offset) and filling every other cell with the original background color. This produces the minimal, consistent transformation across examples.</description>\\n<example>With a known offset and bounding box, copy the object's pixels into the new top-left and leave all other cells as background. If you find a different, smaller object in the examples, apply the same procedure to it separately.</example>\\n</note5>\",\n \"<note1>\\n<description>Isolate the object by finding the smallest rectangle that contains every non-background cell. This bounding box (its top, bottom, left and right coordinates) is the primary unit of transformation because the rule operates on the whole object, not on individual pixels.</description>\\n<example>Imagine a grid mostly filled with one color and a compact cluster of another color. Draw the tightest rectangle around that cluster — that rectangle's boundaries are what you will move or resize in the transformation.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare the bounding-box height and width between input and output to see if the object was scaled. If both dimensions are multiplied by the same integer factor, the object was uniformly scaled; if only one dimension changed, the object was stretched or compressed.</description>\\n<example>If an object's bounding box is 4×4 in the input and the output shows a 4×4 block that is 8×8, the object was scaled by a factor of two. If one side doubled while the other stayed the same, the object was stretched.</example>\\n</note2>\\n\\n<note3>\\n<description>Check how the scaled bounding box is anchored in the grid. The rule may shift the object so its bounding box touches a specific edge (for example, the top or bottom) rather than preserving its original vertical placement.</description>\\n<example>When the object becomes larger, the examples often reposition the object so the top of its bounding box aligns with the grid's top edge; in other cases the bottom may be anchored instead. Determining which edge is used tells you how much to translate the box.</example>\\n</note3>\\n\\n<note4>\\n<description>Ensure the object's color and internal pattern are preserved during the transformation. The operation is a geometric change (move, scale) rather than a recoloring or pattern alteration.</description>\\n<example>If the object is a solid square of color X, the output should still be a square of color X (possibly larger or moved), with no new colors or internal changes introduced.</example>\\n</note4>\\n\\n<note5>\\n<description>Use simple heuristics to pick the right scale factor and anchor: count contiguous rows/columns of the object in the input, and compare the output bounding-box height/width to that count; also look for the same anchor in all training outputs to confirm the intended placement rule.</description>\\n<example>For instance, if the object occupies 4 contiguous rows in the input and the output object occupies 8 contiguous rows, a factor of two is suggested. If every training output places the object's top at row 0, then the top-anchor rule is consistent and should be applied to the test case.</example>\\n</note5>\",\n \"<note1>\\n<description>Isolate the object: find the color that differs from the uniform background and treat its connected component as the object to transform. Working with the object's bounding box (min/max row and column) simplifies the rest of the reasoning.</description>\\n<example>Imagine a 12×12 grid of background color with a single 3×4 block of another color. Record the block's top row, bottom row, left column and right column. Those four numbers summarize the object's position and size for further steps.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object's vertical span (the number of rows it occupies) and the grid height. Use the vertical span to decide how many rows to preserve from the top of the grid for the object.</description>\\n<example>If the grid has 12 rows and the object occupies 4 rows, then the top portion of the grid that will contain the object is the first 4 rows. If the object were 2 rows tall on a 12-row grid, you would consider the top 2 rows for placement.</example>\\n</note2>\\n\\n<note3>\\n<description>Reposition the object so its top row aligns with the computed top portion (i.e., place the object so its top edge sits at the same row index as the top portion). Do not change the object's width or color — only move it vertically.</description>\\n<example>For a 4×3 object on a 12-row grid, slide the object upward so its top row is the first row of the grid; the object will occupy rows 1–4 and columns 2–4 (keeping the same width).</example>\\n</note3>\\n\\n<note4>\\n<description>Keep the object's horizontal alignment unchanged: do not shift left or right unless the examples show a horizontal movement. Maintain the object's internal pattern and color exactly when placing it in the new top position.</description>\\n<example>If the object originally started at column 3 and spans 3 columns, after moving it vertically you should still start at column 3 and keep the same 3-column width; only the row indices change.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate the result: after repositioning, the object should occupy exactly the computed top rows and the same columns as before, and every other cell should remain the original background color. If something else changed, reconsider the rule (e.g., width change or horizontal shift).</description>\\n<example>After placing the object at the top rows, scan the grid: the object's color should appear in the same columns but on the first few rows, and the rest of the grid should be unchanged. If a row below the object or a neighboring column differs, you likely misapplied the vertical-placement rule.</example>\\n</note5>\",\n \"<note1>\\n<description>Isolate the object to transform: identify the single contiguous region that is not the background color. Treat that region as the unit to move rather than changing many scattered cells.</description>\\n<example>Imagine a 12×12 grid where most cells are color A and one compact block of color B sits somewhere inside. Mark all B cells and note their bounding box (top, bottom, left, right). That bounding box is the object you will relocate.</example>\\n</note1>\\n\\n<note2>\\n<description>Use the object's bounding box to define its size and shape: record width and height (and whether it is square or rectangular). The transformation preserves these dimensions and the pattern inside the box.</description>\\n<example>If the B pixels form a 4×4 filled rectangle, note width=4, height=4. You will keep that 4×4 block intact when you move it—no stretching or reshaping is needed.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a single consistent translation vector across examples: check how the object's top-left corner moves from input to output and express that as (Δrow, Δcol). The same vector should apply to every training case.</description>\\n<example>For several training pairs, compute the difference (output_top_left_row − input_top_left_row) and (output_top_left_col − input_top_left_col). If both differences are the same for each example, that difference is the translation to use.</example>\\n</note3>\\n\\n<note4>\\n<description>Apply the translation while preserving the object's internal color and orientation: copy the whole bounding-box pattern and place it at the new coordinates, leaving the background unchanged. Do not rotate or recolor the object.</description>\\n<example>Take the 4×4 block you identified, shift it by the computed vector, and paste it into the grid. The block's internal pattern (every cell still color B) remains identical except for its position.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate by checking invariants: the object should remain contiguous, its color unchanged, and the background should be unchanged except for the moved object. If anything else changes, re-check your bounding-box and translation vector.</description>\\n<example>After moving the block, count B cells and confirm the same number appears in the new location; ensure no other cells were altered. If counts or shape differ, you likely misidentified the object or used the wrong translation.</example>\\n</note5>\",\n \"<note1>\\n<description>Identify the target object by its color and shape: find the contiguous region of a non-background color and compute its bounding box (top, bottom, left, right). This gives you the object's width, height and its original position relative to the grid edges. Working with these four coordinates makes the transformation easy to express and apply.</description>\\n<example>Imagine a 7×7 grid with a single 4×3 rectangle of color A. Its bounding box is top=1, bottom=4, left=2, right=5; width=4 and height=3. If you need to move or resize that object later, these numbers let you compute where the new box should be placed.</example>\\n</note1>\\n\\n<note2>\\n<description>Look for a horizontal translation: many tasks move the object toward the left edge by shifting its columns left by the same offset for every row. In other words, subtract a fixed horizontal offset from each column index while keeping the object's height and row indices unchanged. This keeps the object's shape and color identical but changes its left–right placement.</description>\\n<example>For example, a 3×3 square at columns 4–6 can be shifted so it occupies columns 1–3 by subtracting 3 from every column index (columns 4→1, 5→2, 6→3). The 3 rows remain the same, only the columns have been translated.</example>\\n</note2>\\n\\n<note3>\\n<description>When the object reaches the left edge, do not wrap or reflect it: keep the object's left edge at the grid's leftmost column and keep its rows fixed. The transformation is a rigid translation until the left edge is at 0, after which the object is anchored there. This preserves vertical alignment while anchoring horizontally.</description>\\n<example>If a 2×4 rectangle ends up with its left column at 0 after shifting, it will occupy columns 0–3 (not columns 0–3 and then wrap around). Its top and bottom rows remain unchanged from before the shift.</example>\\n</note3>\\n\\n<note4>\\n<description>Handle overlapping with the background by replacing background cells with the object's color; do not erase the object's pixels. If the shifted object would write into background cells, those cells become the object color; if the object already occupied those cells, they stay the object color. This is a fill/overlay operation rather than a deletion.</description>\\n<example>Suppose a blue rectangle is moved so it covers some black cells; those black cells become blue. If the rectangle already covered those cells before, they remain blue. The operation is \\\"paint the object's color into any cell it covers.\\\"</example>\\n</note4>\\n\\n<note5>\\n<description>Apply the same horizontal offset to every row and preserve the object's color and internal pattern. Treat each row independently when shifting: shift each row by the same column-offset, then write the row back with the object color where appropriate. This ensures the object keeps its shape and color after the transformation.</description>\\n<example>A 1×6 horizontal stripe can be moved by subtracting 3 from each of its 6 column indices; every row of that stripe is translated the same way and then written back with the stripe's color. Doing this for every row produces the same horizontal translation across the object.</example>\\n</note5>\",\n \"<note1>\\n<description>Find the object by color: locate the color that forms a compact contiguous region (often the only non-background color). Treat that region as a single entity to be transformed rather than many separate pixels.</description>\\n<example>Imagine a grid of black with a 4×4 red square somewhere inside. Mark all red pixels as one object; ignore isolated single pixels of other colors when deciding which shape to move.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object's bounding box and its center: the bounding box gives the object's width and height; the center is the midpoint of that box (use integer or half-integer depending on whether the box is odd or even in size).</description>\\n<example>For a 4×4 square the bounding box spans 4 rows and 4 columns, so its center is at the midpoint of that span (e.g., (row_center = (top+bottom)/2, col_center = (left+right)/2)).</example>\\n</note2>\\n\\n<note3>\\n<description>Translate the entire object so its center aligns with the grid center (use the same centering rule for even-sized boxes). This produces a single, symmetric placement of the object in the grid.</description>\\n<example>If the grid is 10×10 and the object's center is at (r0,c0), move the object so its center becomes (5,5) by shifting each pixel by (5 − r0, 5 − c0) while keeping the object's shape and orientation unchanged.</example>\\n</note3>\\n\\n<note4>\\n<description>Keep the object's size, orientation, and color unchanged; only translate it. Do not resize, rotate, or recolor the object when applying the rule.</description>\\n<example>If the object is a 4×4 filled block, after translation it should still be a 4×4 block in the same orientation and with the same color, just in a new location.</example>\\n</note4>\\n\\n<note5>\\n<description>Handle multiple examples by applying the same centering rule consistently (preserve orientation and color), and watch for edge cases such as even-sized boxes or multiple colored objects—examples usually show a single compact object to move.</description>\\n<example>If you see two identical objects in different positions, try centering each on the grid center; if the examples always show one clear object, focus on that object and do not split or merge it.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for a single, compact colored region that stands out from the uniform background. When one color forms a contiguous rectangular block, that block is usually the object to transform.</description>\\n<example>Imagine a mostly gray grid with a solid blue rectangle somewhere inside. Count and compare colors: the blue pixels form a compact block while gray fills most of the grid; that blue block is the likely object to manipulate.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the object’s bounding box: record its minimum and maximum row and column indices. The bounding box gives the block’s height and width and its top-left corner (min row, min column).</description>\\n<example>If the colored pixels occupy rows 3..6 and columns 2..5, then the bounding box is rows 3–6 (height 4) and columns 2–5 (width 4), with top-left at (row 3, column 2).</example>\\n</note2>\\n\\n<note3>\\n<description>Translate the whole block by the same offset in both directions so the bounding-box top-left moves to the grid origin (row 0, column 0). This is a pure translation: every pixel inside the box is moved by the same (row_offset, col_offset).</description>\\n<example>With a bounding box at (3,2), subtract 3 from every row index and 2 from every column index so the block’s top-left lands at (0,0); the relative pattern and colors remain unchanged, only its position does.</example>\\n</note3>\\n\\n<note4>\\n<description>After translation, check that the object fits entirely inside the grid and that no other colored pixels are introduced. The transformation preserves color and shape, so the translated block should be a contiguous rectangle of the same color.</description>\\n<example>If the translated block would extend outside the grid, the examples usually keep it fully inside; if everything fits, the translated rectangle will match the original block’s color and size exactly.</example>\\n</note4>\\n\\n<note5>\\n<description>When you apply the translation, leave every other cell unchanged. The correct operation is a rigid translation of the detected object, not a rotation, reflection, or recoloring of other areas.</description>\\n<example>Take the original grid, move only the bounding-box pixels by the computed offset, and copy the rest of the grid unchanged; the resulting grid will show the object in a new location while the background remains identical.</example>\\n</note5>\"\n]","isConversational":false},"train":{"kind":"string","value":"[{\"input\": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], \"output\": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}, {\"input\": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], \"output\": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}, {\"input\": [[5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5]], \"output\": [[5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 6, 6, 6, 6, 5, 5, 5], [5, 5, 6, 6, 6, 6, 5, 5, 5], [5, 5, 6, 6, 6, 6, 5, 5, 5], [5, 5, 6, 6, 6, 6, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5]]}]"},"test":{"kind":"string","value":"[{\"input\": [[5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5]], \"output\": [[5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5]]}]"},"source":{"kind":"string","value":"barc_heavy"},"prompt":{"kind":"string","value":"You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectangular matrix of integers between 0 and 9 (inclusive). Each number corresponds to a color. 0 is black. Your task is to determine the transformation rule from examples and find out the answer, involving determining the size of the output grid for the test and correctly filling each cell of the grid with the appropriate color or number. The transformation only needs to be unambiguous and applicable to the example inputs and the test input. It doesn't need to work for all possible inputs. Observe the examples carefully, imagine the grid visually, and try to find the pattern. Please output your answer within a code block (```), formatted as a grid of numbers. \n\n# Examples\n## Example 1\nInput:\n```\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n```\n\nOutput:\n```\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 7 7 7 7 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5 5 5\n```\n\n## Example 2\nInput:\n```\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 7 7 7 7 5 5 5 5\n5 5 7 7 7 7 5 5 5 5\n5 5 7 7 7 7 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n```\n\nOutput:\n```\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 5 7 7 7 7 5 5 5\n5 5 5 7 7 7 7 5 5 5\n5 5 5 7 7 7 7 5 5 5\n5 5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5 5\n```\n\n## Example 3\nInput:\n```\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 6 6 6 6\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n```\n\nOutput:\n```\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 6 6 6 6 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n```\n\n# Test Problem:\n```\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n```"},"answer":{"kind":"string","value":"```\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 4 4 4 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n5 5 5 5 5 5 5 5 5\n```"},"num_tokens":{"kind":"number","value":1470,"string":"1,470"}}},{"rowIdx":98,"cells":{"abstraction_prompt":{"kind":"string","value":"<|im_start|>user\nDeveloper: # ARC HINT GENERATOR\n\n## Role & Goal\nYou are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted hint that helps the user discover the core transformation principle for themselves without revealing the answer.\n\nBegin with a concise checklist (3-7 bullets) of what you will do; keep items conceptual, not implementation-level.\n\n---\n\n## Hint Generation Strategy\n1. **Compare** the input and output grids for each example. Identify the shared transformation pattern that allows the input grid to be converted into the output grid.\n2. **Identify the Core Principle**: Review the problem description and ground-truth solution to fully discern the key transformation rule. Break it down into its essential operations (e.g., object completion, pattern repetition, symmetry, gravity), paying close attention to properties such as object count, shapes, colors, sizes, symmetry, repetition, relative positioning, and broader grid-level patterns.\n3. **Craft a Targeted Hint**: Generate a hint that guides the user toward the core insight needed to solve the problem. The hint should assist the user during their attempt without revealing the solution.\n4. Structure each note using the template below:\n - **Description** (up to 3 sentences): Explain the concept, when and why it applies, and why it is effective. Include any relevant general formula or principle in its most general form.\n - **Example** (up to 6 sentences): Present a worked example covering all aspects of the description, using a simplified yet representative scenario (not necessarily from the current problem).\n - Optionally, include **Heuristics** or **Pitfalls** in the note where relevant.\n - Focus on methodologies and core principles over specific calculations or problem details.\n - Ensure each hint applies broadly—at least 80% of analogous problems.\n\nAfter generating a hint, verify that no specifics of the solution are revealed, and that the hint remains at the level of guiding the approach.\n\n### Output Format\nProduce a **sequence of 5** notes in the structure:\n<note1>\n<description>...</description>\n<example>...</example>\n</note1>\n<note2>\n<description>...</description>\n<example>...</example>\n</note2>\n...\n\n### Design Guidelines\n- Clarity: Use precise language and correct sentence structure.\n- Atomicity: Each note addresses one recognizable sub-problem.\n- Self-containment: All information needed to understand the idea and its application is within the note.\n- Generalizability: Avoid problem-specific details or variables.\n- Transferability: Notes should apply across a class of problems.\n- Distinctness: Each note addresses a distinct principle.\n\n---\n\n## Guidelines\n- **Guide, Don't Solve**: Illuminate the approach, not the answer. Emphasize what to observe or consider.\n- **Specific yet Abstract**: Use concrete grid details (e.g., \"note the relationship between the blue and red pixels\") to ground abstract patterns (e.g., \"think about one color containing another\").\n\nValidate your generated hint: confirm it is self-contained, actionable, and nondirective. If any aspect is too revealing, revise before finalizing.\n\n---\n\n## Inputs\n### Problem Description\nA full ARC problem, including input/output pairs for training and testing.\n\nYou will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectangular matrix of integers between 0 and 9 (inclusive). Each number corresponds to a color. 0 is black. Your task is to determine the transformation rule from examples and find out the answer, involving determining the size of the output grid for the test and correctly filling each cell of the grid with the appropriate color or number. The transformation only needs to be unambiguous and applicable to the example inputs and the test input. It doesn't need to work for all possible inputs. Observe the examples carefully, imagine the grid visually, and try to find the pattern. Please output your answer within a code block (```), formatted as a grid of numbers. \n\n# Examples\n## Example 1\nInput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 4 0 0 0 0\n0 0 0 0 4 4 4 0 0 0\n0 4 0 0 0 4 0 0 0 0\n4 4 4 0 0 0 0 0 0 0\n0 4 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 4 0 0 0 0 0 0 0 0\n4 4 4 0 0 0 0 0 0 0\n0 4 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 4 0 0 0 4 0 0 0 0\n0 0 4 0 4 4 4 0 0 0\n0 4 0 4 0 4 0 0 0 0\n4 4 4 0 4 0 0 0 0 0\n0 4 0 0 0 4 0 0 0 0\n0 0 0 0 0 0 4 0 0 0\n0 4 0 0 0 0 0 4 0 0\n4 4 4 0 0 0 0 0 4 0\n0 4 0 0 0 0 0 0 0 4\n```\n\n## Example 2\nInput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 3 0 0 0 0\n0 0 0 0 3 3 3 0 0 0\n0 0 0 0 0 3 0 0 0 0\n0 0 0 0 0 0 0 0 3 0\n0 0 0 0 0 0 0 3 3 3\n0 0 3 0 0 0 0 0 3 0\n0 3 3 3 0 0 0 0 0 0\n0 0 3 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 3 0 0 0 0 0 0 0 0\n0 0 3 0 0 3 0 0 0 0\n0 0 0 3 3 3 3 0 0 0\n0 0 0 0 3 3 0 0 0 0\n0 0 0 0 0 3 0 0 3 0\n0 0 0 0 0 0 3 3 3 3\n0 0 3 0 0 0 0 3 3 0\n0 3 3 3 0 0 0 0 3 0\n0 0 3 0 0 0 0 0 0 3\n```\n\n## Example 3\nInput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 3 0 0 0 0 0\n0 0 0 3 3 3 0 0 0 0\n0 0 0 0 3 0 0 0 0 0\n0 0 3 0 0 0 3 0 0 0\n0 3 3 3 0 3 3 3 0 0\n0 0 3 0 0 0 3 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 3 0 0 3 0 0 0 0 0\n0 0 3 3 3 3 0 0 0 0\n0 0 0 3 3 0 0 0 0 0\n0 0 3 0 3 0 3 0 0 0\n0 3 3 3 0 3 3 3 0 0\n0 0 3 0 0 0 3 0 0 0\n0 0 0 0 0 0 0 3 0 0\n0 0 0 0 0 0 0 0 3 0\n0 0 0 0 0 0 0 0 0 3\n```\n\n# Test Problem:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 5 0 0 0 0 5 0\n0 0 5 5 5 0 0 5 5 5\n0 0 0 5 0 0 0 0 5 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 5 0 0 0\n0 0 0 0 0 5 5 5 0 0\n0 0 0 0 0 0 5 0 0 0\n0 0 0 0 0 0 0 0 0 0\n```\n\n---\n\n\n# Generated Hint<|im_end|>\n<|im_start|>assistant\n"},"abstraction_prompt_length":{"kind":"number","value":2370,"string":"2,370"},"generated_abstractions":{"kind":"list like","value":["<note1>\n<description>Look for repeated objects: many ARC tasks use the same small motif repeated in different places. Identifying that motif reduces the problem to how one instance is transformed rather than many unrelated pixels.</description>\n<example>Imagine a grid with several identical 3‑pixel L‑shapes in different corners. Instead of tracking every pixel, first find the shape (its three colored pixels) and treat each occurrence as an instance of that motif.</example>\n</note1>\n\n<note2>\n<description>Compare corresponding pixels of an instance in input vs. output to detect a rigid transform. If the same relative offsets keep the same color but move to different coordinates, the transform is a translation, rotation, or reflection rather than a color change or recoloring.</description>\n<example>If one L‑shape’s top pixel is at (r,c) in the input and in the output the same L‑shape’s top pixel is at (r+2,c+1), that indicates a consistent translation. Repeat this check for the other two pixels of that L to confirm the same offset everywhere.</example>\n</note2>\n\n<note3>\n<description>Decide which axis the motif is being moved along by checking whether the row indices or column indices change. If rows change while columns are constant, the motif is being moved vertically; if columns change while rows are constant, it is being moved horizontally.</description>\n<example>For example, if every instance’s colored pixels shift down by two rows but keep the same column positions, the motif is translated downward; if instead columns shift while rows remain fixed, the motif is translated horizontally.</example>\n</note3>\n\n<note4>\n<description>Use a single clear anchor (a particular colored pixel or the motif’s top‑left) to compute the displacement vector and apply it to every instance. Doing this consistently for all occurrences avoids inconsistent placements.</description>\n<example>Pick the topmost colored pixel of each L as the anchor; measure how many rows and columns that anchor moves between input and output. Then move every other pixel of each L by the same row/column offsets so all copies are translated uniformly.</example>\n</note4>\n\n<note5>\n<description>Watch for edge cases: clipping, overlap, and the direction of movement. If the predicted destination falls outside the grid, check whether the task preserves or removes pixels; if multiple instances overlap, check whether outputs show merged or preserved pixels.</description>\n<example>If a translated pixel would fall outside the grid, verify whether the examples simply omit it or place it inside the grid instead. Also, after translating all instances, scan the grid to ensure each original motif appears in the same relative orientation and color, and that no extra pixels of that color were introduced.</example>\n</note5>","<note1>\n<description>Find the target color by frequency: the color that appears in multiple small clusters is the one the transformation operates on. Count occurrences and ignore the background color (usually 0) to pick the focus.</description>\n<example>If a grid has many single pixels and a few small groups of the same color, that repeated color is the one you should follow. For instance, if blue appears in several tiny clusters while red appears only once, treat blue as the subject of the transformation.</example>\n</note1>\n\n<note2>\n<description>Isolate each connected component of the target color and compute its bounding box (min/max row and column). This gives you the component’s top, left, width and height so you can reason about placement and alignment.</description>\n<example>For a cluster that spans rows 2–4 and columns 5–7, the bounding box is rows 2..4 and cols 5..7; record top=2, left=5, width=3, height=3 so you can compare and move that whole block consistently.</example>\n</note2>\n\n<note3>\n<description>Look for a vertical reflection: each component’s top and bottom rows are mirrored across the grid’s horizontal midline. The horizontal coordinate (left edge) stays the same; only the vertical position changes.</description>\n<example>If a component’s top row is 1 and the grid height is H, its mirrored top becomes H−1−top; if the component’s top is 4 in a 10-row grid, the mirrored top would be 5 (since 10−1−4=5). This keeps the block width and left edge identical while flipping its vertical placement.</example>\n</note3>\n\n<note4>\n<description>After mirroring, place the component back into the grid and keep its internal pattern intact. Do not rotate or reshape the block—only move it vertically—so the shape’s columns remain aligned with the original left edge.</description>\n<example>A 2×3 block that originally starts at column 6 should still start at column 6 after mirroring; only its row indices are changed so the block occupies the mirrored vertical area but the same horizontal columns.</example>\n</note4>\n\n<note5>\n<description>Decide collision policy: if a mirrored cell would land on a different non-background color, the examples usually preserve the original color at that position. If the mirrored cell is background, it becomes the target color; if the mirrored cell already contains the target color, leave it unchanged.</description>\n<example>If a mirrored pixel would overwrite a different-colored pixel, keep that other color; if it would overwrite background, fill it with the target color; if it would overwrite another instance of the target, do nothing. This keeps the transformation consistent and predictable.</example>\n</note5>","<note1>\n<description>Look for a small, consistent motif: the transformation often uses a tiny 3×3 arrangement of the same color as the unit of change. Recognizing that unit makes it easier to see how the output is built from repeated copies rather than many independent edits.</description>\n<example>Imagine a grid with several small clusters of the same color; each cluster appears to be a 3×3 patch (one cell thick) with a particular arrangement of filled cells. Once you treat that 3×3 as the motif, you can search for the same arrangement elsewhere instead of scanning every pixel individually.</example>\n</note1>\n\n<note2>\n<description>Identify the motif’s anchor (a unique, distinctive cell inside the 3×3) and record its relative coordinates. That anchor is the reference point you will use to place copies of the motif.</description>\n<example>For instance, if a 3×3 motif always has a filled cell at the top-left of the 3×3, label that cell (0,0) relative to the motif. Marking that anchor lets you reproduce the motif by shifting the same relative pattern to other locations.</example>\n</note2>\n\n<note3>\n<description>Search the input for other occurrences of the same motif (same shape and color). If the motif appears multiple times, each occurrence is a candidate for copying rather than being treated as noise.</description>\n<example>Suppose you find two identical 3×3 clusters in different parts of the grid; treat both as instances of the motif. You should not ignore one because it is far away—both are legitimate sources for the transformation.</example>\n</note3>\n\n<note4>\n<description>Place copies of the motif by copying the motif’s internal arrangement relative to its anchor, using the motif’s anchor as the reference point. In other words, translate the 3×3 pattern so its anchor coincides with the anchor of the source motif.</description>\n<example>If a motif’s anchor is at (r,c) inside the 3×3 and you want to place it so its anchor is at (r2,c2), copy every filled cell of the 3×3 by adding the same offset (r2−r, c2−c) to each relative coordinate. This preserves the motif’s shape and orientation when you move it.</example>\n</note4>\n\n<note5>\n<description>After placing copies, check for overlaps and decide whether to overwrite or preserve original pixels. If the examples show that copies are placed on top of originals, expect overwriting; otherwise consider merging or leaving originals intact.</description>\n<example>When you copy a motif onto another motif, the copied pixels may land on the original filled cells. If the training outputs show the copied color replacing originals, overwrite them; if not, keep the originals and only add new pixels outside existing motifs.</example>\n</note5>","<note1>\n<description>Separate objects by color and treat each connected colored region as an independent unit. This simplifies the problem because you can analyze each object's shape and position on its own.</description>\n<example>Imagine a grid with two identical blue blobs and many empty cells. Label each blob (top blob = A, bottom blob = B). Work with A and B separately rather than mixing pixels from different blobs.</example>\n</note1>\n\n<note2>\n<description>Compute the minimal bounding rectangle for each object and record its topmost and leftmost pixels (the object's top-left anchor). These anchor coordinates are the natural reference points for the transformation.</description>\n<example>For a blob whose pixels occupy rows 2–4 and columns 5–7, its bounding box is rows 2..4 × cols 5..7 and its top-left is (row=2,col=5). Use that anchor to locate where the object sits relative to the grid.</example>\n</note2>\n\n<note3>\n<description>Translate each object by subtracting its bounding-box top and left values from every pixel coordinate (a uniform shift). In formula form: new_row = old_row − box_top, new_col = old_col − box_left. This makes each object's top-left pixel land on the grid origin.</description>\n<example>If a blob's top-left is (2,3) and one pixel is at (4,6), translating by (−2,−3) moves that pixel to (2,3). Apply the same subtraction to all pixels of the blob to get the translated object.</example>\n</note3>\n\n<note4>\n<description>After translation, check whether each translated object overlaps other objects or the grid boundary. If overlaps occur, split the object into multiple non-overlapping pieces by partitioning the translated bounding box into contiguous rows or columns (for example, by splitting into equal-width tiles).</description>\n<example>Suppose two identical objects are translated and their translated boxes touch; split each box into two horizontal tiles (top and bottom). Place each tile at the corresponding tile position in the other object's translated box to avoid overlaps while preserving the object's internal pattern.</example>\n</note4>\n\n<note5>\n<description>When placing translated pieces, keep each piece's internal arrangement unchanged and use the same relative ordering (for example, keep the original top row as the top row of the tile). Finally, verify that the translated pieces do not collide and that the number and shape of pieces match the original object.</description>\n<example>If a translated object is a 3×3 block and you split it into three horizontal tiles, each tile should be a contiguous row of the same color and the top tile should remain the original top row. After placement, check that no pixels of different objects occupy the same cell.</example>\n</note5>","<note1>\n<description>Look for repeated small motifs: many ARC tasks use the same small object (a compact cluster of one color) repeated in different places. Identifying the motif’s bounding box and its internal pattern lets you treat every occurrence the same way. This reduces the problem to “what to do with each copy” rather than handling every pixel separately.</description>\n<example>Imagine a 3×3 block that appears twice on a black background: each block is the same shape and color. Once you isolate that 3×3 pattern, you can reason about how the output relates to that pattern in every occurrence instead of scanning the whole grid pixel-by-pixel.</example>\n</note1>\n\n<note2>\n<description>Compare the motif’s internal pattern to its output: check whether the motif is left unchanged, mirrored, rotated, or otherwise transformed. A consistent spatial relationship between input and output cells for a single motif tells you the global operation. This step is about shape transformation, not color changes.</description>\n<example>If the motif is a 3×3 cross, and the output shows that cross rotated 90° in every occurrence, then the transformation is a rotation of the motif (not a simple translation or reflection). Recognizing that rotation tells you how to place the motif in the output.</example>\n</note2>\n\n<note3>\n<description>Check translation: determine whether each motif moves by a fixed vector from its original position. If the same offset appears for every occurrence, the transformation is a translation (possibly combined with the shape change). Knowing the offset lets you predict where to place the motif in the output for any input occurrence.</description>\n<example>Suppose every 3×3 block in the input appears at the same relative coordinates in the output but shifted by the same (row, column) vector; that indicates a uniform translation. You can then apply that same vector to every occurrence when building the output.</example>\n</note3>\n\n<note4>\n<description>Consider stacking: many tasks place transformed copies of the motif so their outlines touch or overlap, forming a larger connected shape. Decide whether copies are stacked in the same direction (all shifted up/down/left/right) or in a different orientation, and whether they are allowed to overlap. This explains why the output shows connected regions rather than isolated motifs.</description>\n<example>If each motif is translated down by the same amount, the transformed copies will form a vertical stack; if instead they are rotated and translated differently, they may form a 2D mosaic. Observing that the output motifs touch or form a continuous region points to stacking behavior.</example>\n</note4>\n\n<note5>\n<description>Validate and watch for pitfalls: apply your inferred rule to one or two occurrences and check for collisions or unexpected colors. If some occurrences are different, re-evaluate whether the rule is uniform or conditional. Also ensure the output uses the same color palette as the input and does not introduce new colors.</description>\n<example>After deducing “rotate motif, then translate by fixed vector,” place that transformed motif at every original location and compare with the example output. If a placed motif would land on a non-black cell or if some motifs in the output differ, adjust whether rotation, translation, or stacking is being applied conditionally.</example>\n</note5>","<note1>\n<description>Find the target object(s) by color: identify the non-background color that appears repeatedly and treat each contiguous group of that color as an object. Working with whole objects (not individual pixels) makes it easier to compare shapes across examples.</description>\n<example>Imagine a grid with several blue blobs on a black background. Mark each connected blue region (use 4‑connectivity) and note their pixel counts and shapes; these marked objects are what you will compare to the outputs.</example>\n</note1>\n\n<note2>\n<description>Compare object positions between input and output: check whether each object’s bounding box or centroid has been translated by the same offset (e.g., moved up and to the right). A constant displacement suggests a uniform geometric shift was applied to every object.</description>\n<example>If a 3‑pixel L‑shaped object in the input appears in the output at a consistent number of rows and columns higher and to the right, that indicates a single translation vector was used for that object rather than a different change.</example>\n</note2>\n\n<note3>\n<description>Look for a rotation or reflection of the object’s internal pattern: an object may be moved and then rotated (e.g., 90°) so that a previously internal pixel becomes an external one. Compare the orientation of distinctive pixels before and after the transformation.</description>\n<example>A horizontal triple in the input might appear as a vertical triple in the output after the same translation; that change in orientation points to a rotation step applied after the translation.</example>\n</note3>\n\n<note4>\n<description>Verify that the transformation preserves object size and color and only moves/rotates them: the number of pixels and their color should remain constant between input and output, so you can match object shapes and count pixels to confirm the rule.</description>\n<example>If a shape has five pixels in the input and you see five pixels of the same color in the output arranged identically (just translated/rotated), that confirms the operation is a rigid transform (no scaling or recoloring).</example>\n</note4>\n\n<note5>\n<description>Combine observations into a single hypothesis: apply the inferred translation to every object, then apply the inferred rotation/reflection to each translated object; check that the resulting positions match the output examples. If something doesn’t match, try the reverse rotation or a different offset until the pattern holds for all objects.</description>\n<example>Take each object, move it by the same vector you observed in the examples, then rotate it (for example 90°) and see whether the rotated positions align with the outputs; if they do, that sequence of steps is likely the correct transformation rule.</example>\n</note5>","<note1>\n<description>Look for repeated, identical non-background objects across the grid. When the same small arrangement of colored pixels appears more than once, those occurrences are likely the units being transformed rather than isolated pixels.</description>\n<example>Imagine a grid with several identical L-shaped clusters of the same color. If the output shows many L-shapes but each is shifted or mirrored compared to the input, treat each L as an atomic object to be moved or reflected instead of moving individual pixels one by one.</example>\n</note1>\n\n<note2>\n<description>Compute the minimal bounding rectangle for each object and record its pixel offsets inside that rectangle. Working with relative offsets (not absolute coordinates) makes it easier to compare and apply the same operation to every object.</description>\n<example>If an L occupies cells at (r,c),(r+1,c),(r+2,c) and (r+1,c+2) inside its bounding box, note the offsets (0,0),(1,0),(2,0),(1,2). This offset list is what you will reposition or reflect when transforming the object.</example>\n</note2>\n\n<note3>\n<description>Compare the input and output bounding boxes to infer the transformation type: a horizontal reflection reverses the left/right order of offsets, a vertical reflection reverses up/down order, and a 180° rotation reverses both. Use the change in ordering to pick the correct axis or axes.</description>\n<example>For an L with offsets [0,0],[1,0],[2,0],[1,2], a horizontal flip would make offsets [0,0],[1,0],[2,0],[1,2] appear in reverse left-to-right order; a vertical flip would reverse top-to-bottom; a 180° rotation reverses both.</example>\n</note3>\n\n<note4>\n<description>Apply the same geometric operation to every detected object and keep the object's color unchanged. The rule is global: every occurrence is transformed the same way, so once you know the operation, use it consistently across the grid.</description>\n<example>If you determine that each L is being mirrored horizontally, place each L's offset list into the mirrored positions while preserving its color; do this for every L in the grid to reproduce the output pattern.</example>\n</note4>\n\n<note5>\n<description>After applying the transformation, check for overlaps and color conflicts: the operation should not introduce new colors or erase existing ones. If overlaps occur, decide whether the examples imply stacking (color preserved) or one color replacing the other, and apply that rule consistently.</description>\n<example>If two transformed objects would land on the same cell, inspect the examples to see whether the same color was used to mark that cell or whether one color overwrote the other; use the same precedence when you place the objects in the test grid.</example>\n</note5>","<note1>\n<description>Look for the smallest repeating object: many tasks use a tiny identical shape repeated across the grid. Identifying that minimal motif (its bounding box and internal pattern) is the first step because the transformation usually operates on whole instances of that motif.</description>\n<example>Imagine a grid with several identical 3×3 blocks scattered around. If every block has the same arrangement of colored pixels inside its 3×3 box, treat that 3×3 as the motif and ignore isolated single pixels that are not part of a full motif.</example>\n</note1>\n\n<note2>\n<description>Measure the motif’s vertical extent: count how many rows the motif occupies (height h). The transformation often treats the motif as two stacked blocks — the top block and the bottom block — so you must know h to split the motif into those two parts.</description>\n<example>If the motif is 4 rows tall, split it into a 2-row top block and a 2-row bottom block; if it’s 3 rows tall, the top block will be the first row and the bottom block the remaining two rows. Use that height when you later try to paste a top block above a bottom block.</example>\n</note2>\n\n<note3>\n<description>Think in terms of “top-left” and “bottom-left” positions: each motif has a leftmost column index. The transformation commonly copies a block’s top rows to the cell immediately to the right of that motif’s left column, while preserving the motif’s bottom rows at the motif’s original left column.</description>\n<example>For a motif that occupies columns c..c+h−1, place its top h rows into columns c+1..c+h, and leave the motif’s bottom h rows in columns c..c+h−1. This keeps the original motif visible while adding a shifted copy to its right.</example>\n</note3>\n\n<note4>\n<description>Apply the copy independently to every occurrence and preserve color: do not change the motif’s color or the original motif pixels. The operation is a translation (copy), not a recoloring or merging, so colors stay the same and originals remain intact.</description>\n<example>If a motif is blue, the pasted copy will also be blue and will sit in the new columns to the right; the original blue pixels in their original columns remain unchanged. Treat each motif separately rather than trying to merge or recolor them.</example>\n</note4>\n\n<note5>\n<description>Watch for edge cases and validation: if a motif sits on the last column, there is no room to paste a copy to its right and that instance should be left unchanged; if a pasted copy would overlap another motif, check whether examples expect overlaps or require a consistent rule (usually pasting is allowed in these problems).</description>\n<example>If a motif’s leftmost column equals the grid’s right edge, skip the paste for that instance. If a pasted copy would land on top of a different motif, re-check the motif detection and split height — if the examples show no such conflicts, the paste is typically placed without conflict.</example>\n</note5>","<note1>\n<description>Locate the motif: scan for a compact, small set of pixels (often a 3×3 block) whose internal arrangement (which cells are filled) is consistent across examples. Treat that small set as the atomic object to transform rather than as isolated pixels.</description>\n<example>Imagine a grid where a small group of three pixels forms a compact L or a short line. That small group is the motif: mark its bounding box and internal pattern so you can reason about how it moves or is copied as a whole.</example>\n</note1>\n\n<note2>\n<description>Compare coordinates: for each pixel of the motif in the input, check whether the same color appears at a predictable offset in the output (for example, one row down and one column left). If a consistent offset appears for every motif pixel, that offset is the translation vector to apply to the motif.</description>\n<example>If an L-shape at positions (r,c), (r,c+1), (r+1,c+1) in the input has the same L-shape at (r+1,c-1), (r+1,c), (r+2,c) in the output, the vector (dr,dc) = (+1, -1) is the translation to try on other motifs.</example>\n</note2>\n\n<note3>\n<description>Apply the translation to every occurrence of the motif independently and preserve its internal pattern and color. The transformation is a rigid shift of the motif, not a rotation, reflection, or recoloring.</description>\n<example>Two identical L-shapes in different places should each move by the same vector; after translation they remain identical L-shapes but in new positions, producing two shifted copies of the original motif.</example>\n</note3>\n\n<note4>\n<description>Decide how to handle overlaps: when a translated copy would land on existing colored pixels, check whether the examples show merging (both colors present) or replacement (one color overwrites). Use the training pairs to infer which behavior to apply.</description>\n<example>If a translated pixel would fall on an existing non-background pixel in the examples, inspect that output cell: if it shows both colors then merge; if it shows only the translated color then overwrite. Apply the same rule consistently across all overlaps.</example>\n</note4>\n\n<note5>\n<description>Validate and iterate: after translating each motif and handling overlaps according to the inferred rule, compare the result to the example outputs. If the overall pattern matches, the rule is consistent; if not, re-check whether you misidentified the motif or the translation vector.</description>\n<example>Translate all detected motifs by your vector and check whether the relative arrangement and counts of colored pixels match the examples. If one motif fails, re-evaluate whether that motif is the same shape or whether a different offset is needed for some motifs.</example>\n</note5>","<note1>\n<description>First isolate the active color and the objects made from it. Many tasks work on a single non-background color so focus on those pixels and ignore the background.</description>\n<example>Imagine a grid with only blue pixels forming two separate blobs. Treat every blue cell as part of the pattern to transform rather than as isolated noise. This reduces the problem to moving or copying a small set of shapes instead of the whole grid.</example>\n</note1>\n\n<note2>\n<description>Compare the relative positions of pixels inside each object between input and output. If pixels keep the same local arrangement but appear at different coordinates, the transformation is a rigid translation (a constant vector added to every pixel).</description>\n<example>For a small 3×3 L-shape in the input, check the output: if the L-shape is still an L but shifted by the same number of rows and columns everywhere, you have a uniform translation. That tells you to search for a single (dr, dc) that explains every object's change.</example>\n</note2>\n\n<note3>\n<description>Look for a consistent offset applied to the entire grid: many tasks move the whole pattern by the same vector (a constant dr and dc). If so, you can compute the translation from one object and apply it to all objects.</description>\n<example>If one object's top-left moves by (dr,dc) and the same (dr,dc) is seen for another object, then the whole grid is being shifted by that vector. Use that single vector to predict where every pixel should go.</example>\n</note3>\n\n<note4>\n<description>Check how the translation affects the grid edges: if objects move toward the border and some disappear, the rule may be \"translate until the object touches a border\" rather than a fixed vector. In other words, the movement stops when the object reaches an edge.</description>\n<example>A small object that is pushed toward the top edge will be stopped once any of its pixels reaches row 0; the visible output shows only the part that remains on the grid. Recognizing this stopping condition explains why some objects appear partially clipped in the outputs.</example>\n</note4>\n\n<note5>\n<description>Finally, verify invariants: the color, the local shape and relative ordering of pixels should be preserved. If those are unchanged, you can confidently apply the same translation to the test input and expect similar behavior.</description>\n<example>When the transformation is pure translation, each object's internal pattern is identical before and after (only position changes). Use that to check your candidate vector and to avoid assuming rotations, reflections, or recoloring occurred.</example>\n</note5>","<note1>\n<description>Isolate the object by finding all cells of the non-background color and computing the minimal bounding rectangle that contains them. This reduces the problem to a small set of coordinates and makes spatial relationships obvious.</description>\n<example>Imagine a grid with a single red shape occupying rows 2–4 and columns 1–3. The bounding box is rows 2–4, cols 1–3; listing those coordinates (e.g., (2,1),(2,3),(3,2)) lets you reason about where the shape sits relative to the grid edges.</example>\n</note1>\n\n<note2>\n<description>Look for a translation that moves the bounding box so its top-left corner touches the top-left edge of the grid. In other words, translate every coordinate by the negative of the box's top-left offset from (0,0).</description>\n<example>If the bounding box starts at row 2 and column 1, subtracting those offsets from each pixel's coordinates will move the whole object so its top-left becomes (0,0), preserving internal offsets.</example>\n</note2>\n\n<note3>\n<description>After translating, check whether the translated object is exactly the same as the original object. If so, the object is already anchored at the top-left and no further change is needed.</description>\n<example>For instance, if a 3×3 pattern at (0,0) equals the original pattern after translation, then that pattern already sits at the grid origin and you can stop here.</example>\n</note3>\n\n<note4>\n<description>If the translated object is not identical to the original, the transformation usually adds a single extra row or column to the translated object to make it fit the grid, and then places that enlarged object at the top-left. In general, append the missing row/column(s) so the translated bounding box becomes one cell larger in the direction away from the grid edge.</description>\n<example>Suppose the translated box would extend one cell past the right edge; adding a single column on the right side of the translated box and then placing that enlarged box at (0,0) is a common way to complete the pattern.</example>\n</note4>\n\n<note5>\n<description>Keep the color and orientation unchanged and do not rotate, flip, or recolor the object. The operation is a translation and optional one-cell extension, not a geometric modification of the shape.</description>\n<example>If the object is a small L-shaped cluster of color X, the final grid should show the same L-shape (possibly one extra pixel added) in the same orientation and color; only its position and size may have changed.</example>\n</note5>","<note1>\n<description>Separate the grid into connected components using orthogonal adjacency (up/down/left/right). Each non-background connected group is treated as an individual object to analyze.</description>\n<example>Imagine a grid with two separate blue blobs. Mark each blob as its own object by tracing cells that touch orthogonally; you will have two objects even though they share the same color.</example>\n</note1>\n\n<note2>\n<description>For each object, compute its bounding box (min/max row and column) and record the object's width and height. These dimensions tell you the object's horizontal and vertical extents and which edge is closest to the grid border.</description>\n<example>If an object occupies rows 2–4 and columns 5–7, its bounding box is rows 2..4 by columns 5..7 (width 3, height 3). If another object's box starts at column 1, that object has a different horizontal extent than the one whose box starts at column 5.</example>\n</note2>\n\n<note3>\n<description>Classify each object by which side of its bounding box is nearest the grid edge: left (closest column to column 0), right (closest column to last column), top (closest row to row 0), or bottom (closest row to last row). This tells you whether the object is a \"left/right\" object or a \"top/bottom\" object.</description>\n<example>A 3×3 box whose min column is 0 is a left object; a 3×3 box whose max column equals the grid width is a right object. A 3×3 box whose min row is 0 is a top object; one whose max row equals the grid height is a bottom object.</example>\n</note3>\n\n<note4>\n<description>Apply a single, consistent translation rule to each object based on its classification: move each object horizontally or vertically by one cell toward the nearest grid edge (do not rotate or mirror). If an object touches both a top and a left edge, treat it as both top and left; if it touches both a left and bottom edge, treat it as both left and bottom, etc.</description>\n<example>A left object with min column 1 should be shifted one column to the left (to column 0). A top object with min row 2 should be shifted one row up (to row 1). If an object is already adjacent to the edge, it stays where it is.</example>\n</note4>\n\n<note5>\n<description>When multiple objects are translated, apply the translations independently and check for overlaps or collisions. If two translated objects would occupy the same cell, resolve by a consistent priority (for example, objects closer to the edge move first, or objects that touch an edge are not moved).</description>\n<example>Two separate objects both touching the same border will each move one step inward; if their inward moves would collide, use a fixed tie-break rule (e.g., move the one nearer the border first). Always preserve the object's color and shape—only translate it.</example>\n</note5>","<note1>\n<description>Look first for a consistent global offset: many tasks move every non-background pixel by the same row/column amount. Finding one example that is shifted by (r,c) suggests a uniform translation applied to the whole grid.</description>\n<example>Imagine a single red pixel at (2,3) in the input and the output shows a red pixel at (5,2). That single pair points to a translation of (3,-1). If another colored pixel also moves by the same (dr,dc), you likely have a global translation to test on the whole grid.</example>\n</note1>\n\n<note2>\n<description>Check whether colors are preserved: the transformation often only relocates pixels of a specific color and leaves other colors (and background) unchanged. Confirming color invariance narrows the set of possible operations.</description>\n<example>Suppose the input has red and blue pixels and the output still contains red and blue at different coordinates but no new colors appear. That indicates the rule moves the red/blue pixels but does not alter their identity or introduce new colors.</example>\n</note2>\n\n<note3>\n<description>Decide how the rule treats boundaries: a pure translation can move pixels off-grid (clipping) or wrap them around (toroidal). Use example pairs to see whether missing pixels imply clipping or whether pixels reappear on the opposite side.</description>\n<example>If a pixel at the top row after translation would be at a negative row index but you still see the color in the output, that suggests wrapping. Conversely, if a pixel disappears from the output, that suggests the transformation clips pixels that move outside the grid.</example>\n</note3>\n\n<note4>\n<description>Verify the operation is applied to every occurrence of the target color and not selectively: the correct rule usually applies the same mapping to every pixel of the chosen color in the input. If examples show all occurrences transformed identically, expect the same for the test input.</description>\n<example>If two red pixels in the input both appear in the output at positions shifted by the same vector, then applying that same shift to every red pixel in a new input is the expected behavior. If only some pixels change, look for a different selection rule instead.</example>\n</note4>\n\n<note5>\n<description>Use the examples to infer whether the mapping is deterministic (one output per input cell) and whether it is the only change. If every example pair can be explained by a single, consistent mapping, apply that mapping to the test input.</description>\n<example>When every training input/output pair can be explained by the same rule (e.g., \"every red pixel moves by (dr,dc)\"), then that rule is the most likely transformation. Before finalizing, mentally apply the inferred mapping to the test grid to see if it reproduces the same kind of consistent change seen in the examples.</example>\n</note5>","<note1>\n<description>Look for a repeating sub-shape: many tasks use the same small motif (often a horizontal 3-pixel run) repeated in the grid. Treat that motif as the atomic unit to follow rather than as isolated pixels.</description>\n<example>Imagine a grid where the same \"three in a row\" appears in three different places. Instead of analyzing each pixel separately, mark the motif locations and their relative offsets from one another so you can compare their arrangements.</example>\n</note1>\n\n<note2>\n<description>Compare motif positions by offset from a reference (for example, the topmost-leftmost motif). The consistent offset between repeated motifs reveals the translation vector used by the transformation.</description>\n<example>If one motif sits directly above-left of another and the same offset repeats for other pairs, that offset is likely the translation; record that offset (row change and column change) as the candidate rule.</example>\n</note2>\n\n<note3>\n<description>Examine how the motif is altered when it is moved: does the horizontal run become vertical, is a corner copied, or are extra pixels added at a fixed relative position (for example, a pixel at the motif's top-left)? These are common local transformations.</description>\n<example>Take a horizontal three-pixel motif and compare its original and moved forms: you might find that the moved motif is a vertical three-pixel column or that a small corner pixel appears at the same relative spot each time.</example>\n</note3>\n\n<note4>\n<description>Decide whether the rule is applied to every occurrence or only to a subset (for example, the leftmost occurrence). Check which occurrences are changed in the outputs to infer the selection criterion.</description>\n<example>If only the motif that is leftmost in the top row is altered while others remain, then the transformation targets a particular occurrence rather than all motifs.</example>\n</note4>\n\n<note5>\n<description>Reconstruct the output by applying the observed translation and the observed local change to the chosen motif(s), and verify by checking that other pixels remain unchanged and that the grid dimensions are preserved. This confirms you have the correct rule.</description>\n<example>Move the chosen motif by the recorded offset, apply the recorded local change (corner or orientation), and then scan the grid: every other pixel should match the input, and the moved motif should match the output pattern.</example>\n</note5>","<note1>\n<description>Look for the object of interest: a single non-zero color that appears as repeated small shapes. When one color forms multiple identical motifs, treat each motif as an atomic unit to be transformed.</description>\n<example>Imagine a grid with several identical L-shaped clusters of green pixels. Rather than treating each pixel independently, first identify which color is repeated and which clusters belong to that color; working at the cluster level makes the transformation easier to spot.</example>\n</note1>\n\n<note2>\n<description>Compare the positions of corresponding pixels inside each cluster between input and output to detect a consistent translation. If the same offset appears for many clusters, that offset is the translation vector to apply.</description>\n<example>If in several clusters a pixel that was at (r,c) in the input appears at (r-1,c) in the output, that suggests a consistent (−1,0) shift for those clusters. Confirm this offset across multiple clusters before applying it globally.</example>\n</note2>\n\n<note3>\n<description>Check whether the transformation preserves colors and relative geometry: the operation is typically a rigid translation (no rotation, reflection, or recoloring). This tells you to move pixels without changing their shape or color.</description>\n<example>If an L-shaped cluster remains an L-shaped cluster in the output but appears in a different location, you have a pure translation. If colors or orientations change, consider other operations instead.</example>\n</note3>\n\n<note4>\n<description>Account for edges and overlaps: translated pixels that fall outside the grid are simply lost, and overlapping translated pixels merge into a single filled cell. Use these observations to predict where new pixels will appear and where originals may be erased.</description>\n<example>When you shift a cluster up by one, pixels that land on or above row 0 disappear; when two translated clusters collide, the result is one pixel in the output rather than two. This helps explain missing pixels and merged clusters in the outputs.</example>\n</note4>\n\n<note5>\n<description>Apply the inferred translation uniformly to every cluster of the target color and then validate by checking consistency across examples. If the transformed clusters match the training outputs, the same rule should produce the test output.</description>\n<example>After deducing a translation vector from the examples, move every pixel of the target color by that vector in the test input and verify that the resulting pattern follows the same placement rules seen before. If any cluster fails, re-check whether the offset or the cluster selection was misinterpreted.</example>\n</note5>","<note1>\n<description>Look for a repeated, minimal unit that appears multiple times; this unit is the likely building block of the transformation. When you can partition the grid into identical small shapes, work with that unit rather than individual pixels.</description>\n<example>Imagine a 6×6 grid that contains several identical L-shaped clusters. If each cluster is the same orientation and size, treat each cluster as one atomic object and record its bounding box and internal pixel pattern before any further changes.</example>\n</note1>\n\n<note2>\n<description>Check whether the output keeps each atomic unit's shape and orientation but relocates it. If shapes remain identical and only their positions change, the rule is a geometric move (translation, rotation, or reflection) of those units.</description>\n<example>If a 2×2 square appears in the input and in the output you see the same 2×2 square in a different place with the same orientation, that indicates the whole square was moved rather than recolored or reshaped.</example>\n</note2>\n\n<note3>\n<description>Try a simple translation: each atomic unit is shifted by a fixed offset (same row and column step for every unit). A consistent offset across all examples is a strong sign of a uniform translation rule.</description>\n<example>Suppose every detected unit in the input is moved two cells to the right and one cell down in the output; that uniform shift (dx=2, dy=1) explains how all instances were repositioned.</example>\n</note3>\n\n<note4>\n<description>Confirm that colors and internal structure are preserved: the transformation usually only repositions the colored pixels, not changes their color or the pattern inside each unit. This helps you ignore color changes when searching for the rule.</description>\n<example>If the input has red pixels forming a small cross and the output shows the same cross shape in a new location but still red, then color preservation is part of the rule and you should treat color as invariant.</example>\n</note4>\n\n<note5>\n<description>Validate the hypothesis by applying the suspected operation to every atomic unit and checking for overlaps or collisions. If multiple units would land on the same cell, the examples will either show a consistent collision rule or indicate the offset is different for some units.</description>\n<example>After hypothesizing a fixed offset, move every detected unit by that offset and mark the new positions; if any predicted positions coincide, re-examine whether the offset is constant or whether some units were rotated/translated differently.</example>\n</note5>"],"string":"[\n \"<note1>\\n<description>Look for repeated objects: many ARC tasks use the same small motif repeated in different places. Identifying that motif reduces the problem to how one instance is transformed rather than many unrelated pixels.</description>\\n<example>Imagine a grid with several identical 3‑pixel L‑shapes in different corners. Instead of tracking every pixel, first find the shape (its three colored pixels) and treat each occurrence as an instance of that motif.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare corresponding pixels of an instance in input vs. output to detect a rigid transform. If the same relative offsets keep the same color but move to different coordinates, the transform is a translation, rotation, or reflection rather than a color change or recoloring.</description>\\n<example>If one L‑shape’s top pixel is at (r,c) in the input and in the output the same L‑shape’s top pixel is at (r+2,c+1), that indicates a consistent translation. Repeat this check for the other two pixels of that L to confirm the same offset everywhere.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide which axis the motif is being moved along by checking whether the row indices or column indices change. If rows change while columns are constant, the motif is being moved vertically; if columns change while rows are constant, it is being moved horizontally.</description>\\n<example>For example, if every instance’s colored pixels shift down by two rows but keep the same column positions, the motif is translated downward; if instead columns shift while rows remain fixed, the motif is translated horizontally.</example>\\n</note3>\\n\\n<note4>\\n<description>Use a single clear anchor (a particular colored pixel or the motif’s top‑left) to compute the displacement vector and apply it to every instance. Doing this consistently for all occurrences avoids inconsistent placements.</description>\\n<example>Pick the topmost colored pixel of each L as the anchor; measure how many rows and columns that anchor moves between input and output. Then move every other pixel of each L by the same row/column offsets so all copies are translated uniformly.</example>\\n</note4>\\n\\n<note5>\\n<description>Watch for edge cases: clipping, overlap, and the direction of movement. If the predicted destination falls outside the grid, check whether the task preserves or removes pixels; if multiple instances overlap, check whether outputs show merged or preserved pixels.</description>\\n<example>If a translated pixel would fall outside the grid, verify whether the examples simply omit it or place it inside the grid instead. Also, after translating all instances, scan the grid to ensure each original motif appears in the same relative orientation and color, and that no extra pixels of that color were introduced.</example>\\n</note5>\",\n \"<note1>\\n<description>Find the target color by frequency: the color that appears in multiple small clusters is the one the transformation operates on. Count occurrences and ignore the background color (usually 0) to pick the focus.</description>\\n<example>If a grid has many single pixels and a few small groups of the same color, that repeated color is the one you should follow. For instance, if blue appears in several tiny clusters while red appears only once, treat blue as the subject of the transformation.</example>\\n</note1>\\n\\n<note2>\\n<description>Isolate each connected component of the target color and compute its bounding box (min/max row and column). This gives you the component’s top, left, width and height so you can reason about placement and alignment.</description>\\n<example>For a cluster that spans rows 2–4 and columns 5–7, the bounding box is rows 2..4 and cols 5..7; record top=2, left=5, width=3, height=3 so you can compare and move that whole block consistently.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a vertical reflection: each component’s top and bottom rows are mirrored across the grid’s horizontal midline. The horizontal coordinate (left edge) stays the same; only the vertical position changes.</description>\\n<example>If a component’s top row is 1 and the grid height is H, its mirrored top becomes H−1−top; if the component’s top is 4 in a 10-row grid, the mirrored top would be 5 (since 10−1−4=5). This keeps the block width and left edge identical while flipping its vertical placement.</example>\\n</note3>\\n\\n<note4>\\n<description>After mirroring, place the component back into the grid and keep its internal pattern intact. Do not rotate or reshape the block—only move it vertically—so the shape’s columns remain aligned with the original left edge.</description>\\n<example>A 2×3 block that originally starts at column 6 should still start at column 6 after mirroring; only its row indices are changed so the block occupies the mirrored vertical area but the same horizontal columns.</example>\\n</note4>\\n\\n<note5>\\n<description>Decide collision policy: if a mirrored cell would land on a different non-background color, the examples usually preserve the original color at that position. If the mirrored cell is background, it becomes the target color; if the mirrored cell already contains the target color, leave it unchanged.</description>\\n<example>If a mirrored pixel would overwrite a different-colored pixel, keep that other color; if it would overwrite background, fill it with the target color; if it would overwrite another instance of the target, do nothing. This keeps the transformation consistent and predictable.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for a small, consistent motif: the transformation often uses a tiny 3×3 arrangement of the same color as the unit of change. Recognizing that unit makes it easier to see how the output is built from repeated copies rather than many independent edits.</description>\\n<example>Imagine a grid with several small clusters of the same color; each cluster appears to be a 3×3 patch (one cell thick) with a particular arrangement of filled cells. Once you treat that 3×3 as the motif, you can search for the same arrangement elsewhere instead of scanning every pixel individually.</example>\\n</note1>\\n\\n<note2>\\n<description>Identify the motif’s anchor (a unique, distinctive cell inside the 3×3) and record its relative coordinates. That anchor is the reference point you will use to place copies of the motif.</description>\\n<example>For instance, if a 3×3 motif always has a filled cell at the top-left of the 3×3, label that cell (0,0) relative to the motif. Marking that anchor lets you reproduce the motif by shifting the same relative pattern to other locations.</example>\\n</note2>\\n\\n<note3>\\n<description>Search the input for other occurrences of the same motif (same shape and color). If the motif appears multiple times, each occurrence is a candidate for copying rather than being treated as noise.</description>\\n<example>Suppose you find two identical 3×3 clusters in different parts of the grid; treat both as instances of the motif. You should not ignore one because it is far away—both are legitimate sources for the transformation.</example>\\n</note3>\\n\\n<note4>\\n<description>Place copies of the motif by copying the motif’s internal arrangement relative to its anchor, using the motif’s anchor as the reference point. In other words, translate the 3×3 pattern so its anchor coincides with the anchor of the source motif.</description>\\n<example>If a motif’s anchor is at (r,c) inside the 3×3 and you want to place it so its anchor is at (r2,c2), copy every filled cell of the 3×3 by adding the same offset (r2−r, c2−c) to each relative coordinate. This preserves the motif’s shape and orientation when you move it.</example>\\n</note4>\\n\\n<note5>\\n<description>After placing copies, check for overlaps and decide whether to overwrite or preserve original pixels. If the examples show that copies are placed on top of originals, expect overwriting; otherwise consider merging or leaving originals intact.</description>\\n<example>When you copy a motif onto another motif, the copied pixels may land on the original filled cells. If the training outputs show the copied color replacing originals, overwrite them; if not, keep the originals and only add new pixels outside existing motifs.</example>\\n</note5>\",\n \"<note1>\\n<description>Separate objects by color and treat each connected colored region as an independent unit. This simplifies the problem because you can analyze each object's shape and position on its own.</description>\\n<example>Imagine a grid with two identical blue blobs and many empty cells. Label each blob (top blob = A, bottom blob = B). Work with A and B separately rather than mixing pixels from different blobs.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the minimal bounding rectangle for each object and record its topmost and leftmost pixels (the object's top-left anchor). These anchor coordinates are the natural reference points for the transformation.</description>\\n<example>For a blob whose pixels occupy rows 2–4 and columns 5–7, its bounding box is rows 2..4 × cols 5..7 and its top-left is (row=2,col=5). Use that anchor to locate where the object sits relative to the grid.</example>\\n</note2>\\n\\n<note3>\\n<description>Translate each object by subtracting its bounding-box top and left values from every pixel coordinate (a uniform shift). In formula form: new_row = old_row − box_top, new_col = old_col − box_left. This makes each object's top-left pixel land on the grid origin.</description>\\n<example>If a blob's top-left is (2,3) and one pixel is at (4,6), translating by (−2,−3) moves that pixel to (2,3). Apply the same subtraction to all pixels of the blob to get the translated object.</example>\\n</note3>\\n\\n<note4>\\n<description>After translation, check whether each translated object overlaps other objects or the grid boundary. If overlaps occur, split the object into multiple non-overlapping pieces by partitioning the translated bounding box into contiguous rows or columns (for example, by splitting into equal-width tiles).</description>\\n<example>Suppose two identical objects are translated and their translated boxes touch; split each box into two horizontal tiles (top and bottom). Place each tile at the corresponding tile position in the other object's translated box to avoid overlaps while preserving the object's internal pattern.</example>\\n</note4>\\n\\n<note5>\\n<description>When placing translated pieces, keep each piece's internal arrangement unchanged and use the same relative ordering (for example, keep the original top row as the top row of the tile). Finally, verify that the translated pieces do not collide and that the number and shape of pieces match the original object.</description>\\n<example>If a translated object is a 3×3 block and you split it into three horizontal tiles, each tile should be a contiguous row of the same color and the top tile should remain the original top row. After placement, check that no pixels of different objects occupy the same cell.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for repeated small motifs: many ARC tasks use the same small object (a compact cluster of one color) repeated in different places. Identifying the motif’s bounding box and its internal pattern lets you treat every occurrence the same way. This reduces the problem to “what to do with each copy” rather than handling every pixel separately.</description>\\n<example>Imagine a 3×3 block that appears twice on a black background: each block is the same shape and color. Once you isolate that 3×3 pattern, you can reason about how the output relates to that pattern in every occurrence instead of scanning the whole grid pixel-by-pixel.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare the motif’s internal pattern to its output: check whether the motif is left unchanged, mirrored, rotated, or otherwise transformed. A consistent spatial relationship between input and output cells for a single motif tells you the global operation. This step is about shape transformation, not color changes.</description>\\n<example>If the motif is a 3×3 cross, and the output shows that cross rotated 90° in every occurrence, then the transformation is a rotation of the motif (not a simple translation or reflection). Recognizing that rotation tells you how to place the motif in the output.</example>\\n</note2>\\n\\n<note3>\\n<description>Check translation: determine whether each motif moves by a fixed vector from its original position. If the same offset appears for every occurrence, the transformation is a translation (possibly combined with the shape change). Knowing the offset lets you predict where to place the motif in the output for any input occurrence.</description>\\n<example>Suppose every 3×3 block in the input appears at the same relative coordinates in the output but shifted by the same (row, column) vector; that indicates a uniform translation. You can then apply that same vector to every occurrence when building the output.</example>\\n</note3>\\n\\n<note4>\\n<description>Consider stacking: many tasks place transformed copies of the motif so their outlines touch or overlap, forming a larger connected shape. Decide whether copies are stacked in the same direction (all shifted up/down/left/right) or in a different orientation, and whether they are allowed to overlap. This explains why the output shows connected regions rather than isolated motifs.</description>\\n<example>If each motif is translated down by the same amount, the transformed copies will form a vertical stack; if instead they are rotated and translated differently, they may form a 2D mosaic. Observing that the output motifs touch or form a continuous region points to stacking behavior.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate and watch for pitfalls: apply your inferred rule to one or two occurrences and check for collisions or unexpected colors. If some occurrences are different, re-evaluate whether the rule is uniform or conditional. Also ensure the output uses the same color palette as the input and does not introduce new colors.</description>\\n<example>After deducing “rotate motif, then translate by fixed vector,” place that transformed motif at every original location and compare with the example output. If a placed motif would land on a non-black cell or if some motifs in the output differ, adjust whether rotation, translation, or stacking is being applied conditionally.</example>\\n</note5>\",\n \"<note1>\\n<description>Find the target object(s) by color: identify the non-background color that appears repeatedly and treat each contiguous group of that color as an object. Working with whole objects (not individual pixels) makes it easier to compare shapes across examples.</description>\\n<example>Imagine a grid with several blue blobs on a black background. Mark each connected blue region (use 4‑connectivity) and note their pixel counts and shapes; these marked objects are what you will compare to the outputs.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare object positions between input and output: check whether each object’s bounding box or centroid has been translated by the same offset (e.g., moved up and to the right). A constant displacement suggests a uniform geometric shift was applied to every object.</description>\\n<example>If a 3‑pixel L‑shaped object in the input appears in the output at a consistent number of rows and columns higher and to the right, that indicates a single translation vector was used for that object rather than a different change.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a rotation or reflection of the object’s internal pattern: an object may be moved and then rotated (e.g., 90°) so that a previously internal pixel becomes an external one. Compare the orientation of distinctive pixels before and after the transformation.</description>\\n<example>A horizontal triple in the input might appear as a vertical triple in the output after the same translation; that change in orientation points to a rotation step applied after the translation.</example>\\n</note3>\\n\\n<note4>\\n<description>Verify that the transformation preserves object size and color and only moves/rotates them: the number of pixels and their color should remain constant between input and output, so you can match object shapes and count pixels to confirm the rule.</description>\\n<example>If a shape has five pixels in the input and you see five pixels of the same color in the output arranged identically (just translated/rotated), that confirms the operation is a rigid transform (no scaling or recoloring).</example>\\n</note4>\\n\\n<note5>\\n<description>Combine observations into a single hypothesis: apply the inferred translation to every object, then apply the inferred rotation/reflection to each translated object; check that the resulting positions match the output examples. If something doesn’t match, try the reverse rotation or a different offset until the pattern holds for all objects.</description>\\n<example>Take each object, move it by the same vector you observed in the examples, then rotate it (for example 90°) and see whether the rotated positions align with the outputs; if they do, that sequence of steps is likely the correct transformation rule.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for repeated, identical non-background objects across the grid. When the same small arrangement of colored pixels appears more than once, those occurrences are likely the units being transformed rather than isolated pixels.</description>\\n<example>Imagine a grid with several identical L-shaped clusters of the same color. If the output shows many L-shapes but each is shifted or mirrored compared to the input, treat each L as an atomic object to be moved or reflected instead of moving individual pixels one by one.</example>\\n</note1>\\n\\n<note2>\\n<description>Compute the minimal bounding rectangle for each object and record its pixel offsets inside that rectangle. Working with relative offsets (not absolute coordinates) makes it easier to compare and apply the same operation to every object.</description>\\n<example>If an L occupies cells at (r,c),(r+1,c),(r+2,c) and (r+1,c+2) inside its bounding box, note the offsets (0,0),(1,0),(2,0),(1,2). This offset list is what you will reposition or reflect when transforming the object.</example>\\n</note2>\\n\\n<note3>\\n<description>Compare the input and output bounding boxes to infer the transformation type: a horizontal reflection reverses the left/right order of offsets, a vertical reflection reverses up/down order, and a 180° rotation reverses both. Use the change in ordering to pick the correct axis or axes.</description>\\n<example>For an L with offsets [0,0],[1,0],[2,0],[1,2], a horizontal flip would make offsets [0,0],[1,0],[2,0],[1,2] appear in reverse left-to-right order; a vertical flip would reverse top-to-bottom; a 180° rotation reverses both.</example>\\n</note3>\\n\\n<note4>\\n<description>Apply the same geometric operation to every detected object and keep the object's color unchanged. The rule is global: every occurrence is transformed the same way, so once you know the operation, use it consistently across the grid.</description>\\n<example>If you determine that each L is being mirrored horizontally, place each L's offset list into the mirrored positions while preserving its color; do this for every L in the grid to reproduce the output pattern.</example>\\n</note4>\\n\\n<note5>\\n<description>After applying the transformation, check for overlaps and color conflicts: the operation should not introduce new colors or erase existing ones. If overlaps occur, decide whether the examples imply stacking (color preserved) or one color replacing the other, and apply that rule consistently.</description>\\n<example>If two transformed objects would land on the same cell, inspect the examples to see whether the same color was used to mark that cell or whether one color overwrote the other; use the same precedence when you place the objects in the test grid.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the smallest repeating object: many tasks use a tiny identical shape repeated across the grid. Identifying that minimal motif (its bounding box and internal pattern) is the first step because the transformation usually operates on whole instances of that motif.</description>\\n<example>Imagine a grid with several identical 3×3 blocks scattered around. If every block has the same arrangement of colored pixels inside its 3×3 box, treat that 3×3 as the motif and ignore isolated single pixels that are not part of a full motif.</example>\\n</note1>\\n\\n<note2>\\n<description>Measure the motif’s vertical extent: count how many rows the motif occupies (height h). The transformation often treats the motif as two stacked blocks — the top block and the bottom block — so you must know h to split the motif into those two parts.</description>\\n<example>If the motif is 4 rows tall, split it into a 2-row top block and a 2-row bottom block; if it’s 3 rows tall, the top block will be the first row and the bottom block the remaining two rows. Use that height when you later try to paste a top block above a bottom block.</example>\\n</note2>\\n\\n<note3>\\n<description>Think in terms of “top-left” and “bottom-left” positions: each motif has a leftmost column index. The transformation commonly copies a block’s top rows to the cell immediately to the right of that motif’s left column, while preserving the motif’s bottom rows at the motif’s original left column.</description>\\n<example>For a motif that occupies columns c..c+h−1, place its top h rows into columns c+1..c+h, and leave the motif’s bottom h rows in columns c..c+h−1. This keeps the original motif visible while adding a shifted copy to its right.</example>\\n</note3>\\n\\n<note4>\\n<description>Apply the copy independently to every occurrence and preserve color: do not change the motif’s color or the original motif pixels. The operation is a translation (copy), not a recoloring or merging, so colors stay the same and originals remain intact.</description>\\n<example>If a motif is blue, the pasted copy will also be blue and will sit in the new columns to the right; the original blue pixels in their original columns remain unchanged. Treat each motif separately rather than trying to merge or recolor them.</example>\\n</note4>\\n\\n<note5>\\n<description>Watch for edge cases and validation: if a motif sits on the last column, there is no room to paste a copy to its right and that instance should be left unchanged; if a pasted copy would overlap another motif, check whether examples expect overlaps or require a consistent rule (usually pasting is allowed in these problems).</description>\\n<example>If a motif’s leftmost column equals the grid’s right edge, skip the paste for that instance. If a pasted copy would land on top of a different motif, re-check the motif detection and split height — if the examples show no such conflicts, the paste is typically placed without conflict.</example>\\n</note5>\",\n \"<note1>\\n<description>Locate the motif: scan for a compact, small set of pixels (often a 3×3 block) whose internal arrangement (which cells are filled) is consistent across examples. Treat that small set as the atomic object to transform rather than as isolated pixels.</description>\\n<example>Imagine a grid where a small group of three pixels forms a compact L or a short line. That small group is the motif: mark its bounding box and internal pattern so you can reason about how it moves or is copied as a whole.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare coordinates: for each pixel of the motif in the input, check whether the same color appears at a predictable offset in the output (for example, one row down and one column left). If a consistent offset appears for every motif pixel, that offset is the translation vector to apply to the motif.</description>\\n<example>If an L-shape at positions (r,c), (r,c+1), (r+1,c+1) in the input has the same L-shape at (r+1,c-1), (r+1,c), (r+2,c) in the output, the vector (dr,dc) = (+1, -1) is the translation to try on other motifs.</example>\\n</note2>\\n\\n<note3>\\n<description>Apply the translation to every occurrence of the motif independently and preserve its internal pattern and color. The transformation is a rigid shift of the motif, not a rotation, reflection, or recoloring.</description>\\n<example>Two identical L-shapes in different places should each move by the same vector; after translation they remain identical L-shapes but in new positions, producing two shifted copies of the original motif.</example>\\n</note3>\\n\\n<note4>\\n<description>Decide how to handle overlaps: when a translated copy would land on existing colored pixels, check whether the examples show merging (both colors present) or replacement (one color overwrites). Use the training pairs to infer which behavior to apply.</description>\\n<example>If a translated pixel would fall on an existing non-background pixel in the examples, inspect that output cell: if it shows both colors then merge; if it shows only the translated color then overwrite. Apply the same rule consistently across all overlaps.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate and iterate: after translating each motif and handling overlaps according to the inferred rule, compare the result to the example outputs. If the overall pattern matches, the rule is consistent; if not, re-check whether you misidentified the motif or the translation vector.</description>\\n<example>Translate all detected motifs by your vector and check whether the relative arrangement and counts of colored pixels match the examples. If one motif fails, re-evaluate whether that motif is the same shape or whether a different offset is needed for some motifs.</example>\\n</note5>\",\n \"<note1>\\n<description>First isolate the active color and the objects made from it. Many tasks work on a single non-background color so focus on those pixels and ignore the background.</description>\\n<example>Imagine a grid with only blue pixels forming two separate blobs. Treat every blue cell as part of the pattern to transform rather than as isolated noise. This reduces the problem to moving or copying a small set of shapes instead of the whole grid.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare the relative positions of pixels inside each object between input and output. If pixels keep the same local arrangement but appear at different coordinates, the transformation is a rigid translation (a constant vector added to every pixel).</description>\\n<example>For a small 3×3 L-shape in the input, check the output: if the L-shape is still an L but shifted by the same number of rows and columns everywhere, you have a uniform translation. That tells you to search for a single (dr, dc) that explains every object's change.</example>\\n</note2>\\n\\n<note3>\\n<description>Look for a consistent offset applied to the entire grid: many tasks move the whole pattern by the same vector (a constant dr and dc). If so, you can compute the translation from one object and apply it to all objects.</description>\\n<example>If one object's top-left moves by (dr,dc) and the same (dr,dc) is seen for another object, then the whole grid is being shifted by that vector. Use that single vector to predict where every pixel should go.</example>\\n</note3>\\n\\n<note4>\\n<description>Check how the translation affects the grid edges: if objects move toward the border and some disappear, the rule may be \\\"translate until the object touches a border\\\" rather than a fixed vector. In other words, the movement stops when the object reaches an edge.</description>\\n<example>A small object that is pushed toward the top edge will be stopped once any of its pixels reaches row 0; the visible output shows only the part that remains on the grid. Recognizing this stopping condition explains why some objects appear partially clipped in the outputs.</example>\\n</note4>\\n\\n<note5>\\n<description>Finally, verify invariants: the color, the local shape and relative ordering of pixels should be preserved. If those are unchanged, you can confidently apply the same translation to the test input and expect similar behavior.</description>\\n<example>When the transformation is pure translation, each object's internal pattern is identical before and after (only position changes). Use that to check your candidate vector and to avoid assuming rotations, reflections, or recoloring occurred.</example>\\n</note5>\",\n \"<note1>\\n<description>Isolate the object by finding all cells of the non-background color and computing the minimal bounding rectangle that contains them. This reduces the problem to a small set of coordinates and makes spatial relationships obvious.</description>\\n<example>Imagine a grid with a single red shape occupying rows 2–4 and columns 1–3. The bounding box is rows 2–4, cols 1–3; listing those coordinates (e.g., (2,1),(2,3),(3,2)) lets you reason about where the shape sits relative to the grid edges.</example>\\n</note1>\\n\\n<note2>\\n<description>Look for a translation that moves the bounding box so its top-left corner touches the top-left edge of the grid. In other words, translate every coordinate by the negative of the box's top-left offset from (0,0).</description>\\n<example>If the bounding box starts at row 2 and column 1, subtracting those offsets from each pixel's coordinates will move the whole object so its top-left becomes (0,0), preserving internal offsets.</example>\\n</note2>\\n\\n<note3>\\n<description>After translating, check whether the translated object is exactly the same as the original object. If so, the object is already anchored at the top-left and no further change is needed.</description>\\n<example>For instance, if a 3×3 pattern at (0,0) equals the original pattern after translation, then that pattern already sits at the grid origin and you can stop here.</example>\\n</note3>\\n\\n<note4>\\n<description>If the translated object is not identical to the original, the transformation usually adds a single extra row or column to the translated object to make it fit the grid, and then places that enlarged object at the top-left. In general, append the missing row/column(s) so the translated bounding box becomes one cell larger in the direction away from the grid edge.</description>\\n<example>Suppose the translated box would extend one cell past the right edge; adding a single column on the right side of the translated box and then placing that enlarged box at (0,0) is a common way to complete the pattern.</example>\\n</note4>\\n\\n<note5>\\n<description>Keep the color and orientation unchanged and do not rotate, flip, or recolor the object. The operation is a translation and optional one-cell extension, not a geometric modification of the shape.</description>\\n<example>If the object is a small L-shaped cluster of color X, the final grid should show the same L-shape (possibly one extra pixel added) in the same orientation and color; only its position and size may have changed.</example>\\n</note5>\",\n \"<note1>\\n<description>Separate the grid into connected components using orthogonal adjacency (up/down/left/right). Each non-background connected group is treated as an individual object to analyze.</description>\\n<example>Imagine a grid with two separate blue blobs. Mark each blob as its own object by tracing cells that touch orthogonally; you will have two objects even though they share the same color.</example>\\n</note1>\\n\\n<note2>\\n<description>For each object, compute its bounding box (min/max row and column) and record the object's width and height. These dimensions tell you the object's horizontal and vertical extents and which edge is closest to the grid border.</description>\\n<example>If an object occupies rows 2–4 and columns 5–7, its bounding box is rows 2..4 by columns 5..7 (width 3, height 3). If another object's box starts at column 1, that object has a different horizontal extent than the one whose box starts at column 5.</example>\\n</note2>\\n\\n<note3>\\n<description>Classify each object by which side of its bounding box is nearest the grid edge: left (closest column to column 0), right (closest column to last column), top (closest row to row 0), or bottom (closest row to last row). This tells you whether the object is a \\\"left/right\\\" object or a \\\"top/bottom\\\" object.</description>\\n<example>A 3×3 box whose min column is 0 is a left object; a 3×3 box whose max column equals the grid width is a right object. A 3×3 box whose min row is 0 is a top object; one whose max row equals the grid height is a bottom object.</example>\\n</note3>\\n\\n<note4>\\n<description>Apply a single, consistent translation rule to each object based on its classification: move each object horizontally or vertically by one cell toward the nearest grid edge (do not rotate or mirror). If an object touches both a top and a left edge, treat it as both top and left; if it touches both a left and bottom edge, treat it as both left and bottom, etc.</description>\\n<example>A left object with min column 1 should be shifted one column to the left (to column 0). A top object with min row 2 should be shifted one row up (to row 1). If an object is already adjacent to the edge, it stays where it is.</example>\\n</note4>\\n\\n<note5>\\n<description>When multiple objects are translated, apply the translations independently and check for overlaps or collisions. If two translated objects would occupy the same cell, resolve by a consistent priority (for example, objects closer to the edge move first, or objects that touch an edge are not moved).</description>\\n<example>Two separate objects both touching the same border will each move one step inward; if their inward moves would collide, use a fixed tie-break rule (e.g., move the one nearer the border first). Always preserve the object's color and shape—only translate it.</example>\\n</note5>\",\n \"<note1>\\n<description>Look first for a consistent global offset: many tasks move every non-background pixel by the same row/column amount. Finding one example that is shifted by (r,c) suggests a uniform translation applied to the whole grid.</description>\\n<example>Imagine a single red pixel at (2,3) in the input and the output shows a red pixel at (5,2). That single pair points to a translation of (3,-1). If another colored pixel also moves by the same (dr,dc), you likely have a global translation to test on the whole grid.</example>\\n</note1>\\n\\n<note2>\\n<description>Check whether colors are preserved: the transformation often only relocates pixels of a specific color and leaves other colors (and background) unchanged. Confirming color invariance narrows the set of possible operations.</description>\\n<example>Suppose the input has red and blue pixels and the output still contains red and blue at different coordinates but no new colors appear. That indicates the rule moves the red/blue pixels but does not alter their identity or introduce new colors.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide how the rule treats boundaries: a pure translation can move pixels off-grid (clipping) or wrap them around (toroidal). Use example pairs to see whether missing pixels imply clipping or whether pixels reappear on the opposite side.</description>\\n<example>If a pixel at the top row after translation would be at a negative row index but you still see the color in the output, that suggests wrapping. Conversely, if a pixel disappears from the output, that suggests the transformation clips pixels that move outside the grid.</example>\\n</note3>\\n\\n<note4>\\n<description>Verify the operation is applied to every occurrence of the target color and not selectively: the correct rule usually applies the same mapping to every pixel of the chosen color in the input. If examples show all occurrences transformed identically, expect the same for the test input.</description>\\n<example>If two red pixels in the input both appear in the output at positions shifted by the same vector, then applying that same shift to every red pixel in a new input is the expected behavior. If only some pixels change, look for a different selection rule instead.</example>\\n</note4>\\n\\n<note5>\\n<description>Use the examples to infer whether the mapping is deterministic (one output per input cell) and whether it is the only change. If every example pair can be explained by a single, consistent mapping, apply that mapping to the test input.</description>\\n<example>When every training input/output pair can be explained by the same rule (e.g., \\\"every red pixel moves by (dr,dc)\\\"), then that rule is the most likely transformation. Before finalizing, mentally apply the inferred mapping to the test grid to see if it reproduces the same kind of consistent change seen in the examples.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for a repeating sub-shape: many tasks use the same small motif (often a horizontal 3-pixel run) repeated in the grid. Treat that motif as the atomic unit to follow rather than as isolated pixels.</description>\\n<example>Imagine a grid where the same \\\"three in a row\\\" appears in three different places. Instead of analyzing each pixel separately, mark the motif locations and their relative offsets from one another so you can compare their arrangements.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare motif positions by offset from a reference (for example, the topmost-leftmost motif). The consistent offset between repeated motifs reveals the translation vector used by the transformation.</description>\\n<example>If one motif sits directly above-left of another and the same offset repeats for other pairs, that offset is likely the translation; record that offset (row change and column change) as the candidate rule.</example>\\n</note2>\\n\\n<note3>\\n<description>Examine how the motif is altered when it is moved: does the horizontal run become vertical, is a corner copied, or are extra pixels added at a fixed relative position (for example, a pixel at the motif's top-left)? These are common local transformations.</description>\\n<example>Take a horizontal three-pixel motif and compare its original and moved forms: you might find that the moved motif is a vertical three-pixel column or that a small corner pixel appears at the same relative spot each time.</example>\\n</note3>\\n\\n<note4>\\n<description>Decide whether the rule is applied to every occurrence or only to a subset (for example, the leftmost occurrence). Check which occurrences are changed in the outputs to infer the selection criterion.</description>\\n<example>If only the motif that is leftmost in the top row is altered while others remain, then the transformation targets a particular occurrence rather than all motifs.</example>\\n</note4>\\n\\n<note5>\\n<description>Reconstruct the output by applying the observed translation and the observed local change to the chosen motif(s), and verify by checking that other pixels remain unchanged and that the grid dimensions are preserved. This confirms you have the correct rule.</description>\\n<example>Move the chosen motif by the recorded offset, apply the recorded local change (corner or orientation), and then scan the grid: every other pixel should match the input, and the moved motif should match the output pattern.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the object of interest: a single non-zero color that appears as repeated small shapes. When one color forms multiple identical motifs, treat each motif as an atomic unit to be transformed.</description>\\n<example>Imagine a grid with several identical L-shaped clusters of green pixels. Rather than treating each pixel independently, first identify which color is repeated and which clusters belong to that color; working at the cluster level makes the transformation easier to spot.</example>\\n</note1>\\n\\n<note2>\\n<description>Compare the positions of corresponding pixels inside each cluster between input and output to detect a consistent translation. If the same offset appears for many clusters, that offset is the translation vector to apply.</description>\\n<example>If in several clusters a pixel that was at (r,c) in the input appears at (r-1,c) in the output, that suggests a consistent (−1,0) shift for those clusters. Confirm this offset across multiple clusters before applying it globally.</example>\\n</note2>\\n\\n<note3>\\n<description>Check whether the transformation preserves colors and relative geometry: the operation is typically a rigid translation (no rotation, reflection, or recoloring). This tells you to move pixels without changing their shape or color.</description>\\n<example>If an L-shaped cluster remains an L-shaped cluster in the output but appears in a different location, you have a pure translation. If colors or orientations change, consider other operations instead.</example>\\n</note3>\\n\\n<note4>\\n<description>Account for edges and overlaps: translated pixels that fall outside the grid are simply lost, and overlapping translated pixels merge into a single filled cell. Use these observations to predict where new pixels will appear and where originals may be erased.</description>\\n<example>When you shift a cluster up by one, pixels that land on or above row 0 disappear; when two translated clusters collide, the result is one pixel in the output rather than two. This helps explain missing pixels and merged clusters in the outputs.</example>\\n</note4>\\n\\n<note5>\\n<description>Apply the inferred translation uniformly to every cluster of the target color and then validate by checking consistency across examples. If the transformed clusters match the training outputs, the same rule should produce the test output.</description>\\n<example>After deducing a translation vector from the examples, move every pixel of the target color by that vector in the test input and verify that the resulting pattern follows the same placement rules seen before. If any cluster fails, re-check whether the offset or the cluster selection was misinterpreted.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for a repeated, minimal unit that appears multiple times; this unit is the likely building block of the transformation. When you can partition the grid into identical small shapes, work with that unit rather than individual pixels.</description>\\n<example>Imagine a 6×6 grid that contains several identical L-shaped clusters. If each cluster is the same orientation and size, treat each cluster as one atomic object and record its bounding box and internal pixel pattern before any further changes.</example>\\n</note1>\\n\\n<note2>\\n<description>Check whether the output keeps each atomic unit's shape and orientation but relocates it. If shapes remain identical and only their positions change, the rule is a geometric move (translation, rotation, or reflection) of those units.</description>\\n<example>If a 2×2 square appears in the input and in the output you see the same 2×2 square in a different place with the same orientation, that indicates the whole square was moved rather than recolored or reshaped.</example>\\n</note2>\\n\\n<note3>\\n<description>Try a simple translation: each atomic unit is shifted by a fixed offset (same row and column step for every unit). A consistent offset across all examples is a strong sign of a uniform translation rule.</description>\\n<example>Suppose every detected unit in the input is moved two cells to the right and one cell down in the output; that uniform shift (dx=2, dy=1) explains how all instances were repositioned.</example>\\n</note3>\\n\\n<note4>\\n<description>Confirm that colors and internal structure are preserved: the transformation usually only repositions the colored pixels, not changes their color or the pattern inside each unit. This helps you ignore color changes when searching for the rule.</description>\\n<example>If the input has red pixels forming a small cross and the output shows the same cross shape in a new location but still red, then color preservation is part of the rule and you should treat color as invariant.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate the hypothesis by applying the suspected operation to every atomic unit and checking for overlaps or collisions. If multiple units would land on the same cell, the examples will either show a consistent collision rule or indicate the offset is different for some units.</description>\\n<example>After hypothesizing a fixed offset, move every detected unit by that offset and mark the new positions; if any predicted positions coincide, re-examine whether the offset is constant or whether some units were rotated/translated differently.</example>\\n</note5>\"\n]","isConversational":false},"train":{"kind":"string","value":"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 4, 0, 0, 0], [0, 4, 0, 0, 0, 4, 0, 0, 0, 0], [4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0]], \"output\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 4, 0, 4, 4, 4, 0, 0, 0], [0, 4, 0, 4, 0, 4, 0, 0, 0, 0], [4, 4, 4, 0, 4, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 4, 0, 0], [4, 4, 4, 0, 0, 0, 0, 0, 4, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 4]]}, {\"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, 3, 0, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 3, 3, 3], [0, 0, 3, 0, 0, 0, 0, 0, 3, 0], [0, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0]], \"output\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 3], [0, 0, 3, 0, 0, 0, 0, 3, 3, 0], [0, 3, 3, 3, 0, 0, 0, 0, 3, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 3]]}, {\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 3, 3, 3, 0, 3, 3, 3, 0, 0], [0, 0, 3, 0, 0, 0, 3, 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]], \"output\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 3, 0, 0, 0, 0], [0, 0, 0, 3, 3, 0, 0, 0, 0, 0], [0, 0, 3, 0, 3, 0, 3, 0, 0, 0], [0, 3, 3, 3, 0, 3, 3, 3, 0, 0], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]}]"},"test":{"kind":"string","value":"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 5, 0], [0, 0, 5, 5, 5, 0, 0, 5, 5, 5], [0, 0, 0, 5, 0, 0, 0, 0, 5, 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, 5, 0, 0, 0], [0, 0, 0, 0, 0, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], \"output\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 5, 0, 0, 0, 0, 5, 0], [0, 0, 5, 5, 5, 0, 0, 5, 5, 5], [0, 0, 0, 5, 0, 0, 0, 0, 5, 0], [0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 5, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]}]"},"source":{"kind":"string","value":"barc_heavy"},"prompt":{"kind":"string","value":"You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectangular matrix of integers between 0 and 9 (inclusive). Each number corresponds to a color. 0 is black. Your task is to determine the transformation rule from examples and find out the answer, involving determining the size of the output grid for the test and correctly filling each cell of the grid with the appropriate color or number. The transformation only needs to be unambiguous and applicable to the example inputs and the test input. It doesn't need to work for all possible inputs. Observe the examples carefully, imagine the grid visually, and try to find the pattern. Please output your answer within a code block (```), formatted as a grid of numbers. \n\n# Examples\n## Example 1\nInput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 4 0 0 0 0\n0 0 0 0 4 4 4 0 0 0\n0 4 0 0 0 4 0 0 0 0\n4 4 4 0 0 0 0 0 0 0\n0 4 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 4 0 0 0 0 0 0 0 0\n4 4 4 0 0 0 0 0 0 0\n0 4 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 4 0 0 0 4 0 0 0 0\n0 0 4 0 4 4 4 0 0 0\n0 4 0 4 0 4 0 0 0 0\n4 4 4 0 4 0 0 0 0 0\n0 4 0 0 0 4 0 0 0 0\n0 0 0 0 0 0 4 0 0 0\n0 4 0 0 0 0 0 4 0 0\n4 4 4 0 0 0 0 0 4 0\n0 4 0 0 0 0 0 0 0 4\n```\n\n## Example 2\nInput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 3 0 0 0 0\n0 0 0 0 3 3 3 0 0 0\n0 0 0 0 0 3 0 0 0 0\n0 0 0 0 0 0 0 0 3 0\n0 0 0 0 0 0 0 3 3 3\n0 0 3 0 0 0 0 0 3 0\n0 3 3 3 0 0 0 0 0 0\n0 0 3 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 3 0 0 0 0 0 0 0 0\n0 0 3 0 0 3 0 0 0 0\n0 0 0 3 3 3 3 0 0 0\n0 0 0 0 3 3 0 0 0 0\n0 0 0 0 0 3 0 0 3 0\n0 0 0 0 0 0 3 3 3 3\n0 0 3 0 0 0 0 3 3 0\n0 3 3 3 0 0 0 0 3 0\n0 0 3 0 0 0 0 0 0 3\n```\n\n## Example 3\nInput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 3 0 0 0 0 0\n0 0 0 3 3 3 0 0 0 0\n0 0 0 0 3 0 0 0 0 0\n0 0 3 0 0 0 3 0 0 0\n0 3 3 3 0 3 3 3 0 0\n0 0 3 0 0 0 3 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n0 0 0 0 0 0 0 0 0 0\n0 3 0 0 3 0 0 0 0 0\n0 0 3 3 3 3 0 0 0 0\n0 0 0 3 3 0 0 0 0 0\n0 0 3 0 3 0 3 0 0 0\n0 3 3 3 0 3 3 3 0 0\n0 0 3 0 0 0 3 0 0 0\n0 0 0 0 0 0 0 3 0 0\n0 0 0 0 0 0 0 0 3 0\n0 0 0 0 0 0 0 0 0 3\n```\n\n# Test Problem:\n```\n0 0 0 0 0 0 0 0 0 0\n0 0 0 5 0 0 0 0 5 0\n0 0 5 5 5 0 0 5 5 5\n0 0 0 5 0 0 0 0 5 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 5 0 0 0\n0 0 0 0 0 5 5 5 0 0\n0 0 0 0 0 0 5 0 0 0\n0 0 0 0 0 0 0 0 0 0\n```"},"answer":{"kind":"string","value":"```\n0 0 0 0 0 0 0 0 0 0\n0 5 0 5 0 0 0 0 5 0\n0 0 5 5 5 0 0 5 5 5\n0 0 0 5 0 0 0 0 5 0\n0 0 0 0 5 0 0 0 0 0\n0 0 0 0 0 5 0 0 0 0\n0 0 0 0 0 0 5 0 0 0\n0 0 0 0 0 5 5 5 0 0\n0 0 0 0 0 0 5 0 5 0\n0 0 0 0 0 0 0 0 0 5\n```"},"num_tokens":{"kind":"number","value":1666,"string":"1,666"}}},{"rowIdx":99,"cells":{"abstraction_prompt":{"kind":"string","value":"<|im_start|>user\nDeveloper: # ARC HINT GENERATOR\n\n## Role & Goal\nYou are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted hint that helps the user discover the core transformation principle for themselves without revealing the answer.\n\nBegin with a concise checklist (3-7 bullets) of what you will do; keep items conceptual, not implementation-level.\n\n---\n\n## Hint Generation Strategy\n1. **Compare** the input and output grids for each example. Identify the shared transformation pattern that allows the input grid to be converted into the output grid.\n2. **Identify the Core Principle**: Review the problem description and ground-truth solution to fully discern the key transformation rule. Break it down into its essential operations (e.g., object completion, pattern repetition, symmetry, gravity), paying close attention to properties such as object count, shapes, colors, sizes, symmetry, repetition, relative positioning, and broader grid-level patterns.\n3. **Craft a Targeted Hint**: Generate a hint that guides the user toward the core insight needed to solve the problem. The hint should assist the user during their attempt without revealing the solution.\n4. Structure each note using the template below:\n - **Description** (up to 3 sentences): Explain the concept, when and why it applies, and why it is effective. Include any relevant general formula or principle in its most general form.\n - **Example** (up to 6 sentences): Present a worked example covering all aspects of the description, using a simplified yet representative scenario (not necessarily from the current problem).\n - Optionally, include **Heuristics** or **Pitfalls** in the note where relevant.\n - Focus on methodologies and core principles over specific calculations or problem details.\n - Ensure each hint applies broadly—at least 80% of analogous problems.\n\nAfter generating a hint, verify that no specifics of the solution are revealed, and that the hint remains at the level of guiding the approach.\n\n### Output Format\nProduce a **sequence of 5** notes in the structure:\n<note1>\n<description>...</description>\n<example>...</example>\n</note1>\n<note2>\n<description>...</description>\n<example>...</example>\n</note2>\n...\n\n### Design Guidelines\n- Clarity: Use precise language and correct sentence structure.\n- Atomicity: Each note addresses one recognizable sub-problem.\n- Self-containment: All information needed to understand the idea and its application is within the note.\n- Generalizability: Avoid problem-specific details or variables.\n- Transferability: Notes should apply across a class of problems.\n- Distinctness: Each note addresses a distinct principle.\n\n---\n\n## Guidelines\n- **Guide, Don't Solve**: Illuminate the approach, not the answer. Emphasize what to observe or consider.\n- **Specific yet Abstract**: Use concrete grid details (e.g., \"note the relationship between the blue and red pixels\") to ground abstract patterns (e.g., \"think about one color containing another\").\n\nValidate your generated hint: confirm it is self-contained, actionable, and nondirective. If any aspect is too revealing, revise before finalizing.\n\n---\n\n## Inputs\n### Problem Description\nA full ARC problem, including input/output pairs for training and testing.\n\nYou will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectangular matrix of integers between 0 and 9 (inclusive). Each number corresponds to a color. 0 is black. Your task is to determine the transformation rule from examples and find out the answer, involving determining the size of the output grid for the test and correctly filling each cell of the grid with the appropriate color or number. The transformation only needs to be unambiguous and applicable to the example inputs and the test input. It doesn't need to work for all possible inputs. Observe the examples carefully, imagine the grid visually, and try to find the pattern. Please output your answer within a code block (```), formatted as a grid of numbers. \n\n# Examples\n## Example 1\nInput:\n```\n0 0 0 0 0 0 0 6 0 6 0 0 0 0\n0 0 0 0 0 0 0 6 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 6 0 0 0 0 6 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 6 6 0 0 0 0\n0 0 0 0 0 0 0 0 0 6 0 0 0 0\n0 0 0 0 0 0 6 0 0 0 6 0 0 0\n0 0 0 0 0 0 0 6 0 0 0 0 0 0\n0 0 0 0 0 6 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n6 6 6 6 6 6 6 6 6 6 6 6 6 6\n```\n\n## Example 2\nInput:\n```\n4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4\n0 0 0 0 0 4 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0\n0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0\n0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 4\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0\n0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0\n0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\n```\n\n## Example 3\nInput:\n```\n3 0 0 0\n3 0 0 0\n3 0 3 0\n3 0 0 0\n3 0 0 3\n0 0 3 0\n0 3 3 3\n3 0 0 3\n0 3 3 0\n0 0 0 0\n3 0 3 3\n3 3 0 0\n3 3 3 3\n0 3 0 0\n```\n\nOutput:\n```\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n```\n\n# Test Problem:\n```\n0 6 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n6 0 0 0 0 0 0 0 0 0 0\n6 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 6 0 0 0 0\n0 0 0 0 0 0 0 0 0 6 0\n6 0 0 6 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 6 0 0 6 0 0 0\n0 0 0 0 0 0 0 0 0 6 0\n0 6 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 6\n0 0 0 0 0 0 0 0 6 0 0\n```\n\n---\n\n\n# Generated Hint<|im_end|>\n<|im_start|>assistant\n"},"abstraction_prompt_length":{"kind":"number","value":2324,"string":"2,324"},"generated_abstractions":{"kind":"list like","value":["<note1>\n<description>Look for a single non-background color that consistently appears across the examples and is the only color that changes in the outputs. When one color dominates the input and the output is uniform, that color is usually the source of the transformation.</description>\n<example>Imagine a grid filled with zeros except for a few scattered blue pixels; the outputs in similar tasks are all blue. That pattern tells you to focus on the blue pixels rather than on background zeros or other colors.</example>\n</note1>\n\n<note2>\n<description>Count occurrences of that dominant color in the input: the number of occurrences is often the key parameter for the output. This count is typically the number of distinct pixels, not the number of connected components or other aggregates.</description>\n<example>If you find 12 scattered red pixels in the input, record 12 as the quantity to use; many problems then use that exact count to determine how many times the color should appear in the result.</example>\n</note2>\n\n<note3>\n<description>Decide whether the output is a single horizontal line (one row) filled with the chosen color. Many ARC tasks with a uniform output simply produce a single row whose length encodes the chosen quantity.</description>\n<example>For instance, if the chosen color is green and the count is 7, a plausible output is a single row of 7 green cells; the shape is not a larger block but a linear row.</example>\n</note3>\n\n<note4>\n<description>Use the input’s width (number of columns) as the target width for that single row. The transformation often places the colored cells in a contiguous block that spans the full width of the input, rather than producing multiple rows or smaller blocks.</description>\n<example>On a 10-column input, the output row is usually 10 cells long; the count you extracted earlier becomes the color count placed across that full-width row.</example>\n</note4>\n\n<note5>\n<description>Watch for common pitfalls: do not confuse background zeros with the target color, do not sum connected components or unique positions, and do not add or remove the background color. Always verify the chosen color is the only non-background color that is preserved across examples.</description>\n<example>If a grid has both black and a few yellow pixels but the outputs are all yellow, ignore black and count only yellow pixels; if outputs are uniform and match the yellow count, you have the right rule.</example>\n</note5>","<note1>\n<description>Look first for a single non-background color that appears repeatedly across the input. When one color dominates and the background is uniform, that color is a strong candidate for the transformation's output color.</description>\n<example>Imagine a grid filled with black except for a few scattered red pixels. If red is the only color that appears many times and is not the background, it is natural to suspect red will be the color used in the output.</example>\n</note1>\n<note2>\n<description>Count how many pixels of that candidate color exist in the input. The total count often becomes the key quantity that determines the output's length or number of repetitions.</description>\n<example>For example, if you find exactly 12 red pixels scattered in the input, recording 12 is a useful numeric summary that can be used to build the output.</example>\n</note2>\n<note3>\n<description>Check the output examples' shape and whether it is uniform. If every example output is a single row and every cell in that row is the same color, the transformation likely produces a uniform row whose length encodes the input.</description>\n<example>Suppose each training output is a one-row grid with no mixed colors. That pattern suggests the output is a single-color row rather than a transformed image of the original shapes.</example>\n</note3>\n<note4>\n<description>Relate the counted quantity to the output's length: the count frequently equals the number of output cells. In other words, the numeric summary (often the count of the dominant color) may be used as the output width.</description>\n<example>If the input contains 15 green pixels and the examples show outputs whose length equals that count, then constructing an output row with that many green cells is a natural next step.</example>\n</note4>\n<note5>\n<description>Use a simple verification: pick a representative color from the input (preferably the most frequent non-background color), count its pixels, and then produce a single row whose length equals that count and whose color matches the chosen pixel. This heuristic often matches ARC tasks that summarize color counts into a uniform row.</description>\n<example>As a quick test, count the dominant color in a sample input, form a one-row grid with that many cells filled with the color, and check whether the structure matches the training outputs' pattern before finalizing the answer.</example>\n</note5>","<note1>\n<description>Look for the dominant non-background color: the transformation uses the single color that appears most often in the input. This is effective because many ARC tasks reduce a scattered pattern to the color that carries the bulk of the information.</description>\n<example>Imagine a grid where most colored pixels are red and the rest are background (or zero). Counting occurrences shows red is the dominant color, so the next step is to use red as the candidate for the output.</example>\n</note1>\n\n<note2>\n<description>Confirm uniqueness of the dominant color: the examples imply there is exactly one color that is chosen (not a tie). If two colors had equal counts you would need additional rules, but here the pattern selects the single most frequent color.</description>\n<example>For instance, if blue appears 12 times and green 3 times in a grid, blue is unambiguously the color to use; if counts were tied, you would need a different tie-breaker (not required here).</example>\n</note2>\n\n<note3>\n<description>Form the output by repeating that chosen color across a single row: the output is a horizontal sequence whose length equals the number of columns in the original grid. This preserves the grid's horizontal dimension while encoding the dominant color.</description>\n<example>For a 4-column input and a chosen color X, the output would be a single row of length 4 filled with X (e.g., [X X X X]).</example>\n</note3>\n\n<note4>\n<description>Ignore background and internal structure when deciding the color: do not base the choice on shape, adjacency, or clusters — only on raw frequency. The examples do not preserve spatial layout, only the dominant color's count.</description>\n<example>Even if the chosen color forms several disconnected blobs or isolated pixels, the rule still picks it by total count, not by the number of connected components or the shape of the blobs.</example>\n</note4>\n\n<note5>\n<description>Handle edge cases and pitfalls: if the grid is already a single row, the output should still be a single-row fill; if the dominant color is already the background, re-check whether the task actually uses the background color or if you need to select a non-background color. Always validate your choice against the training examples.</description>\n<example>If the input is a single-row grid with many colored pixels, producing a single-row output filled with the dominant color is consistent; if two colors tie, apply the same tie-break rule seen in examples (or check whether the task expects a different behavior).</example>\n</note5>","<note1>\n<description>Look for the single non-background color that consistently appears in the examples. If one color is the only one that differs from the background, it is usually the element the task is about.</description>\n<example>Imagine a grid mostly filled with zeros but with several scattered blue pixels; the blue pixels are the only non-background elements. Focusing on blue (not the zeros) narrows the problem to a single color to analyze further.</example>\n</note1>\n\n<note2>\n<description>Count how many times that color appears across the whole input grid. The transformation often depends on the total number of occurrences rather than their spatial arrangement.</description>\n<example>For instance, if you find exactly five red pixels in the input, record the count 5. That numeric summary is the key quantity to use when constructing the output.</example>\n</note2>\n\n<note3>\n<description>Check whether the output is a one-dimensional representation: many ARC tasks convert a 2D pattern into a 1×N row where each cell encodes a property of the input (commonly the count). Determine the output's width by comparing examples.</description>\n<example>If every training output is a single row, then the output shape is likely 1×(some width); the width is the property you will encode (for example, the number of target pixels).</example>\n</note3>\n\n<note4>\n<description>Decide how the numeric property (the count) is encoded into the output row: typically each output cell is set to the target color, so the row becomes a uniform stripe whose length equals the count. This preserves the color identity while showing the quantity.</description>\n<example>For example, if the target color is green and the count is 6, the output row would be six green cells in a row: [green, green, green, green, green, green].</example>\n</note4>\n\n<note5>\n<description>Be mindful of common pitfalls: confirm you are counting the correct color (ignore background zeros), verify the output width from examples, and ensure the output is a single row. If the count equals the number of columns or rows, the uniform row will visually match those dimensions.</description>\n<example>Before finalizing, double-check that no other color is the focus and that the training outputs are indeed uniform single rows. If they are, then a uniform row of the chosen color with length equal to the count is the natural, consistent transformation to apply.</example>\n</note5>","<note1>\n<description>Check the output dimensions first: if the output is a single row (or a single column), the transformation reduces the input to a 1D representation. This often means the solver is summarizing the input with one value per row (or per column) rather than producing a full transformed grid.</description>\n<example>Imagine an input that is 6 rows by 4 columns and the output is a single row of 4 cells. That tells you the rule is \"one output cell per input column\" and you should focus on column-level properties rather than trying to reproduce the whole 2D pattern.</example>\n</note1>\n\n<note2>\n<description>Count occurrences of each non-background color per row. Many ARC tasks use the count of a particular color (often the non-background color) as the summary value for that row.</description>\n<example>For a row like [0, X, 0, X, 0] the count of X is 2. If every row in the input has X as the only non-background color, then the row summary is simply that count (2 in this case).</example>\n</note2>\n\n<note3>\n<description>Decide how the input is ordered into rows. If the input has many rows and the output has fewer rows, the ordering can be top-to-bottom; if the output is a single row, the ordering is preserved left-to-right across columns.</description>\n<example>If the input has three rows and the output has three entries, then each output entry likely corresponds to one input row (in the same order). If the output is one row, then each column of the output corresponds to one input column (keeping left-to-right order).</example>\n</note3>\n\n<note4>\n<description>Use the dominant non-background color as the color to report. When only one non-background color appears across the input, that color is the natural choice for the output cells; if multiple colors appear, the examples usually indicate which color is preferred (often the most frequent).</description>\n<example>If the input contains only color Y scattered across rows and no other colors, then each output cell will be Y. If two colors appear but Y is much more frequent, prefer Y as the color to fill the output cells.</example>\n</note4>\n\n<note5>\n<description>Validate your hypothesis by applying it to every training example and checking consistency. If your rule reproduces each training output, apply it to the test input; if not, adjust whether you count per row or per column, or whether you use a different color.</description>\n<example>Try the rule: for each input row, count the chosen color and place that count as an output entry in the same row order. If this matches all examples, the rule is confirmed; otherwise, try counting per column or use the other dominant color and re-check.</example>\n</note5>","<note1>\n<description>Look first for the target color: the output is built from a single color that appears in the input. This color is not the background (usually 0) and is the one the transformation focuses on.</description>\n<example>Imagine a grid with mostly black background and a few red pixels scattered around. The output will be composed only of red; so identify red as the color to use before doing any further steps.</example>\n</note1>\n\n<note2>\n<description>Count occurrences of that color across the whole input. The number of times the chosen color appears is the key numeric quantity that determines the output length.</description>\n<example>If you find the color 8 times in the grid, that count (8) is the number of cells you will place in the output; the exact locations of those pixels do not matter for this count.</example>\n</note2>\n\n<note3>\n<description>Construct the output as a single horizontal row (a 1×N grid) where N equals the count from the previous step. The output is a straight line of that color with no extra background or separators.</description>\n<example>With a count of 6, the output becomes a single row containing six identical colored cells placed side by side, forming a continuous horizontal segment.</example>\n</note3>\n\n<note4>\n<description>Do not include background cells (zeros) or other colors when counting; ignore shapes, clusters, or gaps and treat every occurrence of the target color as contributing to the total.</description>\n<example>If the color appears in isolated single pixels or in a small cluster, simply add all such pixels together. For instance, three scattered single pixels and one cluster of two pixels still give a total of five occurrences.</example>\n</note4>\n\n<note5>\n<description>Be careful about identical colors: if there are multiple colors that look alike, verify which one is the intended color by checking training examples or which color is consistently used in outputs. Also confirm the output orientation is always a single row.</description>\n<example>If two colors both appear in the input, compare example outputs to decide which color to count; then form a single horizontal row whose length equals the chosen color's total count.</example>\n</note5>","<note1>\n<description>Look for the single non-background color that appears in the input. This color is the element being transformed; the background (usually 0) is ignored when deciding the output.</description>\n<example>Imagine a grid of zeros with a handful of red pixels scattered around. The red color is the only one that matters; count how many red pixels there are and treat that count as the key quantity for the next step.</example>\n</note1>\n<note2>\n<description>Count every occurrence of that chosen color across the entire input grid, including pixels that touch each other. The count is a single integer that summarizes the object's presence and is used to construct the output.</description>\n<example>If you find 12 red pixels (even if some are adjacent in a block), record the total 12. That total is the only number you need to carry forward to produce the output.</example>\n</note2>\n<note3>\n<description>Form a 1×N output row where N equals the color count. The output is a horizontal sequence of N cells, not a multi-row or multi-column structure.</description>\n<example>If the count is 8, the output should be a single row with eight cells in a row. The shape is determined solely by the count, not by any spatial pattern in the input.</example>\n</note3>\n<note4>\n<description>Fill every cell of that 1×N row with the same color you identified in step 1. The output is a uniform line of the chosen color, length equal to the count.</description>\n<example>With a chosen color blue and count 5, the output row becomes five blue cells in a row. The repetition is uniform and does not mix other colors.</example>\n</note4>\n<note5>\n<description>Watch for common pitfalls: don’t count the background, don’t split the count into separate rows/columns, and don’t preserve the input’s shape—only the count and the chosen color determine the final 1×N row. Also, if more than one non-background color appears, choose the one that consistently appears across examples (or the one that is the object of transformation).</description>\n<example>If the input contains both red and green pixels but red is the color that repeats in the examples, use red for the output. If two colors appear equally often, re-check which one the examples consistently highlight or which one forms the object being transformed.</example>\n</note5>","<note1>\n<description>Look for the non-background color that appears repeatedly and is not the filler (usually 0). If there is a single dominant color against a uniform background, that color is the likely candidate to drive the transformation.</description>\n<example>Imagine a grid filled with 0s except for a handful of 2s scattered around; the repeated 2s stand out as the meaningful color. Count occurrences and ignore the background to decide which color to focus on.</example>\n</note1>\n\n<note2>\n<description>Count how many pixels of that chosen color exist in the input. The total number of occurrences is a strong candidate for the final output length or repetition count.</description>\n<example>For example, if you find exactly five 7s in the input, treat 5 as the quantity to use in the next step. This count is simple and often matches the output dimension in these tasks.</example>\n</note2>\n\n<note3>\n<description>Consider whether the output is a single-row, uniform line whose length equals the count you found. Many ARC tasks compress spatial patterns into one-dimensional sequences by length.</description>\n<example>If the color count is 8, produce one row of 8 cells; the output is not necessarily a larger pattern but a one-dimensional summary of the color’s presence.</example>\n</note3>\n\n<note4>\n<description>When forming the output row, fill every cell with the chosen color so the output is a uniform stripe of that color. Do not mix colors or introduce other values—keep it simple and consistent.</description>\n<example>With color X and count N, create a row with N cells all set to X. The transformation typically uses the same color repeated across the entire output line.</example>\n</note4>\n\n<note5>\n<description>Be cautious of edge cases: if multiple colors appear, prefer the one with the highest count; if counts tie, prefer the color that forms the largest contiguous region or the one that is most spatially prominent. Always verify your choice against the training examples’ behavior.</description>\n<example>If two colors each appear twice but one forms a compact block while the other is scattered, choose the compact block. Also check whether the examples ever use a different rule for ties or for background pixels.</example>\n</note5>","<note1>\n<description>Look for the single non-background color that is consistently present across all training inputs; that color is the transformation’s focus. The examples use one dominant color repeated many times while the background is uniform (often 0).</description>\n<example>Imagine several 6×6 grids where every grid contains mostly zeros and only blue pixels scattered around; the blue is the only color to count. Noting that one color appears repeatedly across examples tells you which color to track.</example>\n</note1>\n\n<note2>\n<description>Count how many pixels of that chosen color appear in each input grid. The transformation is based on this numeric quantity rather than on the positions or shapes of those pixels.</description>\n<example>For instance, if one input has ten blue pixels and another has seven, record those counts. The same numeric property (how many) will be used in the output, regardless of whether the blue pixels form a line or a scattered pattern.</example>\n</note2>\n\n<note3>\n<description>Use the counted value as the length of the output row: the output is a single row whose number of cells equals that count. This converts a per-pixel count into a linear representation of the same quantity.</description>\n<example>If you counted six green pixels in the input, produce an output row with six cells; if you counted twelve, produce a row with twelve cells. The length is determined solely by the count you found.</example>\n</note3>\n\n<note4>\n<description>Fill every cell of that row with the chosen color so the output is a uniform horizontal stripe. The output’s color and shape are derived from the input’s dominant color and its count.</description>\n<example>Continuing the previous example, if the chosen color is red and the count is four, the output should be a single row containing four red cells in a row. The important point is uniformity by color across the row.</example>\n</note4>\n\n<note5>\n<description>When multiple colors exist, prefer the color that is repeated most often (the dominant color). If counts tie, use a simple tie-breaker such as the color that appears earlier when scanning the grid from top-left; avoid picking the background color (0).</description>\n<example>Suppose two colors each appear five times but red appears earlier in the grid than yellow; choose red. If there is a clear background color (0) that is the most frequent, exclude it and pick the next most frequent color instead.</example>\n</note5>","<note1>\n<description>Look for the single non-background color that appears repeatedly across the input. When one color forms the dominant pattern and the rest is background, that color is the most likely candidate to be used in the output.</description>\n<example>Imagine a grid mostly filled with black but with many red pixels scattered. Counting or visually scanning shows red is the only color besides black, so red is the natural candidate to carry into the output.</example>\n</note1>\n\n<note2>\n<description>Decide whether the transformation is about counts or about positions: does the output show how many times the color appears, or does it use the color’s location (for example, a vertical projection)? Compare the number of output cells to the number of input occurrences to disambiguate.</description>\n<example>If an input has 7 blue pixels and the output is a single row of 7 blue cells, that indicates a count-based operation. If the output’s length equals the number of distinct columns that contain blue, that would indicate a projection-based operation instead.</example>\n</note2>\n\n<note3>\n<description>If the output is a single row, determine how its length was derived from the input. Possible rules include the total number of occurrences of the chosen color, the number of distinct columns that contain that color, or the number of distinct rows that contain it.</description>\n<example>For instance, if blue appears 12 times across the grid, a count rule would produce a row of 12 blue cells; if blue appears in 6 different columns, a column-based rule would produce a row of length 6.</example>\n</note3>\n\n<note4>\n<description>Check whether the output is filled uniformly with the chosen color. If so, the operation is likely to compress or summarize the scattered occurrences into a single run of that color rather than preserving individual shapes or spatial relationships.</description>\n<example>When a scattered pattern of green pixels is transformed into a single horizontal stripe of green, the spatial arrangement is lost and only the color and its quantity remain important.</example>\n</note4>\n\n<note5>\n<description>Use simple consistency checks: confirm the output color matches the dominant non-background color, that the output’s length equals the quantity you inferred, and that the output is a single uniform row. If any check fails, revisit the earlier steps (which color, which quantity, and whether the output should be uniform).</description>\n<example>If your hypothesis predicts an output row of length N made of color C, compare that to the example outputs: if the examples match this pattern, your rule is consistent; if not, try the alternative interpretations (different color, different quantity measure, or different output form).</example>\n</note5>","<note1>\n<description>Scan the input for the color that is not the background (0). If only one non-background color appears, that color is usually the one used to build the output; if several non-background colors appear, the task often reduces to one of them (e.g., the dominant color). This helps you identify the \"source\" color to use.</description>\n<example>Imagine a grid with many 1s and only a few 0s scattered around. The 1s are the only non-background color, so they are the natural candidate to be used when creating the output. Conversely, if you see both 2s and 3s in the input, you will need to decide which one to use by comparing counts or other selection rules.</example>\n</note1>\n\n<note2>\n<description>Count how many pixels of the chosen color exist in the input. The output's width is typically a simple function of that count (commonly the count itself). Recognizing this mapping is the key step before constructing the output row.</description>\n<example>For instance, if you detect 8 pixels of color X in the input, a likely output is a single row of 8 Xs. If the input had 12 pixels of X, expect a row of 12 Xs. The important part is the count, not the positions of those pixels.</example>\n</note2>\n\n<note3>\n<description>Construct the output as a single horizontal row (a 1×N grid) where N equals the count from the previous step and every cell in that row is the chosen color. This reduces a 2D pattern to a 1D repetition.</description>\n<example>Suppose the chosen color is Y and you counted 7 Ys; the output should be a one-row grid with seven Ys placed side by side. The output grid is therefore much simpler in form than the input while preserving the color information.</example>\n</note3>\n\n<note4>\n<description>Ignore the background (zeros) and other colors when deciding which color to use. Background cells are typically not part of the pattern to reproduce and should not be treated as the source color. If multiple non-background colors are present, prefer the color that best fits the examples (usually the most frequent one).</description>\n<example>If the grid contains mostly 0s and a few 4s and a few 5s, count the 4s and 5s and choose the one with the higher count. Do not include the zeros in your count when determining the output length.</example>\n</note4>\n\n<note5>\n<description>Be careful about edge cases: if two colors tie, use a consistent tie-breaker (for example, pick the color with the larger numeric value or the one that appears in the examples). Also, verify that the examples always use the same selection rule so your rule is consistent across cases.</description>\n<example>When color A and color B each occur 6 times, choose the one that matches the example behavior (e.g., the one with the larger numeric value). Avoid assuming a particular color just because it appears in a corner or at the center—rely on counts and the examples' pattern instead.</example>\n</note5>","<note1>\n<description>Spot the active color: many ARC tasks reduce the grid to a single color by first identifying which non-background color is the meaningful object. This is effective when one color consistently appears as the target across examples and the background is uniform.</description>\n<example>Imagine a grid with mostly zeros and a few isolated red pixels; the red pixels are the object to track. Counting or visually noting that red is the only non-background color tells you what to extract.</example>\n</note1>\n\n<note2>\n<description>Count occurrences: the core operation is often the total number of object pixels (not area, not bounding-box size). A simple count of the target color across the whole grid gives a single scalar that drives the transformation.</description>\n<example>If there are five green pixels scattered in different rows and columns, the count is 5. That single number is the key value used to produce the output rather than the arrangement of those pixels.</example>\n</note2>\n\n<note3>\n<description>Convert the count to a horizontal stripe: the output is frequently a single row whose length equals the count and whose cells are filled with the target color. In other words, the count becomes the run length of that color in a horizontal line.</description>\n<example>With a count of 7, produce a single row of seven identical colored cells. This keeps the output a simple, one-dimensional representation of the original object count.</example>\n</note3>\n\n<note4>\n<description>Preserve color identity: the output uses the same color that was counted in the input, not a new or background color. The transformation is a recoloring of the count into the original object color.</description>\n<example>If the object color is blue and the count is 9, the output row should be nine blue cells. The color value is preserved from the input to the output.</example>\n</note4>\n\n<note5>\n<description>Handle edge cases by checking examples: if multiple colors exist, the rule usually picks the color that is consistently the target (often the only non-background color). If the output row would be empty, verify whether the task expects a zero-length row or a different fallback.</description>\n<example>If two colors appear but one is always the object in the training pairs, use that one. If you find no object pixels, look back at the examples to see whether an empty row or another convention is implied.</example>\n</note5>","<note1>\n<description>Look for the dominant non-background color and count its occurrences across the whole input. This is usually the color that the output is constructed from and gives you the target quantity to fill.</description>\n<example>Imagine a 7×7 grid with 0 as background and a single non-zero color A appearing in several scattered cells. Count how many A pixels there are (for instance 10). That count becomes the key number you will use to build the output.</example>\n</note1>\n\n<note2>\n<description>Check the output's dimensions: if the output is a single row (or a single column) whose length equals the count of that color, the transformation is a horizontal (or vertical) repetition of the chosen color. This tells you how many times to place the color in a straight line.</description>\n<example>If the output is a 1×N row and you counted N occurrences of color A, then the rule is \"make a single row containing N copies of A\". You do not need to preserve the original layout — only the quantity matters for the output shape.</example>\n</note2>\n\n<note3>\n<description>Ignore the background color when deciding the output content. The examples usually use one non-background color as the filler and do not include the background in the count or in the output.</description>\n<example>For example, if a grid contains zeros everywhere except a few B pixels, treat zeros as background and count only B; the output should be filled with B, not with zeros.</example>\n</note3>\n\n<note4>\n<description>When there are multiple non-background colors, pick the one that is consistently used across examples and whose occurrences best match the output length. If two colors are present, prefer the color whose total count equals the output length in the examples.</description>\n<example>Suppose a grid has colors X and Y and the training outputs are uniform rows whose length equals the number of X pixels. Then use X as the filler and repeat it that many times to form the output row.</example>\n</note4>\n\n<note5>\n<description>Finally, produce the output as a single row of the chosen color repeated exactly as many times as the color's count; do not include other colors or background in that row. This yields a simple, repeatable transformation from the input to the output.</description>\n<example>If you decide on color Z and its count is M, create a 1×M row filled entirely with Z. The final grid should be uniform along that single row and have length M.</example>\n</note5>","<note1>\n<description>First locate the color that is not the background and count how many times it appears across the entire grid. This single global count is the primary quantity the transformation uses.</description>\n<example>Imagine a grid with many black cells and a handful of red cells scattered around. If you count every red cell you get a number (for example 11). That number is what you will use to build the output.</example>\n</note1>\n\n<note2>\n<description>Ignore the original layout and shape: the transformation does not preserve where those colored pixels were. Instead it treats the color as a single value to be repeated.</description>\n<example>If red pixels form a diagonal in the input, the output will not show that diagonal shape — it will still be a uniform line of red. The spatial pattern is discarded and replaced by the count.</example>\n</note2>\n\n<note3>\n<description>Use the global count as the length of a single-row output. The output is a horizontal stripe whose width equals the number of colored pixels.</description>\n<example>If your count is 7, the output should be one row that is 7 cells long. If your count is 15, the output should be one row that is 15 cells long.</example>\n</note3>\n\n<note4>\n<description>Fill every cell of that single-row stripe with the non-background color you counted. There are no other colors or empty cells in the output.</description>\n<example>With a count of 9 and the chosen color blue, the output row would be nine blue cells in a row, not a mixture of colors or gaps.</example>\n</note4>\n\n<note5>\n<description>When multiple colors appear, choose the color that is clearly not the background (usually the one that appears in the examples or the one that forms the repeated object). Verify your choice by ensuring the same color is used in every training output.</description>\n<example>If two colors are present but one is mostly background while the other forms the repeated pattern, pick the pattern color. If two colors are equally frequent, re-check the examples to see which color is consistently the target.</example>\n</note5>","<note1>\n<description>Start by identifying the non-background color(s) that are being transformed. In many ARC tasks one color stands out as the object of interest and is the only color that appears in the output; treat that color as the primary candidate to track.</description>\n<example>Imagine a grid where zeros are background and only red pixels form shapes. If every training output contains only red, focus on red as the target color rather than trying to infer a new color from the background.</example>\n</note1>\n\n<note2>\n<description>Count the occurrences of the chosen color across the whole input grid. The transformation often depends on a simple global statistic, such as the total number of pixels of that color.</description>\n<example>For example, if there are 12 red pixels scattered in the input and the outputs are all filled with red, the number 12 is likely the key quantity the task is using to determine the output.</example>\n</note2>\n\n<note3>\n<description>Check whether the output is a one-dimensional representation of that count: the examples may be producing a single row whose length equals the counted quantity and whose entries are the chosen color. This is a common pattern when the goal is to \"encode\" a number as a uniform line.</description>\n<example>If the counted number is 7, a plausible output is a single row of seven identical cells filled with the target color, rather than a 2D arrangement of the same color.</example>\n</note3>\n\n<note4>\n<description>Verify that the output ignores spatial arrangement and background: the transformation typically preserves the target color's numeric count but does not reproduce the shapes or positions that originally formed it. Focus on the numeric summary, not the geometry.</description>\n<example>Even if the red pixels in the input form a complex cluster, the output should reflect the total count in a simple linear form (e.g., a row of red cells) rather than attempting to recreate that cluster.</example>\n</note4>\n\n<note5>\n<description>Confirm uniqueness and avoid false candidates: if multiple non-background colors exist, select the one whose count matches the outputs' behavior. If two colors have similar counts, prefer the color that is consistently used across examples or that forms the clear object in the inputs.</description>\n<example>If blue and yellow both appear but only blue's count matches the outputs, use blue as the target; if both counts match, re-check which color the examples consistently encode before choosing.</example>\n</note5>","<note1>\n<description>Look for the single non-background color that appears repeatedly across the input; the transformation usually uses that color as the primary element to reproduce. This is effective because the examples consistently compress or repeat one color while ignoring background noise.</description>\n<example>Imagine a grid where every colored cell is color A and all other cells are background. The output will be built from A rather than from any other colors present, so first identify which color is dominant and repeated.</example>\n</note1>\n\n<note2>\n<description>Count how many times that chosen color appears in the input; this count is the key numeric parameter for the output. The examples use the exact number of occurrences as the quantity to repeat, so a simple tally is the right starting point.</description>\n<example>For example, if color A appears 7 times in the input, that count (7) becomes the number of elements you will place in the output sequence, regardless of their original positions.</example>\n</note2>\n\n<note3>\n<description>Decide the output dimensions by mapping the input grid to a single row: the output's width is determined by the input's height (or another fixed rule consistent across examples). In these tasks the output is a horizontal row whose length is derived from the input's vertical size.</description>\n<example>If the input has 14 rows, plan to produce a single row whose width equals that 14; the actual number of colored cells is then used to fill that row, not to change its width.</example>\n</note3>\n\n<note4>\n<description>Construct the output as a contiguous horizontal sequence of the chosen color, using the counted occurrences as the sequence length. The examples compress the scattered pixels into a single run of that color, so order and gaps in the input do not matter.</description>\n<example>If you counted 9 occurrences of color A, produce a row of 9 A cells placed consecutively; the result is a uniform stripe of that color whose length equals the count.</example>\n</note4>\n\n<note5>\n<description>Watch for common pitfalls: ignore background zeros and any other colors when counting, and do not preserve original coordinates or shapes. The rule is purely a count-based repetition into a single-row output, so focus on the tally and the mapping to row width.</description>\n<example>If the input contains many zeros and a few pixels of color B, only the occurrences of the dominant color A should be counted; the final output is a single row of A cells whose length equals that count, not a reconstruction of the input pattern.</example>\n</note5>"],"string":"[\n \"<note1>\\n<description>Look for a single non-background color that consistently appears across the examples and is the only color that changes in the outputs. When one color dominates the input and the output is uniform, that color is usually the source of the transformation.</description>\\n<example>Imagine a grid filled with zeros except for a few scattered blue pixels; the outputs in similar tasks are all blue. That pattern tells you to focus on the blue pixels rather than on background zeros or other colors.</example>\\n</note1>\\n\\n<note2>\\n<description>Count occurrences of that dominant color in the input: the number of occurrences is often the key parameter for the output. This count is typically the number of distinct pixels, not the number of connected components or other aggregates.</description>\\n<example>If you find 12 scattered red pixels in the input, record 12 as the quantity to use; many problems then use that exact count to determine how many times the color should appear in the result.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide whether the output is a single horizontal line (one row) filled with the chosen color. Many ARC tasks with a uniform output simply produce a single row whose length encodes the chosen quantity.</description>\\n<example>For instance, if the chosen color is green and the count is 7, a plausible output is a single row of 7 green cells; the shape is not a larger block but a linear row.</example>\\n</note3>\\n\\n<note4>\\n<description>Use the input’s width (number of columns) as the target width for that single row. The transformation often places the colored cells in a contiguous block that spans the full width of the input, rather than producing multiple rows or smaller blocks.</description>\\n<example>On a 10-column input, the output row is usually 10 cells long; the count you extracted earlier becomes the color count placed across that full-width row.</example>\\n</note4>\\n\\n<note5>\\n<description>Watch for common pitfalls: do not confuse background zeros with the target color, do not sum connected components or unique positions, and do not add or remove the background color. Always verify the chosen color is the only non-background color that is preserved across examples.</description>\\n<example>If a grid has both black and a few yellow pixels but the outputs are all yellow, ignore black and count only yellow pixels; if outputs are uniform and match the yellow count, you have the right rule.</example>\\n</note5>\",\n \"<note1>\\n<description>Look first for a single non-background color that appears repeatedly across the input. When one color dominates and the background is uniform, that color is a strong candidate for the transformation's output color.</description>\\n<example>Imagine a grid filled with black except for a few scattered red pixels. If red is the only color that appears many times and is not the background, it is natural to suspect red will be the color used in the output.</example>\\n</note1>\\n<note2>\\n<description>Count how many pixels of that candidate color exist in the input. The total count often becomes the key quantity that determines the output's length or number of repetitions.</description>\\n<example>For example, if you find exactly 12 red pixels scattered in the input, recording 12 is a useful numeric summary that can be used to build the output.</example>\\n</note2>\\n<note3>\\n<description>Check the output examples' shape and whether it is uniform. If every example output is a single row and every cell in that row is the same color, the transformation likely produces a uniform row whose length encodes the input.</description>\\n<example>Suppose each training output is a one-row grid with no mixed colors. That pattern suggests the output is a single-color row rather than a transformed image of the original shapes.</example>\\n</note3>\\n<note4>\\n<description>Relate the counted quantity to the output's length: the count frequently equals the number of output cells. In other words, the numeric summary (often the count of the dominant color) may be used as the output width.</description>\\n<example>If the input contains 15 green pixels and the examples show outputs whose length equals that count, then constructing an output row with that many green cells is a natural next step.</example>\\n</note4>\\n<note5>\\n<description>Use a simple verification: pick a representative color from the input (preferably the most frequent non-background color), count its pixels, and then produce a single row whose length equals that count and whose color matches the chosen pixel. This heuristic often matches ARC tasks that summarize color counts into a uniform row.</description>\\n<example>As a quick test, count the dominant color in a sample input, form a one-row grid with that many cells filled with the color, and check whether the structure matches the training outputs' pattern before finalizing the answer.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the dominant non-background color: the transformation uses the single color that appears most often in the input. This is effective because many ARC tasks reduce a scattered pattern to the color that carries the bulk of the information.</description>\\n<example>Imagine a grid where most colored pixels are red and the rest are background (or zero). Counting occurrences shows red is the dominant color, so the next step is to use red as the candidate for the output.</example>\\n</note1>\\n\\n<note2>\\n<description>Confirm uniqueness of the dominant color: the examples imply there is exactly one color that is chosen (not a tie). If two colors had equal counts you would need additional rules, but here the pattern selects the single most frequent color.</description>\\n<example>For instance, if blue appears 12 times and green 3 times in a grid, blue is unambiguously the color to use; if counts were tied, you would need a different tie-breaker (not required here).</example>\\n</note2>\\n\\n<note3>\\n<description>Form the output by repeating that chosen color across a single row: the output is a horizontal sequence whose length equals the number of columns in the original grid. This preserves the grid's horizontal dimension while encoding the dominant color.</description>\\n<example>For a 4-column input and a chosen color X, the output would be a single row of length 4 filled with X (e.g., [X X X X]).</example>\\n</note3>\\n\\n<note4>\\n<description>Ignore background and internal structure when deciding the color: do not base the choice on shape, adjacency, or clusters — only on raw frequency. The examples do not preserve spatial layout, only the dominant color's count.</description>\\n<example>Even if the chosen color forms several disconnected blobs or isolated pixels, the rule still picks it by total count, not by the number of connected components or the shape of the blobs.</example>\\n</note4>\\n\\n<note5>\\n<description>Handle edge cases and pitfalls: if the grid is already a single row, the output should still be a single-row fill; if the dominant color is already the background, re-check whether the task actually uses the background color or if you need to select a non-background color. Always validate your choice against the training examples.</description>\\n<example>If the input is a single-row grid with many colored pixels, producing a single-row output filled with the dominant color is consistent; if two colors tie, apply the same tie-break rule seen in examples (or check whether the task expects a different behavior).</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the single non-background color that consistently appears in the examples. If one color is the only one that differs from the background, it is usually the element the task is about.</description>\\n<example>Imagine a grid mostly filled with zeros but with several scattered blue pixels; the blue pixels are the only non-background elements. Focusing on blue (not the zeros) narrows the problem to a single color to analyze further.</example>\\n</note1>\\n\\n<note2>\\n<description>Count how many times that color appears across the whole input grid. The transformation often depends on the total number of occurrences rather than their spatial arrangement.</description>\\n<example>For instance, if you find exactly five red pixels in the input, record the count 5. That numeric summary is the key quantity to use when constructing the output.</example>\\n</note2>\\n\\n<note3>\\n<description>Check whether the output is a one-dimensional representation: many ARC tasks convert a 2D pattern into a 1×N row where each cell encodes a property of the input (commonly the count). Determine the output's width by comparing examples.</description>\\n<example>If every training output is a single row, then the output shape is likely 1×(some width); the width is the property you will encode (for example, the number of target pixels).</example>\\n</note3>\\n\\n<note4>\\n<description>Decide how the numeric property (the count) is encoded into the output row: typically each output cell is set to the target color, so the row becomes a uniform stripe whose length equals the count. This preserves the color identity while showing the quantity.</description>\\n<example>For example, if the target color is green and the count is 6, the output row would be six green cells in a row: [green, green, green, green, green, green].</example>\\n</note4>\\n\\n<note5>\\n<description>Be mindful of common pitfalls: confirm you are counting the correct color (ignore background zeros), verify the output width from examples, and ensure the output is a single row. If the count equals the number of columns or rows, the uniform row will visually match those dimensions.</description>\\n<example>Before finalizing, double-check that no other color is the focus and that the training outputs are indeed uniform single rows. If they are, then a uniform row of the chosen color with length equal to the count is the natural, consistent transformation to apply.</example>\\n</note5>\",\n \"<note1>\\n<description>Check the output dimensions first: if the output is a single row (or a single column), the transformation reduces the input to a 1D representation. This often means the solver is summarizing the input with one value per row (or per column) rather than producing a full transformed grid.</description>\\n<example>Imagine an input that is 6 rows by 4 columns and the output is a single row of 4 cells. That tells you the rule is \\\"one output cell per input column\\\" and you should focus on column-level properties rather than trying to reproduce the whole 2D pattern.</example>\\n</note1>\\n\\n<note2>\\n<description>Count occurrences of each non-background color per row. Many ARC tasks use the count of a particular color (often the non-background color) as the summary value for that row.</description>\\n<example>For a row like [0, X, 0, X, 0] the count of X is 2. If every row in the input has X as the only non-background color, then the row summary is simply that count (2 in this case).</example>\\n</note2>\\n\\n<note3>\\n<description>Decide how the input is ordered into rows. If the input has many rows and the output has fewer rows, the ordering can be top-to-bottom; if the output is a single row, the ordering is preserved left-to-right across columns.</description>\\n<example>If the input has three rows and the output has three entries, then each output entry likely corresponds to one input row (in the same order). If the output is one row, then each column of the output corresponds to one input column (keeping left-to-right order).</example>\\n</note3>\\n\\n<note4>\\n<description>Use the dominant non-background color as the color to report. When only one non-background color appears across the input, that color is the natural choice for the output cells; if multiple colors appear, the examples usually indicate which color is preferred (often the most frequent).</description>\\n<example>If the input contains only color Y scattered across rows and no other colors, then each output cell will be Y. If two colors appear but Y is much more frequent, prefer Y as the color to fill the output cells.</example>\\n</note4>\\n\\n<note5>\\n<description>Validate your hypothesis by applying it to every training example and checking consistency. If your rule reproduces each training output, apply it to the test input; if not, adjust whether you count per row or per column, or whether you use a different color.</description>\\n<example>Try the rule: for each input row, count the chosen color and place that count as an output entry in the same row order. If this matches all examples, the rule is confirmed; otherwise, try counting per column or use the other dominant color and re-check.</example>\\n</note5>\",\n \"<note1>\\n<description>Look first for the target color: the output is built from a single color that appears in the input. This color is not the background (usually 0) and is the one the transformation focuses on.</description>\\n<example>Imagine a grid with mostly black background and a few red pixels scattered around. The output will be composed only of red; so identify red as the color to use before doing any further steps.</example>\\n</note1>\\n\\n<note2>\\n<description>Count occurrences of that color across the whole input. The number of times the chosen color appears is the key numeric quantity that determines the output length.</description>\\n<example>If you find the color 8 times in the grid, that count (8) is the number of cells you will place in the output; the exact locations of those pixels do not matter for this count.</example>\\n</note2>\\n\\n<note3>\\n<description>Construct the output as a single horizontal row (a 1×N grid) where N equals the count from the previous step. The output is a straight line of that color with no extra background or separators.</description>\\n<example>With a count of 6, the output becomes a single row containing six identical colored cells placed side by side, forming a continuous horizontal segment.</example>\\n</note3>\\n\\n<note4>\\n<description>Do not include background cells (zeros) or other colors when counting; ignore shapes, clusters, or gaps and treat every occurrence of the target color as contributing to the total.</description>\\n<example>If the color appears in isolated single pixels or in a small cluster, simply add all such pixels together. For instance, three scattered single pixels and one cluster of two pixels still give a total of five occurrences.</example>\\n</note4>\\n\\n<note5>\\n<description>Be careful about identical colors: if there are multiple colors that look alike, verify which one is the intended color by checking training examples or which color is consistently used in outputs. Also confirm the output orientation is always a single row.</description>\\n<example>If two colors both appear in the input, compare example outputs to decide which color to count; then form a single horizontal row whose length equals the chosen color's total count.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the single non-background color that appears in the input. This color is the element being transformed; the background (usually 0) is ignored when deciding the output.</description>\\n<example>Imagine a grid of zeros with a handful of red pixels scattered around. The red color is the only one that matters; count how many red pixels there are and treat that count as the key quantity for the next step.</example>\\n</note1>\\n<note2>\\n<description>Count every occurrence of that chosen color across the entire input grid, including pixels that touch each other. The count is a single integer that summarizes the object's presence and is used to construct the output.</description>\\n<example>If you find 12 red pixels (even if some are adjacent in a block), record the total 12. That total is the only number you need to carry forward to produce the output.</example>\\n</note2>\\n<note3>\\n<description>Form a 1×N output row where N equals the color count. The output is a horizontal sequence of N cells, not a multi-row or multi-column structure.</description>\\n<example>If the count is 8, the output should be a single row with eight cells in a row. The shape is determined solely by the count, not by any spatial pattern in the input.</example>\\n</note3>\\n<note4>\\n<description>Fill every cell of that 1×N row with the same color you identified in step 1. The output is a uniform line of the chosen color, length equal to the count.</description>\\n<example>With a chosen color blue and count 5, the output row becomes five blue cells in a row. The repetition is uniform and does not mix other colors.</example>\\n</note4>\\n<note5>\\n<description>Watch for common pitfalls: don’t count the background, don’t split the count into separate rows/columns, and don’t preserve the input’s shape—only the count and the chosen color determine the final 1×N row. Also, if more than one non-background color appears, choose the one that consistently appears across examples (or the one that is the object of transformation).</description>\\n<example>If the input contains both red and green pixels but red is the color that repeats in the examples, use red for the output. If two colors appear equally often, re-check which one the examples consistently highlight or which one forms the object being transformed.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the non-background color that appears repeatedly and is not the filler (usually 0). If there is a single dominant color against a uniform background, that color is the likely candidate to drive the transformation.</description>\\n<example>Imagine a grid filled with 0s except for a handful of 2s scattered around; the repeated 2s stand out as the meaningful color. Count occurrences and ignore the background to decide which color to focus on.</example>\\n</note1>\\n\\n<note2>\\n<description>Count how many pixels of that chosen color exist in the input. The total number of occurrences is a strong candidate for the final output length or repetition count.</description>\\n<example>For example, if you find exactly five 7s in the input, treat 5 as the quantity to use in the next step. This count is simple and often matches the output dimension in these tasks.</example>\\n</note2>\\n\\n<note3>\\n<description>Consider whether the output is a single-row, uniform line whose length equals the count you found. Many ARC tasks compress spatial patterns into one-dimensional sequences by length.</description>\\n<example>If the color count is 8, produce one row of 8 cells; the output is not necessarily a larger pattern but a one-dimensional summary of the color’s presence.</example>\\n</note3>\\n\\n<note4>\\n<description>When forming the output row, fill every cell with the chosen color so the output is a uniform stripe of that color. Do not mix colors or introduce other values—keep it simple and consistent.</description>\\n<example>With color X and count N, create a row with N cells all set to X. The transformation typically uses the same color repeated across the entire output line.</example>\\n</note4>\\n\\n<note5>\\n<description>Be cautious of edge cases: if multiple colors appear, prefer the one with the highest count; if counts tie, prefer the color that forms the largest contiguous region or the one that is most spatially prominent. Always verify your choice against the training examples’ behavior.</description>\\n<example>If two colors each appear twice but one forms a compact block while the other is scattered, choose the compact block. Also check whether the examples ever use a different rule for ties or for background pixels.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the single non-background color that is consistently present across all training inputs; that color is the transformation’s focus. The examples use one dominant color repeated many times while the background is uniform (often 0).</description>\\n<example>Imagine several 6×6 grids where every grid contains mostly zeros and only blue pixels scattered around; the blue is the only color to count. Noting that one color appears repeatedly across examples tells you which color to track.</example>\\n</note1>\\n\\n<note2>\\n<description>Count how many pixels of that chosen color appear in each input grid. The transformation is based on this numeric quantity rather than on the positions or shapes of those pixels.</description>\\n<example>For instance, if one input has ten blue pixels and another has seven, record those counts. The same numeric property (how many) will be used in the output, regardless of whether the blue pixels form a line or a scattered pattern.</example>\\n</note2>\\n\\n<note3>\\n<description>Use the counted value as the length of the output row: the output is a single row whose number of cells equals that count. This converts a per-pixel count into a linear representation of the same quantity.</description>\\n<example>If you counted six green pixels in the input, produce an output row with six cells; if you counted twelve, produce a row with twelve cells. The length is determined solely by the count you found.</example>\\n</note3>\\n\\n<note4>\\n<description>Fill every cell of that row with the chosen color so the output is a uniform horizontal stripe. The output’s color and shape are derived from the input’s dominant color and its count.</description>\\n<example>Continuing the previous example, if the chosen color is red and the count is four, the output should be a single row containing four red cells in a row. The important point is uniformity by color across the row.</example>\\n</note4>\\n\\n<note5>\\n<description>When multiple colors exist, prefer the color that is repeated most often (the dominant color). If counts tie, use a simple tie-breaker such as the color that appears earlier when scanning the grid from top-left; avoid picking the background color (0).</description>\\n<example>Suppose two colors each appear five times but red appears earlier in the grid than yellow; choose red. If there is a clear background color (0) that is the most frequent, exclude it and pick the next most frequent color instead.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the single non-background color that appears repeatedly across the input. When one color forms the dominant pattern and the rest is background, that color is the most likely candidate to be used in the output.</description>\\n<example>Imagine a grid mostly filled with black but with many red pixels scattered. Counting or visually scanning shows red is the only color besides black, so red is the natural candidate to carry into the output.</example>\\n</note1>\\n\\n<note2>\\n<description>Decide whether the transformation is about counts or about positions: does the output show how many times the color appears, or does it use the color’s location (for example, a vertical projection)? Compare the number of output cells to the number of input occurrences to disambiguate.</description>\\n<example>If an input has 7 blue pixels and the output is a single row of 7 blue cells, that indicates a count-based operation. If the output’s length equals the number of distinct columns that contain blue, that would indicate a projection-based operation instead.</example>\\n</note2>\\n\\n<note3>\\n<description>If the output is a single row, determine how its length was derived from the input. Possible rules include the total number of occurrences of the chosen color, the number of distinct columns that contain that color, or the number of distinct rows that contain it.</description>\\n<example>For instance, if blue appears 12 times across the grid, a count rule would produce a row of 12 blue cells; if blue appears in 6 different columns, a column-based rule would produce a row of length 6.</example>\\n</note3>\\n\\n<note4>\\n<description>Check whether the output is filled uniformly with the chosen color. If so, the operation is likely to compress or summarize the scattered occurrences into a single run of that color rather than preserving individual shapes or spatial relationships.</description>\\n<example>When a scattered pattern of green pixels is transformed into a single horizontal stripe of green, the spatial arrangement is lost and only the color and its quantity remain important.</example>\\n</note4>\\n\\n<note5>\\n<description>Use simple consistency checks: confirm the output color matches the dominant non-background color, that the output’s length equals the quantity you inferred, and that the output is a single uniform row. If any check fails, revisit the earlier steps (which color, which quantity, and whether the output should be uniform).</description>\\n<example>If your hypothesis predicts an output row of length N made of color C, compare that to the example outputs: if the examples match this pattern, your rule is consistent; if not, try the alternative interpretations (different color, different quantity measure, or different output form).</example>\\n</note5>\",\n \"<note1>\\n<description>Scan the input for the color that is not the background (0). If only one non-background color appears, that color is usually the one used to build the output; if several non-background colors appear, the task often reduces to one of them (e.g., the dominant color). This helps you identify the \\\"source\\\" color to use.</description>\\n<example>Imagine a grid with many 1s and only a few 0s scattered around. The 1s are the only non-background color, so they are the natural candidate to be used when creating the output. Conversely, if you see both 2s and 3s in the input, you will need to decide which one to use by comparing counts or other selection rules.</example>\\n</note1>\\n\\n<note2>\\n<description>Count how many pixels of the chosen color exist in the input. The output's width is typically a simple function of that count (commonly the count itself). Recognizing this mapping is the key step before constructing the output row.</description>\\n<example>For instance, if you detect 8 pixels of color X in the input, a likely output is a single row of 8 Xs. If the input had 12 pixels of X, expect a row of 12 Xs. The important part is the count, not the positions of those pixels.</example>\\n</note2>\\n\\n<note3>\\n<description>Construct the output as a single horizontal row (a 1×N grid) where N equals the count from the previous step and every cell in that row is the chosen color. This reduces a 2D pattern to a 1D repetition.</description>\\n<example>Suppose the chosen color is Y and you counted 7 Ys; the output should be a one-row grid with seven Ys placed side by side. The output grid is therefore much simpler in form than the input while preserving the color information.</example>\\n</note3>\\n\\n<note4>\\n<description>Ignore the background (zeros) and other colors when deciding which color to use. Background cells are typically not part of the pattern to reproduce and should not be treated as the source color. If multiple non-background colors are present, prefer the color that best fits the examples (usually the most frequent one).</description>\\n<example>If the grid contains mostly 0s and a few 4s and a few 5s, count the 4s and 5s and choose the one with the higher count. Do not include the zeros in your count when determining the output length.</example>\\n</note4>\\n\\n<note5>\\n<description>Be careful about edge cases: if two colors tie, use a consistent tie-breaker (for example, pick the color with the larger numeric value or the one that appears in the examples). Also, verify that the examples always use the same selection rule so your rule is consistent across cases.</description>\\n<example>When color A and color B each occur 6 times, choose the one that matches the example behavior (e.g., the one with the larger numeric value). Avoid assuming a particular color just because it appears in a corner or at the center—rely on counts and the examples' pattern instead.</example>\\n</note5>\",\n \"<note1>\\n<description>Spot the active color: many ARC tasks reduce the grid to a single color by first identifying which non-background color is the meaningful object. This is effective when one color consistently appears as the target across examples and the background is uniform.</description>\\n<example>Imagine a grid with mostly zeros and a few isolated red pixels; the red pixels are the object to track. Counting or visually noting that red is the only non-background color tells you what to extract.</example>\\n</note1>\\n\\n<note2>\\n<description>Count occurrences: the core operation is often the total number of object pixels (not area, not bounding-box size). A simple count of the target color across the whole grid gives a single scalar that drives the transformation.</description>\\n<example>If there are five green pixels scattered in different rows and columns, the count is 5. That single number is the key value used to produce the output rather than the arrangement of those pixels.</example>\\n</note2>\\n\\n<note3>\\n<description>Convert the count to a horizontal stripe: the output is frequently a single row whose length equals the count and whose cells are filled with the target color. In other words, the count becomes the run length of that color in a horizontal line.</description>\\n<example>With a count of 7, produce a single row of seven identical colored cells. This keeps the output a simple, one-dimensional representation of the original object count.</example>\\n</note3>\\n\\n<note4>\\n<description>Preserve color identity: the output uses the same color that was counted in the input, not a new or background color. The transformation is a recoloring of the count into the original object color.</description>\\n<example>If the object color is blue and the count is 9, the output row should be nine blue cells. The color value is preserved from the input to the output.</example>\\n</note4>\\n\\n<note5>\\n<description>Handle edge cases by checking examples: if multiple colors exist, the rule usually picks the color that is consistently the target (often the only non-background color). If the output row would be empty, verify whether the task expects a zero-length row or a different fallback.</description>\\n<example>If two colors appear but one is always the object in the training pairs, use that one. If you find no object pixels, look back at the examples to see whether an empty row or another convention is implied.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the dominant non-background color and count its occurrences across the whole input. This is usually the color that the output is constructed from and gives you the target quantity to fill.</description>\\n<example>Imagine a 7×7 grid with 0 as background and a single non-zero color A appearing in several scattered cells. Count how many A pixels there are (for instance 10). That count becomes the key number you will use to build the output.</example>\\n</note1>\\n\\n<note2>\\n<description>Check the output's dimensions: if the output is a single row (or a single column) whose length equals the count of that color, the transformation is a horizontal (or vertical) repetition of the chosen color. This tells you how many times to place the color in a straight line.</description>\\n<example>If the output is a 1×N row and you counted N occurrences of color A, then the rule is \\\"make a single row containing N copies of A\\\". You do not need to preserve the original layout — only the quantity matters for the output shape.</example>\\n</note2>\\n\\n<note3>\\n<description>Ignore the background color when deciding the output content. The examples usually use one non-background color as the filler and do not include the background in the count or in the output.</description>\\n<example>For example, if a grid contains zeros everywhere except a few B pixels, treat zeros as background and count only B; the output should be filled with B, not with zeros.</example>\\n</note3>\\n\\n<note4>\\n<description>When there are multiple non-background colors, pick the one that is consistently used across examples and whose occurrences best match the output length. If two colors are present, prefer the color whose total count equals the output length in the examples.</description>\\n<example>Suppose a grid has colors X and Y and the training outputs are uniform rows whose length equals the number of X pixels. Then use X as the filler and repeat it that many times to form the output row.</example>\\n</note4>\\n\\n<note5>\\n<description>Finally, produce the output as a single row of the chosen color repeated exactly as many times as the color's count; do not include other colors or background in that row. This yields a simple, repeatable transformation from the input to the output.</description>\\n<example>If you decide on color Z and its count is M, create a 1×M row filled entirely with Z. The final grid should be uniform along that single row and have length M.</example>\\n</note5>\",\n \"<note1>\\n<description>First locate the color that is not the background and count how many times it appears across the entire grid. This single global count is the primary quantity the transformation uses.</description>\\n<example>Imagine a grid with many black cells and a handful of red cells scattered around. If you count every red cell you get a number (for example 11). That number is what you will use to build the output.</example>\\n</note1>\\n\\n<note2>\\n<description>Ignore the original layout and shape: the transformation does not preserve where those colored pixels were. Instead it treats the color as a single value to be repeated.</description>\\n<example>If red pixels form a diagonal in the input, the output will not show that diagonal shape — it will still be a uniform line of red. The spatial pattern is discarded and replaced by the count.</example>\\n</note2>\\n\\n<note3>\\n<description>Use the global count as the length of a single-row output. The output is a horizontal stripe whose width equals the number of colored pixels.</description>\\n<example>If your count is 7, the output should be one row that is 7 cells long. If your count is 15, the output should be one row that is 15 cells long.</example>\\n</note3>\\n\\n<note4>\\n<description>Fill every cell of that single-row stripe with the non-background color you counted. There are no other colors or empty cells in the output.</description>\\n<example>With a count of 9 and the chosen color blue, the output row would be nine blue cells in a row, not a mixture of colors or gaps.</example>\\n</note4>\\n\\n<note5>\\n<description>When multiple colors appear, choose the color that is clearly not the background (usually the one that appears in the examples or the one that forms the repeated object). Verify your choice by ensuring the same color is used in every training output.</description>\\n<example>If two colors are present but one is mostly background while the other forms the repeated pattern, pick the pattern color. If two colors are equally frequent, re-check the examples to see which color is consistently the target.</example>\\n</note5>\",\n \"<note1>\\n<description>Start by identifying the non-background color(s) that are being transformed. In many ARC tasks one color stands out as the object of interest and is the only color that appears in the output; treat that color as the primary candidate to track.</description>\\n<example>Imagine a grid where zeros are background and only red pixels form shapes. If every training output contains only red, focus on red as the target color rather than trying to infer a new color from the background.</example>\\n</note1>\\n\\n<note2>\\n<description>Count the occurrences of the chosen color across the whole input grid. The transformation often depends on a simple global statistic, such as the total number of pixels of that color.</description>\\n<example>For example, if there are 12 red pixels scattered in the input and the outputs are all filled with red, the number 12 is likely the key quantity the task is using to determine the output.</example>\\n</note2>\\n\\n<note3>\\n<description>Check whether the output is a one-dimensional representation of that count: the examples may be producing a single row whose length equals the counted quantity and whose entries are the chosen color. This is a common pattern when the goal is to \\\"encode\\\" a number as a uniform line.</description>\\n<example>If the counted number is 7, a plausible output is a single row of seven identical cells filled with the target color, rather than a 2D arrangement of the same color.</example>\\n</note3>\\n\\n<note4>\\n<description>Verify that the output ignores spatial arrangement and background: the transformation typically preserves the target color's numeric count but does not reproduce the shapes or positions that originally formed it. Focus on the numeric summary, not the geometry.</description>\\n<example>Even if the red pixels in the input form a complex cluster, the output should reflect the total count in a simple linear form (e.g., a row of red cells) rather than attempting to recreate that cluster.</example>\\n</note4>\\n\\n<note5>\\n<description>Confirm uniqueness and avoid false candidates: if multiple non-background colors exist, select the one whose count matches the outputs' behavior. If two colors have similar counts, prefer the color that is consistently used across examples or that forms the clear object in the inputs.</description>\\n<example>If blue and yellow both appear but only blue's count matches the outputs, use blue as the target; if both counts match, re-check which color the examples consistently encode before choosing.</example>\\n</note5>\",\n \"<note1>\\n<description>Look for the single non-background color that appears repeatedly across the input; the transformation usually uses that color as the primary element to reproduce. This is effective because the examples consistently compress or repeat one color while ignoring background noise.</description>\\n<example>Imagine a grid where every colored cell is color A and all other cells are background. The output will be built from A rather than from any other colors present, so first identify which color is dominant and repeated.</example>\\n</note1>\\n\\n<note2>\\n<description>Count how many times that chosen color appears in the input; this count is the key numeric parameter for the output. The examples use the exact number of occurrences as the quantity to repeat, so a simple tally is the right starting point.</description>\\n<example>For example, if color A appears 7 times in the input, that count (7) becomes the number of elements you will place in the output sequence, regardless of their original positions.</example>\\n</note2>\\n\\n<note3>\\n<description>Decide the output dimensions by mapping the input grid to a single row: the output's width is determined by the input's height (or another fixed rule consistent across examples). In these tasks the output is a horizontal row whose length is derived from the input's vertical size.</description>\\n<example>If the input has 14 rows, plan to produce a single row whose width equals that 14; the actual number of colored cells is then used to fill that row, not to change its width.</example>\\n</note3>\\n\\n<note4>\\n<description>Construct the output as a contiguous horizontal sequence of the chosen color, using the counted occurrences as the sequence length. The examples compress the scattered pixels into a single run of that color, so order and gaps in the input do not matter.</description>\\n<example>If you counted 9 occurrences of color A, produce a row of 9 A cells placed consecutively; the result is a uniform stripe of that color whose length equals the count.</example>\\n</note4>\\n\\n<note5>\\n<description>Watch for common pitfalls: ignore background zeros and any other colors when counting, and do not preserve original coordinates or shapes. The rule is purely a count-based repetition into a single-row output, so focus on the tally and the mapping to row width.</description>\\n<example>If the input contains many zeros and a few pixels of color B, only the occurrences of the dominant color A should be counted; the final output is a single row of A cells whose length equals that count, not a reconstruction of the input pattern.</example>\\n</note5>\"\n]","isConversational":false},"train":{"kind":"string","value":"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 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, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], \"output\": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {\"input\": [[4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 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, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], \"output\": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {\"input\": [[3, 0, 0, 0], [3, 0, 0, 0], [3, 0, 3, 0], [3, 0, 0, 0], [3, 0, 0, 3], [0, 0, 3, 0], [0, 3, 3, 3], [3, 0, 0, 3], [0, 3, 3, 0], [0, 0, 0, 0], [3, 0, 3, 3], [3, 3, 0, 0], [3, 3, 3, 3], [0, 3, 0, 0]], \"output\": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}]"},"test":{"kind":"string","value":"[{\"input\": [[0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [6, 0, 0, 6, 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, 6, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0]], \"output\": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}]"},"source":{"kind":"string","value":"rearc"},"prompt":{"kind":"string","value":"You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectangular matrix of integers between 0 and 9 (inclusive). Each number corresponds to a color. 0 is black. Your task is to determine the transformation rule from examples and find out the answer, involving determining the size of the output grid for the test and correctly filling each cell of the grid with the appropriate color or number. The transformation only needs to be unambiguous and applicable to the example inputs and the test input. It doesn't need to work for all possible inputs. Observe the examples carefully, imagine the grid visually, and try to find the pattern. Please output your answer within a code block (```), formatted as a grid of numbers. \n\n# Examples\n## Example 1\nInput:\n```\n0 0 0 0 0 0 0 6 0 6 0 0 0 0\n0 0 0 0 0 0 0 6 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 6 0 0 0 0 6 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 6 6 0 0 0 0\n0 0 0 0 0 0 0 0 0 6 0 0 0 0\n0 0 0 0 0 0 6 0 0 0 6 0 0 0\n0 0 0 0 0 0 0 6 0 0 0 0 0 0\n0 0 0 0 0 6 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 6 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n6 6 6 6 6 6 6 6 6 6 6 6 6 6\n```\n\n## Example 2\nInput:\n```\n4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4\n0 0 0 0 0 4 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0\n0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0\n0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0\n0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 4\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0\n0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0\n0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n```\n\nOutput:\n```\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\n```\n\n## Example 3\nInput:\n```\n3 0 0 0\n3 0 0 0\n3 0 3 0\n3 0 0 0\n3 0 0 3\n0 0 3 0\n0 3 3 3\n3 0 0 3\n0 3 3 0\n0 0 0 0\n3 0 3 3\n3 3 0 0\n3 3 3 3\n0 3 0 0\n```\n\nOutput:\n```\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n```\n\n# Test Problem:\n```\n0 6 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n6 0 0 0 0 0 0 0 0 0 0\n6 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 6 0 0\n0 0 0 0 0 0 6 0 0 0 0\n0 0 0 0 0 0 0 0 0 6 0\n6 0 0 6 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 6 0 0 6 0 0 0\n0 0 0 0 0 0 0 0 0 6 0\n0 6 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 6\n0 0 0 0 0 0 0 0 6 0 0\n```"},"answer":{"kind":"string","value":"```\n6 6 6 6 6 6 6 6 6 6 6 6 6 6\n```"},"num_tokens":{"kind":"number","value":1620,"string":"1,620"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":0,"numItemsPerPage":100,"numTotalItems":1396,"offset":0,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc4MDcyMjk5MSwic3ViIjoiL2RhdGFzZXRzL2FzaW5naDE1L2FyYy1iYXJjLXByb2Nlc3NlZC1kaXJlY3QtbWF4NGstc2Z0YWJzLTdvZjgiLCJleHAiOjE3ODA3MjY1OTEsImlzcyI6Imh0dHBzOi8vaHVnZ2luZ2ZhY2UuY28ifQ.6DbufCedtGz5e0qStb1dUOKNnqQw3tK4CLx1pBMzrWxtzGduT9p4ERud_3uLEDe3PsoKYgHXcOUKg9xW_ggsAA","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"test","numRows":15,"numBytesParquet":512408},{"config":"default","split":"train","numRows":1396,"numBytesParquet":30023720}]},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
abstraction_prompt stringlengths 4.78k 8.49k | abstraction_prompt_length int64 1.09k 4.8k | generated_abstractions listlengths 16 16 | train stringlengths 270 5.88k | test stringlengths 75 4.84k | source stringclasses 4
values | prompt stringlengths 1.28k 4.99k | answer stringlengths 9 1.81k | num_tokens int64 386 4.09k |
|---|---|---|---|---|---|---|---|---|
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,836 | [
"<note1>\n<description>Find the anchor: the unique non-black pixel in the input is the origin that determines the whole transformation. Treat that pixel as the center of the operation rather than as an isolated dot to be copied.</description>\n<example>Imagine a grid with a single green pixel at (r,c). For the purp... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 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]], "output": [[0, 0, 6, 0, 0, 6, 0, 0], [6, 6, 6, 6, 6, 0, 0, 0], [6, 6, 6, 6, 6, 0, 0, 0], [6, 0, 6, ... | [{"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, 3, 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]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 3 0 3 0 0 0
0 0 0 3 0 3 0 0 0
0 3 0 0 3 0 0 3 0
0 0 3 3 3 3 3 0 0
0 0 3 3 3 3 3 0 0
0 0 3 0 3 0 3 0 0
0 0 0 0 3 0 0 0 0
``` | 1,132 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,552 | [
"<note1>\n<description>Look for a single non-background color that consistently appears in every input; that color is the object being transformed. Treat every pixel of that color as part of one object (ignore other colors and background). This reduces the problem to manipulating one contiguous object instead of ma... | [{"input": [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0], [0, 2, 2, 2, 2, 0], [0, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0], [0, 3, 3, 0, 0, 0], [0, 0, 3, 3, 0, 0], [0, 0, 3, 3, 0, 0], [0, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0], [0,... | [{"input": [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 2, 2, 0], [0, 2, 2, 2, 2, 2, 0], [0, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0], [0, 0, 3, 3, 3, 0, 0], [0, 0, 3, 3, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0], [0, 0, 3, 3, 3, 0, 0... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0
0 0 3 3 3 0 0
0 0 3 3 3 0 0
0 0 3 3 0 0 0
0 0 3 3 3 0 0
0 0 3 3 3 0 0
0 0 0 0 0 0 0
``` | 848 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,190 | [
"<note1>\n<description>Start by comparing the input and output grids to see which pixels change and which remain identical. If the same set of pixels is altered across examples, that set is the target of the transformation.</description>\n<example>Imagine a grid where a few pixels of color A are replaced while all ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 1, 1,... | [{"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], [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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
7 7 7 7 7 7 0 0 0 7 7 7 7 0
7 0 0 0 0 7 0 0 0 7 0 0 7 0
7 0 0 0 0 7 0 0 0 7 7 7 7 0
7 7 7 7 7 7 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 7 7 7 7 0
0 0 0 1 1 1 1 0 0 7 0 0 7 0
0 0 0 1 1 1 1 1 0 7 7 7 7 0
0 0 0 1 1 1 1 1 0 0 0 0 0 0
0 0 0 1 ... | 2,486 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,982 | [
"<note1>\n<description>Find the single non-background color that forms the main object. When one color occupies a contiguous region and all other cells are background, that color is usually the one being transformed.</description>\n<example>Imagine a grid where only blue pixels form a block and every other cell 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, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 0, 0, 0], [0, 0, 0, 8, 8, 8, 8, 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... | [{"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, 5, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
5 5 5 5 5 5
5 5 5 5 5 5
5 5 5 5 5 5
5 5 5 5 5 5
5 5 5 5 5 5
5 5 5 5 5 5
``` | 1,278 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,770 | [
"<note1>\n<description>Isolate the object: many ARC tasks begin with a single non-background pixel or a small cluster. Identifying the object (its color, coordinates, and bounding box) is the first step because the transformation usually acts on that object rather than on the whole grid.</description>\n<example>Ima... | [{"input": [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 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, ... | [{"input": [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 4, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], "output": [[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, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 4 0 0 0 0 0 0 0
0 0 4 0 0 0 0 0 0 0
0 0 4 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
``` | 1,066 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,286 | [
"<note1>\n<description>Identify the object by finding the color that appears as a contiguous region and is different from the uniform background. This object is the element the transformation acts on; everything else is background.</description>\n<example>Imagine a 7×7 grid filled with zeros except for a compact pa... | [{"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, 6, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 6, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6,... | [{"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, 6, 6, 6, 0, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 6, 6, 6], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 6 6 6 1 6 6
1 1 1 1 1 1 1 1 6 6 1 6 6 6
1 1 1 1 1 1 1 1 6 6 6 6 6 6
1 1 1 1 1 1 1 1 6 6 6 6 6 6
1 1 1 1 1 1 1 1 6 6 6 6 6 6
1 1 1 1 1 1 1 1 6 6 6 6 6 6
1 1 1 1 ... | 2,582 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,104 | [
"<note1>\n<description>Look first for full rows or columns that are every cell the same color; these are usually deliberate separators that partition the grid into independent tiles. Treat those lines as boundaries rather than content to be changed.</description>\n<example>Imagine a 9×9 grid where row 4 and column ... | [{"input": [[1, 1, 1, 6, 1, 1, 1, 6, 1, 1, 1], [1, 1, 1, 6, 0, 1, 1, 6, 1, 1, 1], [1, 1, 1, 6, 8, 9, 5, 6, 1, 1, 1], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [1, 1, 1, 6, 1, 1, 1, 6, 7, 8, 0], [1, 1, 1, 6, 1, 1, 1, 6, 4, 9, 7], [1, 1, 1, 6, 1, 1, 1, 6, 0, 8, 5], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [1, 9, 1, 6, 1, 1, 1, 6, 1, ... | [{"input": [[9, 9, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9], [9, 6, 9, 9, 8, 9, 9, 6, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9], [6, 9, 9, 9, 8, 9, 6, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9], [6, 9, 9, 9, 8, 6, 9, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 6, 6, 9, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
9 9 9 9 8 7 4 7 6 8 9 9 9 9 8 9 9 9 9
9 9 9 9 8 6 7 7 6 8 9 9 9 9 8 9 9 9 9
9 9 9 9 8 9 6 6 7 8 9 9 9 9 8 9 9 9 9
9 9 9 9 8 6 6 7 9 8 9 9 9 9 8 9 9 9 9
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
9 9 9 9 8 9 9 9 9 8 9 9 9 9 8 9 9 9 9
9 9 9 9 8 9 9 9 9 8 9 9 9 9 8 9 9 9 9
9 9 9 9 8 9 9 9 9 8 9 9 9 9 8 9 9 9 9
9 9 9 9 8 9 ... | 3,400 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,598 | [
"<note1>\n<description>Look for a one-to-one correspondence between input pixels and output cells by comparing positions: if a non‑zero pixel appears in the input, there is usually a single non‑zero cell in the output at the same relative spot. This suggests the transformation is a per‑pixel mapping rather than a g... | [{"input": [[0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 1, 2, 0, 0], [0, 0, 0, 0, 2, 0, 7, 0]], "output": [[2, 2, 2, 2], [3, 3, 0, 0], [4, 0, 0, 0], [1, 0, 0, 0], [7, 0, 0, 0]]}, {"input": [[0, 0... | [{"input": [[0, 0, 4, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7], [1, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 7, 0, 0, 0, 3, 0, 1], [0, 0, 2, 0, 1, 0, 0, 0, 2], [0, 0, 0, 1, 0, 0, 0, 3, 1], [0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0]], "output": [[4, 4, 4, 0, 0], [2, 2, 2, 2, 2], [... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
4 4 4 0 0
2 2 2 2 2
7 7 0 0 0
1 1 1 1 1
3 3 0 0 0
``` | 894 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,370 | [
"<note1>\n<description>Look for the small, compact objects that are being changed: each input contains one contiguous 2×2 block of non-zero cells. The transformation acts on those exact 2×2 objects, not on scattered single pixels or larger shapes.</description>\n<example>Imagine a 4×4 grid with a single 2×2 red squ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 8, 0, 0, 0, 0, 0, 0], [0, 0, 9, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 2, 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... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 2, 9, 0, 0], [2, 1, 0, 0, 0, 0, 1, 6, 0, 0], [0, 0, 0, 4, 7, 0, 0, 0, 0, 0], [0, 0, 0, 8, 4, 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 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 2 9 0 0
2 1 0 0 0 0 1 6 0 0
3 3 0 4 7 0 3 3 0 0
3 3 0 8 4 0 3 3 0 0
0 0 0 3 3 0 3 3 0 0
0 0 0 3 3 0 3 3 0 0
0 0 0 3 3 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
``` | 1,666 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,406 | [
"<note1>\n<description>Separate the grid into individual objects by treating each contiguous non‑zero cluster as one unit. Work at the object level (not at individual pixels) so you can compare whole shapes and their positions.</description>\n<example>Imagine a 5×5 grid with a 2×2 block of color A at the top-left a... | [{"input": [[0, 0, 0, 0, 0, 0, 0], [0, 5, 8, 5, 0, 0, 0], [0, 5, 8, 5, 0, 0, 0], [0, 8, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0], [0, 8, 5, 8, 0, 0, 0], [0, 8, 5, 8, 0, 0, 0], [0, 5, 5, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0... | [{"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], [0, 3, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 6, 6, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 1, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 3, 3, 0, 0, 0, 0, 0], [0, 2,... | arc 2 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0
0 2 3 3 0 0 0 0 0
0 2 2 3 0 0 0 0 0
0 2 3 3 0 0 0 0 0
0 0 0 0 0 1 1 1 0
0 0 0 0 0 6 6 6 0
0 0 0 0 0 6 1 1 0
0 0 0 0 0 0 0 0 0
``` | 1,702 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,858 | [
"<note1>\n<description>Find the background: the color that fills most of the grid is usually the background. Treat every cell that is not that color as an object to be summarized. This separates the important pixels from the uniform field.</description>\n<example>Imagine a 10×10 grid where 90 cells are blue and fiv... | [{"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1,... | [{"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 8 5
5 5 5
5 5 5
``` | 3,154 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,670 | [
"<note1>\n<description>Look first for a single color that appears in two contiguous regions (a large block and a narrow band). The band is usually a single column or a thin contiguous rectangle and is the key object to transform. Identifying that band reduces the problem to one object and a background color.</descr... | [{"input": [[6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6, 6, 3, 3], [6, 6, 6... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
7 7 7 7 7 7 4 4
2 2 7 7 7 7 4 4
2 2 7 7 7 7 4 4
7 7 2 2 7 7 4 4
7 7 2 2 7 7 4 4
7 7 7 7 2 2 4 4
7 7 7 7 2 2 ... | 3,966 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,734 | [
"<note1>\n<description>Focus on the non-background color: identify which color forms the small, contiguous shape and treat it as the object to transform. This reduces the problem to how that single object is changed rather than the whole grid.</description>\n<example>Imagine a grid where only one color (e.g., blue)... | [{"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, ... | [{"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], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 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 4 4 4 4 0 0 0 0 0 0 0
0 0 0 4 ... | 3,030 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,950 | [
"<note1>\n<description>Isolate the target objects by finding the color that forms multiple distinct patches and compute their bounding boxes. This separates the shapes you will transform from the background and any other colors.</description>\n<example>Imagine a grid with several green blobs on a black background; ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 2, 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, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 2, 2, 0, 0, 0, 2, 0... | [{"input": [[0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0], [2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0
0 4 0 4 4 4 4 4 0 0 4 0 0 0 0 0
4 4 4 0 4 4 4 0 0 4 4 4 0 0 0 0
0 4 0 0 0 4 0 0 0 0 4 4 0 0 0 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 0 4 4 4 4 4 0 0
0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 0
0 0 0 0 0 0 4 0 0 4 4 4 4 4 0 0
0 0 0 0 0 4 4 4 0 4 4 4 4 4 ... | 3,246 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,104 | [
"<note1>\n<description>Start by listing every non-background pixel and recording its color and coordinates. The order in which these pixels appear in reading order (rows then columns) is usually the key sequence that drives the transformation.</description>\n<example>Imagine a tiny grid with a red pixel at (1,1), a... | [{"input": [[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 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, 8, 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, 5, 2], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "ou... | [{"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], [2, 0, 0, 0, 8, 1, 9, 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, 4]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
2 0 0 0 8 1 9 0 0
2 2 0 8 8 8 1 9 0
2 2 2 8 8 8 8 1 9
2 2 2 2 8 1 9 8 1
2 2 2 8 8 8 8 1 9
2 2 0 8 8 8 1 9 4
2 0 0 0 8 1 9 4 4
``` | 1,400 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,296 | [
"<note1>\n<description>Isolate the object: find the single non-background pixel and record its color and coordinates (row, column). This is the only element that is likely to move or be transformed; everything else remains background.</description>\n<example>Imagine a grid with one red pixel at (2,3). Treat that re... | [{"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, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 6, 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]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 6 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
``` | 1,592 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,984 | [
"<note1>\n<description>Isolate the seed: when exactly one non-background pixel exists, treat it as the single element that determines the whole output. The transformation is driven by that pixel's color and position, not by other background pixels.</description>\n<example>Imagine a grid with one blue pixel. In the ... | [{"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, 8, 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]], "output": [[0, 0, 0, 0, 0, 0, 0, 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, 6, 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]], "output": [[6, 6, 6, 6, 6, 0, 0, 0, 0], [6, 6,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 6 6 6 0 0 0 0
6 6 6 6 6 6 0 0 0
6 6 6 6 6 6 0 0 0
6 6 6 6 6 6 0 0 0
6 6 6 6 6 6 0 0 0
6 6 6 6 6 6 0 0 0
6 6 6 6 0 6 0 0 0
6 6 6 6 6 0 0 0 0
0 6 6 0 0 0 0 0 0
``` | 1,280 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,104 | [
"<note1>\n<description>Find the anchor: the task always starts from a single colored pixel (the seed). Treat that pixel as the center of the transformation and ignore all zeros (background) when reasoning about shape placement. This reduces the problem to “what to do around that one point.”</description>\n<example>... | [{"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, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "ou... | [{"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, 6, 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]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 6 0 0 0 0 0 0
6 6 6 6 6 0 0 0 0
6 6 6 6 6 0 0 0 0
6 6 6 6 6 6 0 0 0
6 6 6 6 6 0 0 0 0
6 6 6 6 6 0 0 0 0
0 0 6 0 0 0 0 0 0
``` | 1,400 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,500 | [
"<note1>\n<description>Separate objects by treating each contiguous block of the target color as an independent object. Use 4‑connectivity (up/down/left/right) to determine which pixels belong to the same object so that you can reason about each object as a unit.</description>\n<example>Imagine a 6×6 grid with thre... | [{"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, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5], [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... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 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, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 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, ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0 0 0
0 6 6 0 0 0 0 0 0 0 0
0 6 6 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 6 6 0 0 0 0 0 0 0
0 0 6 6 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 ... | 2,796 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,554 | [
"<note1>\n<description>Look for a single color that appears as a compact, contiguous rectangular patch (a filled block) and is clearly distinct from the dominant background. Such a block is the anchor for the transformation because its bounding box is well-defined and easy to work with. Identifying that color reduc... | [{"input": [[6, 6, 6, 4, 4, 4], [6, 6, 6, 4, 4, 4], [6, 6, 6, 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], [7, 7, 7, 4, 4, 4], [7, 7, 7, 4, 4, 4], [7, 7, 7, 4, 4, 4], [7, 7, 7, 4, 4, 4], [7, 7, 7, 4, 4, 4], [7, 7, 7, 4, 4, 4], [7, 7, 7... | [{"input": [[6, 6, 6, 6, 6, 6], [2, 2, 6, 0, 6, 6], [2, 2, 6, 0, 6, 6], [2, 2, 6, 0, 6, 6], [2, 2, 6, 0, 6, 6], [2, 2, 6, 0, 6, 6], [2, 2, 6, 0, 6, 6], [2, 2, 6, 0, 6, 6], [2, 2, 6, 0, 6, 6], [6, 6, 6, 0, 6, 6], [6, 6, 6, 0, 6, 6], [6, 6, 6, 0, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 6 6 6 6
2 2 6 0 6 6
2 2 8 0 6 6
2 2 8 0 6 6
2 2 8 0 6 6
2 2 8 0 6 6
2 2 8 0 6 6
2 2 8 0 6 6
2 2 6 0 6 6
6 6 6 0 6 6
6 6 6 0 6 6
6 6 6 0 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 6 6 6 6
6 6 ... | 3,850 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,370 | [
"<note1>\n<description>Look for a compact 3×3 neighborhood that contains a distinct central cell and exactly eight other cells all of the same color. When this pattern appears, the task typically treats that 3×3 as a single object rather than as eight separate pixels.</description>\n<example>Imagine a grid where a ... | [{"input": [[2, 7, 7, 1, 0, 3, 0, 0, 0, 3], [0, 0, 0, 9, 0, 0, 0, 0, 3, 7], [0, 0, 0, 1, 0, 0, 0, 6, 0, 9], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 3, 0], [0, 5, 0, 7, 3, 0, 0, 0, 1, 0], [4, 4, 0, 0, 0, 1, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 5, 3, 0], [0, 0, 0, 0, 4, 5, 0... | [{"input": [[0, 0, 0, 0, 2, 5, 7, 0, 0, 0], [0, 0, 0, 5, 6, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 8, 0, 3, 0, 0, 0, 0, 8], [7, 4, 7, 7, 4, 0, 0, 0, 0, 4], [0, 0, 0, 8, 0, 0, 7, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 4, 0, 0], [5, 5, 0, 3, 0, 0, 6, 7, 0, 7], [0, 0, 3, 0, 0, 0, 0, 0, 0, 2], [1, 0, 1, 0, 0, 0, 0... | arc 2 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 2 2 2 0 0 0
0 0 0 0 2 9 2 0 0 0
0 0 0 0 2 2 2 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
``` | 1,666 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,398 | [
"<note1>\n<description>Look for a vertical mirror: the output often contains the input rows in reverse order below the original block. This is a vertical reflection (rows keep their left-to-right order but their top-to-bottom order is reversed).</description>\n<example>Imagine a 3-row input A, B, C. If you see A, B... | [{"input": [[9, 4, 1, 3, 3, 3, 3, 9, 9, 2, 4], [9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9], [9, 9, 1, 9, 9, 9, 2, 1, 9, 9, 9], [2, 8, 9, 3, 3, 9, 9, 1, 5, 2, 5], [9, 3, 8, 9, 9, 9, 3, 9, 9, 9, 9], [9, 5, 9, 2, 3, 8, 9, 8, 9, 9, 3]], "output": [[9, 4, 1, 3, 3, 3, 3, 9, 9, 2, 4], [9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9], [9, 9, 1, 9, 9, ... | [{"input": [[5, 5, 5, 5, 4, 5, 5, 9, 5, 4, 5, 5, 4, 5, 5, 5, 9, 1, 5, 4, 5], [9, 1, 5, 4, 4, 5, 5, 1, 4, 5, 5, 5, 4, 4, 5, 5, 5, 1, 5, 5, 9], [4, 5, 4, 4, 5, 4, 5, 9, 5, 5, 9, 5, 4, 5, 5, 5, 5, 4, 9, 5, 4], [4, 5, 5, 5, 4, 9, 4, 9, 5, 4, 5, 1, 4, 9, 5, 5, 5, 5, 1, 5, 5], [5, 5, 4, 5, 4, 4, 5, 1, 5, 5, 5, 5, 5, 5, 4, 5,... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
5 5 5 5 4 5 5 9 5 4 5 5 4 5 5 5 9 1 5 4 5
9 1 5 4 4 5 5 1 4 5 5 5 4 4 5 5 5 1 5 5 9
4 5 4 4 5 4 5 9 5 5 9 5 4 5 5 5 5 4 9 5 4
4 5 5 5 4 9 4 9 5 4 5 1 4 9 5 5 5 5 1 5 5
5 5 4 5 4 4 5 1 5 5 5 5 5 5 4 5 5 4 5 5 5
9 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1
5 5 5 5 5 5 4 5 5 9 5 5 5 5 5 5 5 5 9 5 5
9 5 5 9 5 5 5 5 5 5 5 ... | 1,694 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,620 | [
"<note1>\n<description>Find the anchor: in these tasks there is typically one cell whose color differs from the uniform background and that cell is the reference for the transformation. Treat that cell as the center of a local change rather than as a color that should be preserved globally.</description>\n<example>... | [{"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, 9, 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]], "output": [[1, 1, 1, 4, 4, 4, 4, 4], [4, 4, 1, 4, 4, 4, 4, 4], [4, 4, 1, 4, 4, 4, 4, 4], [4, 4, 9, ... | [{"input": [[5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 6, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 1, 1, 1, 1], [5, 5, 5, 1, 5, 5, 5], [5, 5, 5, 1, 5, 5, 5], [5, 5, 5, 6, 5, 5, 5], [5, 5, 5, 1, 5, 5, 5], [5, 5, 5, 1, 5, 5, 5... | arc 2 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
5 5 5 1 1 1 1
5 5 5 1 5 5 5
5 5 5 1 5 5 5
5 5 5 6 5 5 5
5 5 5 1 5 5 5
5 5 5 1 5 5 5
1 1 1 1 5 5 5
``` | 916 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,734 | [
"<note1>\n<description>Isolate the seed: many ARC tasks use a single non-background pixel as the anchor for the transformation. Identifying that pixel (its color and coordinates) gives you the reference point for any pattern or expansion that follows.</description>\n<example>If you see exactly one colored pixel on ... | [{"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, ... | [{"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, 1, 0, 0, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 2 0 2 0 2 0
0 0 0 0 0 0 0 0 0 2 2 2 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 2 2 2 0 0
0 0 0 0 0 0 0 0 2 0 2 0 2 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 ... | 3,030 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,390 | [
"<note1>\n<description>First isolate the object by finding every cell whose color differs from the background. Treat the entire set of such cells as one connected object and ignore isolated background pixels or stray noise.</description>\n<example>Imagine a grid of zeros with a compact cluster of ones. Mark every n... | [{"input": [[0, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, 0, 1, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 6, 6, 6, 0], [0, 6, 6, 6, 0], [0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, ... | [{"input": [[0, 0, 0, 0], [0, 1, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0]], "output": [[0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 6, 0], [0, 0, 0, 0]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0
0 0 6 0
0 0 6 0
0 0 0 0
``` | 686 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,122 | [
"<note1>\n<description>Find the object by locating the color that forms a contiguous block and compute its bounding box (min/max row and column). Knowing this box gives the object's height h and width w and is the starting point for any transformation.</description>\n<example>Imagine a solid blue rectangle occupyin... | [{"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, ... | [{"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], [3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0], [3, ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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
3 3 3 3 0 0 0 0 0 0 0 0
3 3 3 3 3 0 0 0 0 0 0 0
3 3 3 3 3 0 0 0 0 0 0 0
3 3 3 3 0 0 0 0 0 0 0 0
3 3 3 3 0 0 0 0 0 0 0 0
3 3 3 3 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 ... | 3,418 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,734 | [
"<note1>\n<description>Separate the background from the foreground by finding the single non-background color that forms the main objects. The foreground is usually a contiguous cluster (or clusters) of that color; everything else is background and is not part of the transformation.</description>\n<example>Imagine ... | [{"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, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, ... | [{"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, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 1 1 1 1 7 7 0 0 0 0
0 1 1 1 1 1 1 1 1 1 1 7 7 0
0 0 1 1 1 1 1 1 1 1 7 7 0 0
0 0 1 1 1 1 1 1 1 1 7 7 0 0
0 1 1 1 1 0 0 1 1 1 1 7 7 0
0 1 1 1 1 0 0 1 1 1 1 7 7 0
0 0 1 1 1 0 0 1 1 1 7 7 0 0
0 1 1 1 1 0 0 1 1 1 1 7 7 0
0 0 1 0 1 0 0 1 0 1 0 7 0 0
0 0 1 1 ... | 3,030 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,322 | [
"<note1>\n<description>Look for the background color: it is usually the single color that occupies large continuous regions and forms a uniform border or field. Identifying that color lets you treat every other color as foreground and focus on the region that actually contains the pattern.</description>\n<example>I... | [{"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [9, 6, 9, 9, 9, 9, 6, 9, 6, 9, 9, 9], [9, 9, 9, 6, 9, 9, 6, 9, 9, 9, 9, 6], [9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9], [6, 9, 6, 9, 9, 9, 6, 9, 9, 9, 6, 9], [9, 9, 9, 9, 6, 6, 9, 6, 9, 9, 9, 9], [6, 6, 9, 6, 9, 6, 6, 6, 9, 9, 9, 9], [9, 9, 9, 9, 6, 6, 6, 9, 6, 9, 6, 6], [9, ... | [{"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 4, 7, 4, 2, 2, 4, 3, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 4, 7, 1, 3, 1, 7, 2, 2, 2, 2, 7, 1, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2,... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
2 1 3 4 7 4
4 7 1 3 1 7
3 2 1 3 1 2
4 2 2 7 7 7
2 2 1 2 3 3
2 2 4 2 7 2
``` | 3,618 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,792 | [
"<note1>\n<description>Look for a color that appears as a continuous rectangular frame (a perimeter) rather than as scattered pixels. Such a frame is usually a single color that forms an uninterrupted border and encloses a distinct interior.</description>\n<example>Imagine a grid where one color fills the outermost... | [{"input": [[2, 2, 2, 2, 7, 2, 5, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 5, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 5, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 5, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 5, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 5, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 5, 1, 2, 2, 2, 2, 2], [6, 6, 6, 6, 7, 6, 5,... | [{"input": [[5, 5, 5, 5, 3, 9, 5, 5, 6, 5, 5, 7, 1, 5, 5, 5, 5], [5, 5, 5, 5, 3, 9, 5, 5, 6, 5, 5, 7, 1, 5, 5, 5, 5], [5, 5, 5, 5, 3, 9, 5, 5, 6, 5, 5, 7, 1, 5, 5, 5, 5], [0, 0, 0, 0, 3, 9, 0, 0, 6, 0, 0, 7, 0, 0, 0, 0, 0], [5, 5, 5, 5, 3, 9, 5, 5, 6, 5, 5, 7, 1, 5, 5, 5, 5], [7, 7, 7, 7, 3, 9, 7, 7, 7, 7, 7, 7, 7, 7, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
2 2 2 2 2 2 2
2 4 4 3 9 4 2
2 2 2 2 2 2 2
``` | 2,088 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,248 | [
"<note1>\n<description>Look first for a size change: if the output's number of rows and columns are swapped (height becomes width and vice versa), the transformation is likely a transposition. A transposition preserves which color appears where but reverses row/column order, so it's effective when the grid dimensio... | [{"input": [[0, 0, 0, 0, 0], [6, 0, 6, 6, 6], [0, 6, 0, 6, 0], [0, 0, 6, 6, 6]], "output": [[0, 6, 0, 0], [0, 0, 6, 0], [0, 6, 0, 6], [0, 6, 6, 6], [0, 6, 0, 6]]}, {"input": [[0, 7, 0, 0], [7, 0, 0, 7], [7, 0, 7, 7], [7, 0, 7, 7], [7, 7, 7, 0]], "output": [[0, 7, 7, 7, 7], [7, 0, 0, 0, 7], [0, 0, 7, 7, 7], [0, 7, 7, 7,... | [{"input": [[6, 6, 0], [0, 0, 6], [0, 6, 6]], "output": [[6, 0, 0], [6, 0, 6], [0, 6, 6]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 0 0
6 0 6
0 6 6
``` | 544 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,336 | [
"<note1>\n<description>Locate the object by finding the color that appears as a compact, multi-cell shape against a uniform background. This color will be the one you will analyze for symmetry and edges. Treat the minimal bounding rectangle of that color as the object to work with.</description>\n<example>Imagine a... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 1, 1, 1, 1, 7, 1, 1, 1, 1, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 1, 7, 7, 7], [7, 7, 7, 1, 1, 1, 1, 7, 1... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 4 4 4 7 7 7 7 7 7
7 7 7 7 7 4 1 1 1 1 7 7 7 7 7
7 7 7 7 7 4 1 7 7 1 7 7 7 7 7
7 7 7 7 7 4 1 7 4 1 7 7 7 7 7
7 7 7 7 7 7 1 1 ... | 2,632 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,498 | [
"<note1>\n<description>Look for a single color that forms a continuous, uninterrupted line across the entire grid (it spans every row or every column). Such a full-length line usually acts as a divider and splits the grid into two separate regions. Recognizing this line is the first step because it tells you where ... | [{"input": [[2, 1, 8, 1, 1, 1, 1, 1, 4, 1, 9, 2, 1, 1, 1], [2, 9, 8, 9, 9, 9, 9, 9, 4, 9, 9, 2, 9, 9, 9], [2, 6, 8, 6, 6, 6, 6, 6, 4, 6, 9, 2, 6, 6, 6], [2, 1, 8, 1, 1, 1, 3, 3, 3, 3, 3, 2, 1, 1, 1], [7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 3, 7, 7, 7, 7], [2, 1, 8, 1, 1, 1, 3, 3, 3, 3, 3, 2, 1, 1, 1], [2, 1, 8, 1, 1, 1, 1, 1, 4... | [{"input": [[9, 9, 8, 9, 9, 2, 4, 5, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 2, 9, 9, 9, 9], [9, 9, 8, 9, 9, 2, 4, 5, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 2, 9, 9, 9, 9], [9, 9, 8, 9, 9, 2, 4, 5, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 2, 9, 9, 9, 9], [9, 9, 8, 9, 9, 2, 4, 5, 9, 9, 6, 9, 9, 9... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
3 3 3 3 3
3 9 9 2 3
3 3 3 3 3
``` | 2,794 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,246 | [
"<note1>\n<description>Look for small identical objects (often 2×2 squares) that repeat in the input. When the same small block appears multiple times, treat each occurrence as an atomic object rather than many independent pixels.</description>\n<example>Imagine a 4×4 grid that contains three identical 2×2 red squa... | [{"input": [[8, 8, 0, 0, 0], [8, 8, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 8, 8], [0, 0, 0, 8, 8]], "output": [[8, 8, 0, 0, 0], [8, 8, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]}, {"input": [[7, 7, 0, 0, 0], [7, 7, 0, 0, 0], [0, 0, 0, 7, 7], [0, 0, 0, 7, 7]], "output": [[7, 7, 0, 0, 0], [7, 7, 0, 0, 0],... | [{"input": [[6, 6, 0, 0], [6, 6, 0, 0], [0, 0, 6, 6], [0, 0, 6, 6]], "output": [[6, 6, 0, 0], [6, 6, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 0 0
6 6 0 0
0 0 0 0
0 0 0 0
``` | 542 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,221 | [
"<note1>\n<description>First check whether the output grid is a simple scaling of the input: if every output dimension is an integer multiple of the input dimension, the transformation is likely a uniform enlargement (a tiling or block expansion). This reduces the problem to figuring out what is being repeated.</de... | [{"input": [[1, 1, 1], [8, 1, 6], [6, 8, 8]], "output": [[1, 1, 1, 1, 1, 1], [8, 1, 6, 6, 1, 8], [6, 8, 8, 8, 8, 6]]}, {"input": [[6, 8, 1], [6, 1, 1], [1, 1, 6]], "output": [[6, 8, 1, 1, 8, 6], [6, 1, 1, 1, 1, 6], [1, 1, 6, 6, 1, 1]]}, {"input": [[1, 1, 1], [1, 6, 6], [6, 6, 6]], "output": [[1, 1, 1, 1, 1, 1], [1, 6, ... | [{"input": [[6, 8, 6], [8, 6, 8], [1, 6, 1]], "output": [[6, 8, 6, 6, 8, 6], [8, 6, 8, 8, 6, 8], [1, 6, 1, 1, 6, 1]]}] | arc 2 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 8 6 6 8 6
8 6 8 8 6 8
1 6 1 1 6 1
``` | 517 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,320 | [
"<note1>\n<description>Look for a single contiguous non-background object: many ARC tasks change only one connected colored region while the background and other regions remain identical. Identifying that object first reduces the problem to a small set of possible transformations.</description>\n<example>Imagine a ... | [{"input": [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 4, 4, 4], [0, 0, 4, 4, 4], [0, 0, 4, 4, 4]], "output": [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 3, 3, 3], [0, 0, 3, 3, 3], [0, 0, 3, 3, 3]]}, {"input": [[0, 0, 0, 0, 0], [0, 3, 3, 0, 0], [0, 3, 3, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0],... | [{"input": [[0, 0, 0, 2, 2], [0, 0, 0, 2, 2], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], "output": [[0, 0, 0, 1, 1], [0, 0, 0, 1, 1], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 1 1
0 0 0 1 1
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
``` | 616 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,836 | [
"<note1>\n<description>Check for a global shift rather than a local recoloring: a uniform translation moves every colored pixel by the same offset while preserving each pixel's color. This is effective when the colored pattern in the output looks identical but located elsewhere in the grid.</description>\n<example>... | [{"input": [[6, 6, 0, 6, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0], [6, 0, 6, 0, 6, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 0, 0, 0, 0], [6, 6, 0, 6, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 6, 0, 6, 6], [0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 0, ... | [{"input": [[6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 6, 0, 0, 0, 0, 0], [6, 0, 0, 6, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 0, 6, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0], [6, 0, 0, 6, 0, 0, 0, 0, 0], [6, 0, 0, 6, 0, 0, 0, 0, 0], [6, 6, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 6, 6], [0, 0,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 6 6
0 0 0 0 0 6 0 6 0
0 0 0 0 0 6 0 0 6
0 0 0 0 0 0 0 6 0
0 0 0 0 0 0 6 6 0
0 0 0 0 0 6 0 0 0
0 0 0 0 0 6 0 0 6
0 0 0 0 0 6 0 0 6
0 0 0 0 0 0 0 6 6
``` | 1,132 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,238 | [
"<note1>\n<description>Look for whole-row repetition: if each output row is identical to an input row, the transformation is likely a horizontal tiling (concatenation) of the input across columns. This is effective because it preserves every cell's color and order while changing only the width.</description>\n<exam... | [{"input": [[8, 2, 4, 8, 0, 0, 2, 8, 2, 9], [8, 8, 2, 2, 8, 8, 2, 2, 2, 2], [9, 8, 0, 2, 2, 2, 2, 0, 0, 4], [2, 2, 8, 8, 9, 2, 2, 4, 2, 2], [8, 9, 2, 2, 2, 2, 2, 0, 2, 9], [2, 2, 2, 0, 4, 8, 2, 2, 9, 4], [2, 2, 2, 2, 9, 9, 4, 9, 9, 4], [2, 2, 9, 2, 2, 2, 8, 2, 8, 2], [8, 0, 2, 4, 9, 2, 2, 2, 2, 4], [2, 4, 2, 2, 0, 0, 9... | [{"input": [[0, 0], [0, 7], [0, 0], [7, 1], [0, 9], [9, 9], [1, 1], [1, 5], [0, 1], [0, 1], [5, 7], [0, 0], [9, 9], [0, 9], [9, 1], [1, 9], [0, 0], [0, 0], [7, 1], [9, 0], [0, 1], [0, 9], [0, 0], [5, 0], [0, 0], [0, 0], [0, 0], [0, 0]], "output": [[0, 0, 0, 0], [0, 7, 0, 7], [0, 0, 0, 0], [7, 1, 7, 1], [0, 9, 0, 9], [9... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0
0 7 0 7
0 0 0 0
7 1 7 1
0 9 0 9
9 9 9 9
1 1 1 1
1 5 1 5
0 1 0 1
0 1 0 1
5 7 5 7
0 0 0 0
9 9 9 9
0 9 0 9
9 1 9 1
1 9 1 9
0 0 0 0
0 0 0 0
7 1 7 1
9 0 9 0
0 1 0 1
0 9 0 9
0 0 0 0
5 0 5 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
``` | 3,534 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,344 | [
"<note1>\n<description>Search the grid for any non-background pixel (a cell whose value is not the background color). If exactly one such pixel exists, that single colored cell usually encodes the transformation's identity.</description>\n<example>Imagine a 6×6 grid with one green pixel somewhere and every other ce... | [{"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, 6, 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, ... | [{"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, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]], "output": [[6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 6 6 6 6 6
6 6 6 6 6 6 6
6 6 6 6 6 6 6
6 6 6 6 6 6 6
6 6 6 6 6 6 6
6 6 6 6 6 6 6
6 6 6 6 6 6 6
``` | 1,640 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,586 | [
"<note1>\n<description>Separate the grid into connected components of the non-background color and treat each as an independent object. This isolates the meaningful shapes from the empty background so you can compare them as whole objects rather than individual pixels.</description>\n<example>Imagine a grid with th... | [{"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, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0], [0, 0, 0, 6, ... | [{"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], [2, 2, 2... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
2 2 2 2 2 0
2 2 2 0 0 2
2 2 2 2 2 0
``` | 1,882 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,856 | [
"<note1>\n<description>Look for a single color that appears repeatedly and forms a diagonal-like line (one occurrence per row, one per column). This color is usually the pivot that the transformation uses to define a region to modify.</description>\n<example>Imagine a 5×5 grid where color A appears at (1,1),(2,2),(... | [{"input": [[9, 2, 3, 2, 9, 3, 6, 8, 9, 7, 3, 6, 9, 6, 8, 3, 9, 8, 2, 2, 9, 6, 2, 7, 9, 7], [7, 9, 3, 9, 7, 9, 3, 9, 7, 9, 6, 9, 6, 9, 7, 9, 8, 9, 2, 9, 8, 9, 7, 9, 8, 9], [8, 2, 9, 7, 7, 2, 9, 2, 6, 3, 9, 3, 3, 2, 9, 8, 6, 2, 9, 3, 6, 8, 9, 3, 7, 3]], "output": [[9, 2, 3, 2, 9, 4, 4, 4, 9, 7, 3, 6, 9, 6, 8, 3, 9, 4, 4... | [{"input": [[5, 2, 2, 2, 2, 2, 7, 7, 5, 6, 7, 2, 6, 6, 3], [2, 5, 2, 3, 3, 6, 3, 5, 3, 5, 7, 7, 2, 7, 2], [6, 3, 5, 3, 2, 6, 5, 3, 6, 2, 5, 3, 3, 2, 5], [6, 3, 7, 5, 6, 5, 3, 7, 2, 3, 2, 5, 6, 5, 2], [3, 2, 7, 3, 5, 3, 7, 3, 3, 7, 3, 7, 5, 7, 3]], "output": [[5, 2, 2, 2, 2, 2, 7, 7, 5, 4, 4, 4, 4, 4, 4], [4, 5, 2, 3, 3... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
5 2 2 2 2 2 7 7 5 4 4 4 4 4 4
4 5 2 3 3 6 3 5 3 5 4 4 4 4 4
4 4 5 3 2 6 5 3 6 2 5 4 4 4 5
4 4 4 5 6 5 3 7 2 3 2 5 4 5 2
4 4 4 4 5 3 7 3 3 7 3 7 5 7 3
``` | 1,152 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,370 | [
"<note1>\n<description>Look for a single contiguous object made of one color that appears in the same place in every training input; that object is the one being transformed. When an object is uniform and unchanged in location between input and output, treat it as the target for the rule.</description>\n<example>Im... | [{"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, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 2 2 2 1 1 1 0
0 0 0 2 2 2 1 1 1 0
0 0 0 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
``` | 1,666 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,564 | [
"<note1>\n<description>Look for a small, compact colored cluster that appears only once in the input and that serves as the template. Such a template is usually a small, symmetric motif (often a 3×3 pattern) and is repeated in the output at several locations.</description>\n<example>Imagine a grid with a single 3×3... | [{"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, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 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, 7, 0, 7, 0... | arc 1 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 4 0 4 0 0 0 0 0 0 0
0 0 0 0 0 4 0 4 0 0 0 0 0 0 0
0 0 0 4 4 0 0 0 4 4 0 0 0 0 0
0 0 0 0 4 0 0 0 4 0 0 0 0 0 0
0 0 4 0 4 4 0 4 4 0 4 0 0 0 0
0 0 0 4 0 7 0 7 0 4 0 0 0 0 0
0 0 0 0 0 0 7 0 0 0 0 0 0 0 0
0 0 0 4 0 7 0 7 0 4 0 0 0 0 0
0 0 4 0 4 4 0 4 4 0 4 0 0 0 0
0 0 0 0 4 0 0 0 ... | 2,860 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,826 | [
"<note1>\n<description>Find the background by frequency and treat every non-background cell as part of an object. The background is usually the most common color (often 0), so everything else is candidate content for the output.</description>\n<example>Imagine a grid with mostly zeros and a few colored pixels. Mark... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 4, 0, 0, 9, 9, 9, 0], [0, 0, 4, 4, 4, 0, 9, 9, 9, 0], [0, 0, 4, 4, 4, 0, 9, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 9, 9, 9, 0, 0, 0, 0], [0, 0, 0, 0, 9, 9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 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... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 9 9 9
0 0 9 9
0 0 0 9
``` | 1,122 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,204 | [
"<note1>\n<description>Look for a single row (or a single column) that contains all the non-background colors in the same order. That ordered sequence is the seed or motif the transformation uses; it is the only sequence that matters when you reconstruct the grid.</description>\n<example>Imagine a grid whose bottom... | [{"input": [[5, 5, 5, 5], [4, 4, 4, 4], [8, 8, 8, 8], [0, 0, 0, 0]], "output": [[5, 5, 5, 5], [4, 4, 4, 4], [8, 8, 8, 8], [5, 5, 5, 5]]}, {"input": [[0, 0, 0, 0, 9, 0, 0, 0, 0, 6, 0, 3, 9], [0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 6, 0, 3], [0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 6], [6, 0, ... | [{"input": [[0, 0, 0, 0, 0], [9, 9, 9, 9, 9], [9, 9, 9, 9, 9], [8, 8, 8, 8, 8], [0, 0, 0, 0, 0]], "output": [[8, 8, 8, 8, 8], [9, 9, 9, 9, 9], [9, 9, 9, 9, 9], [8, 8, 8, 8, 8], [9, 9, 9, 9, 9]]}] | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
8 8 8 8 8
9 9 9 9 9
9 9 9 9 9
8 8 8 8 8
9 9 9 9 9
``` | 2,500 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,534 | [
"<note1>\n<description>Look for a consistent single-cell marker inside each colored object. Many ARC tasks replace an entire connected component with a single cell of the same color, so first identify whether every non-background cluster in the examples has been reduced to one pixel.</description>\n<example>Imagine... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 6, 0, 0, 6, 0, 0, 6, 0, 0], [0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0], [0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 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, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 5 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 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 9 0 0 0 0 0 0 0 0 0
0 0 0 0 ... | 2,830 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,902 | [
"<note1>\n<description>Look for the smallest rectangle that contains all non-background colors and is repeated across the grid. That rectangle is the atomic tile the task is asking you to reproduce. Thinking in terms of a repeating tile simplifies the problem because the output is just a compact version of that uni... | [{"input": [[8, 7, 7, 7, 8, 7, 7, 7, 8], [7, 8, 8, 7, 7, 8, 8, 7, 7], [8, 7, 8, 7, 8, 7, 8, 7, 8], [8, 7, 7, 7, 8, 7, 7, 7, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 7, 8, 7, 8, 0, 0, 7, 8], [8, 7, 7, 8, 8, 0, 0, 8, 8], [8, 8, 8, 8, 8, 0, 0, 8, 8], [8, 7, 7, 7, 8, 0, 0, 7, 8], [7, 8, 8, 7, 7, 0, 0, 7, 7], [8, 7, 8, 7, 8, 0,... | [{"input": [[7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7], [7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7], [7, 5, 7, 1, 7, 5, 7, 1, 7, 5, 7, 1, 7, 5, 7, 1, 7, 5], [7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7], [1, 5, 5, 7, 1, 5, 5, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5], [1, 5, 1, 7, 1, 5, 1, 7, 0, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 5 5 7 1 5 5 7 1
1 5 1 7 1 5 1 7 1
7 1 5 1 7 1 5 1 7
7 7 7 5 7 7 7 5 7
7 7 5 5 7 7 5 5 7
7 5 7 1 7 5 7 1 7
7 7 7 5 7 7 7 5 7
1 5 5 7 1 5 5 7 1
1 5 1 7 1 5 1 7 1
7 1 5 1 7 1 5 1 7
``` | 3,198 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,094 | [
"<note1>\n<description>Look for a single color that occupies a contiguous rectangular region (a filled rectangle or a block). This color usually forms a solid rectangle and is the primary object the transformation isolates.</description>\n<example>Imagine a grid where a large area of one color fills most of a subgr... | [{"input": [[9, 5, 9, 8, 6, 0, 6, 9, 7, 9, 6, 2, 8, 4, 8, 6, 7, 9, 9], [7, 9, 0, 4, 5, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1], [6, 2, 8, 7, 2, 5, 9, 1, 1, 1, 7, 1, 1, 1, 1, 1, 8, 5, 0], [2, 9, 3, 0, 8, 1, 0, 1, 1, 7, 1, 1, 1, 1, 1, 1, 4, 3, 5], [0, 2, 3, 2, 9, 5, 6, 1, 1, 1, 1, 1, 7, 1, 1, 1, 5, 4, 0], [6, 7, 6, 4, ... | [{"input": [[3, 5, 8, 3, 8, 3, 8, 7, 7, 3, 7, 3, 3, 5], [8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 2, 2], [8, 7, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8, 3, 7], [7, 5, 8, 8, 8, 8, 8, 8, 5, 8, 8, 7, 8, 5], [5, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 7, 7, 7], [8, 5, 8, 8, 5, 8, 8, 8, 8, 8, 8, 5, 2, 5], [8, 5, 8, 8, 8, 8, 5, 8, 8, 8, 8, 5, 5, 3], ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
8 5 5 8 5 5 5 5 8
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
8 5 5 8 5 5 5 5 8
``` | 3,390 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,780 | [
"<note1>\n<description>Locate the object by finding the color that differs from the background and compute its minimal bounding rectangle (min/max row and column). This isolates the region you should transform and ignores unrelated cells.</description>\n<example>Imagine a grid with a blue patch on a black backgroun... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0], [0, 0, 0, 2, 2, 2, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 2, 2, 2, 0, 0], [0, 0, 2, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0, 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, 2, 2, 2, 2, 2, 2, 0], [0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 0, 2, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 0 0
0 1 1 1 1 1 1 0 0
0 1 1 0 0 0 0 0 0
0 1 1 1 1 1 1 0 0
0 1 1 1 1 1 1 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
``` | 1,076 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,416 | [
"<note1>\n<description>Look for a single column that is constant across every row and treat it as a divider. When one column is uniform, it cleanly separates the grid into two regions you can analyze independently.</description>\n<example>Imagine a 6×5 grid whose 3rd column is all blue; that blue column is a divide... | [{"input": [[8, 5, 8, 5, 5, 8, 5, 7, 2, 2, 5, 5, 5, 5, 2], [8, 8, 5, 8, 8, 8, 8, 7, 5, 5, 2, 2, 2, 2, 2], [5, 8, 8, 8, 8, 8, 5, 7, 5, 5, 2, 2, 2, 2, 5], [8, 5, 8, 8, 5, 8, 8, 7, 2, 5, 2, 5, 5, 2, 5], [5, 5, 5, 8, 5, 5, 8, 7, 2, 2, 2, 5, 2, 5, 2], [8, 8, 8, 8, 8, 8, 5, 7, 5, 2, 2, 5, 5, 5, 5], [5, 5, 8, 8, 5, 5, 5, 7, 2... | [{"input": [[8, 8, 1, 8, 8, 8, 8, 1, 8, 8, 8, 8, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 7, 6, 6, 6, 6, 1, 6, 1, 6, 6, 6, 6, 6], [1, 8, 1, 8, 8, 1, 8, 8, 1, 1, 8, 1, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [1, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 7, 6, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6], ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 3 1 1 1 1 1 3 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 3 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 3 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 ... | 3,712 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,064 | [
"<note1>\n<description>Look for a single full-length row or column made entirely of one color that spans the grid; this color usually acts as a divider and should be ignored when isolating the two areas. Treat that line as a boundary rather than part of the shapes you will transform.</description>\n<example>Imagine... | [{"input": [[0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 1, 1, 1, 0, 0], [0, 0, 4, 0, 0, 1, 1, 1, 0, 0], [0, 0, 4, 1, 1, 1, 1, 1, 0, 0], [0, 0, 4, 1, 1, 1, 0, 0, 0, 0], [0, 0, 4, 1, 1, 1, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [5, 8, 4, 0, 0, 0, 0, 0, 0, 0], [9, 6, 4, 0, 0, 0, 0... | [{"input": [[3, 7, 4, 0, 0, 0, 0, 0, 0, 0], [6, 8, 4, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 0, 4, 0, 1, 0, 0, 1, 0, 0], [0, 0, 4, 0, 1, 1, 1, 1, 0, 0], [0, 0, 4, 1, 1, 1, 0, 0, 0, 0], [0, 0, 4, 0, 0, 1, 0, 0, 0, 0], [0, 0, 4, 0, 0, 1, 1, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 3 0 0 7 0 0
0 3 3 7 7 0 0
3 3 3 0 0 0 0
0 0 6 0 0 0 0
0 0 6 8 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
``` | 1,360 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,286 | [
"<note1>\n<description>Look for connected components of non-background pixels and treat each as an independent object. The transformation acts on whole objects, not on individual stray pixels, so grouping by connectivity is the first step.</description>\n<example>Imagine a grid with three separated colored blobs. I... | [{"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, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 6 6 0 0 0
0 0 0 0 0 0 0 0 0 6 6 0 0 0
0 0 0 0 0 0 0 0 0 6 6 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0 0 0 0
0 4 4 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 6 6 0 0 0 0 0 0 0 0 0 0
0 0 6 6 0 0 0 0 0 0 0 0 0 0
0 0 6 6 0 0 0 0 0 0 0 0 0 0
0 0 6 6 ... | 2,582 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,296 | [
"<note1>\n<description>Look for a single isolated non-background pixel that is the source of the change; treat its color and coordinates as the anchor for the transformation. This anchor is usually unique and determines the color used to draw the new pattern.</description>\n<example>Imagine a grid with one green pi... | [{"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, 5, 0], [0, 0, 0, 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, 9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 9 0
0 0 0 0 0 0 9 0 0
0 0 0 0 0 9 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 0
4 0 0 0 0 0 0 0 0
``` | 1,592 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,554 | [
"<note1>\n<description>Look first for the minority color(s) that differ from the dominant background. These rare pixels act as anchors that mark the corners or edges of the region the transformation will focus on.</description>\n<example>Imagine a mostly-blue grid with a few red pixels only at the top-left and bott... | [{"input": [[6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, ... | [{"input": [[4, 0, 0, 0, 0, 0, 0, 4], [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, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
4 4 0 0 0 0 0 4
0 4 4 0 0 0 4 0
0 0 4 4 0 4 0 0
0 0 0 4 4 0 0 0
0 0 0 4 4 4 0 0
0 0 4 0 0 4 4 0
0 4 0 0 0 0 4 4
4 0 0 0 0 0 4 4
0 4 0 0 0 4 4 0
0 0 4 0 4 4 0 0
0 0 0 4 4 0 0 0
0 0 4 4 4 0 0 0
0 4 4 0 0 4 0 0
4 4 0 0 0 0 4 0
4 4 0 0 0 0 0 4
0 4 4 0 0 0 4 0
0 0 4 4 0 4 0 0
0 0 0 4 4 0 0 0
0 0 0 4 4 4 0 0
0 0 4 0 0 4 ... | 1,850 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,182 | [
"<note1>\n<description>Look for a small, compact object that sits inside a larger uniform area: one color usually forms a rectangle, and a different color appears only as a small patch inside it. That inner patch is the key feature to focus on.</description>\n<example>Imagine a grid where most cells are color A, an... | [{"input": [[7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7], [5, 5, 5, 5, 7, 7], [5, 5, 5, 5, 7, 7], [5, 5, 5, 5, 7, 7], [5, 5, 5, 5, 7, 7], [5, 5, 5, 5, 7, 7], [5, 5, 5, 5, 7, 7], [5, 5, 5, 5, 7, 7], [5, 8, 8, 5, 7, 7], [5, 8, 8, 5, 7, 7], [5, 8, 8, 5, 7, 7], [5, 8, 8, 5, 7, 7], [5, 8, 8, 5, 7, 7], [5, 8, 8... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]], "output... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 1 1 7 7
7 7 7 7 7 7 7 1 1 7 7
7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7
``` | 2,478 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,682 | [
"<note1>\n<description>Check the output dimensions first: if the output is an integer multiple of the input in both directions, the transformation is likely a uniform tiling or scaling. This reduces the problem to finding the tile size and how the tile is arranged.</description>\n<example>For instance, if an input ... | [{"input": [[0, 0, 0, 0], [0, 0, 5, 0], [0, 0, 0, 0], [0, 0, 0, 0]], "output": [[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, ... | [{"input": [[9, 9, 9, 9], [9, 9, 9, 0]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0], [9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 0, 0, 0, 0, 0]]}] | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 0 9 9 9 0 9 9 9 0 9 9 9 0
9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0
9 9 9 0 9 9 9 0 9 9 9 0 0 0 0 0
``` | 1,978 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,170 | [
"<note1>\n<description>Find the single non-background color and treat its connected component as the motif to transform. Working with that whole component (not individual pixels) makes it easier to see how it is enlarged or copied in the output.</description>\n<example>Imagine a small L-shaped cluster of one color ... | [{"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], [1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 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... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 1, 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... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 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 ... | 3,466 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,026 | [
"<note1>\n<description>Find the background by frequency: the background is usually the color that occupies most cells in the grid. This color is the one that will remain unchanged in the output and is the reference for where to draw the new object.</description>\n<example>Imagine a 6×6 grid where 30 cells are color... | [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4], [4, 4, 4, 4, 4, 4, 9, 0, 4, 4, 4], [4, 9, 4, 4, 4, 1, 4, 4, 0, 4, 4], [4, 4, 4, 0, 4, 4, 4, 4, 4, 1, 4], [4, 0, 4, 4, 4, 0, 0, 4, 4, 1, 4], [4, 9, 4, 9, 4, 4, 4, 4, 4, 4, 9], [4, 4, 9, 4, 4, 4, 4, 4, 0, 4, 4], [0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 1, 0, 4, 4, 4, 4, ... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 4, 7, 9, 0, 4, 7, 7], [7, 7, 7, 7, 0, 7, 7, 7, 9, 7, 7, 7, 7, 7], [7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 0, 4, 4, 7], [7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7, 9, 7], [7, 7, 7, 7, 7, 7, 9, 7, 4, 4, 7, 0, 7, 7], [9, 7, 7, 0, 7, 1, 7, 4, 7, 7, 0, 7, 7, 9], [0, 4, 7, 7, 7, 9, 7, 4, 7, 0, 0, 7, 4, 7], ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 2 2 2 7 7 7 7 7 7 7
7 7 7 7 2 1 2 7 7 7 7 7 7 7
7 7 7 7 2 2 2 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
7 7 7 7 7 7 7 7 7 7 7 7 7 7
``` | 3,322 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,498 | [
"<note1>\n<description>Look first for a uniform enlargement: if every output region looks like a single-color square and the grid is a whole-number multiple of the input size, the transformation is likely a uniform scale. This tells you to treat each input cell as a single unit that is being expanded.</description>... | [{"input": [[2, 6, 1, 6], [2, 1, 1, 6], [1, 2, 7, 7]], "output": [[2, 2, 2, 6, 6, 6, 1, 1, 1, 6, 6, 6], [2, 2, 2, 6, 6, 6, 1, 1, 1, 6, 6, 6], [2, 2, 2, 6, 6, 6, 1, 1, 1, 6, 6, 6], [2, 2, 2, 1, 1, 1, 1, 1, 1, 6, 6, 6], [2, 2, 2, 1, 1, 1, 1, 1, 1, 6, 6, 6], [2, 2, 2, 1, 1, 1, 1, 1, 1, 6, 6, 6], [1, 1, 1, 2, 2, 2, 7, 7, 7... | [{"input": [[9, 9, 0], [5, 5, 0], [7, 4, 7]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
9 9 9 9 9 9 9 9 0 0 0 0
9 9 9 9 9 9 9 9 0 0 0 0
9 9 9 9 9 9 9 9 0 0 0 0
9 9 9 9 9 9 9 9 0 0 0 0
5 5 5 5 5 5 5 5 0 0 0 0
5 5 5 5 5 5 5 5 0 0 0 0
5 5 5 5 5 5 5 5 0 0 0 0
5 5 5 5 5 5 5 5 0 0 0 0
7 7 7 7 4 4 4 4 7 7 7 7
7 7 7 7 4 4 4 4 7 7 7 7
7 7 7 7 4 4 4 4 7 7 7 7
7 7 7 7 4 4 4 4 7 7 7 7
``` | 1,794 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,392 | [
"<note1>\n<description>Look for a complete row or column made of one color; such a full line usually acts as a deliberate divider between two regions. Identifying that line is the first step because it tells you which half of the grid to focus on.</description>\n<example>Imagine a grid where one row is entirely col... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0], [9, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 9, 0, 0], [0, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 9], [0, 0, 9, 0, 0, 0, 0, 0, 0... | [{"input": [[8, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8], [8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 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... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
3 3 8 8 8 8 8 8 3 8 8 8 8 8 8 8 8 8 8 3 8 8 8 3 8 3
3 8 8 8 8 8 3 8 8 8 3 8 8 3 8 8 8 8 8 8 8 8 8 3 8 8
8 8 8 3 8 8 3 8 8 8 3 8 8 8 8 8 8 8 3 3 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 8 8 8 8 8 8
8 8 8 8 8 8 3 8 8 8 8 8 3 8 8 8 8 3 8 8 8 8 8 8 8 8
8 3 8 3 3 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 8 3 8 8
8 8 ... | 3,688 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,986 | [
"<note1>\n<description>Find the object that is being transformed by looking for a connected component made of a single color that appears only once in the input. That isolated object is the candidate for the change in the output.</description>\n<example>Imagine a grid where every other colored object is repeated or... | [{"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, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 7, 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, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 0, 0, 8, 0, 5, 5], [0, 0, 0, 0, 5, 5, 0, 8, 8, 0, 0, 0], [0, ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 1 0 1 0 0 0 0 0 0
0 0 0 1 0 1 0 0 0 0 0 0
0 0 0 0 1 1 1 0 0 0 0 0
0 0 0 0 5 5 0 0 1 0 3 3
0 0 0 0 5 5 0 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 4 4
0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
``` | 2,282 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,734 | [
"<note1>\n<description>Decide whether the transformation is a global fill: if every output cell is the same color, the rule is likely \"choose one color and paint the whole grid with it.\" This applies whenever outputs show uniformity across all positions and across examples.</description>\n<example>Imagine several... | [{"input": [[0, 4, 0, 7, 0, 0, 0, 9, 7, 0, 0, 0, 9, 9, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 7, 1, 5, 0, 0, 0, 9, 4, 0, 0], [0, 0, 0, 0, 0, 0, 6, 9, 9, 5, 0, 0, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 5, 3, 8, 5, 0, 0, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 1, 5, 5, 2, 0, 0, 0, 0, ... | [{"input": [[0, 2, 0, 0, 2, 2, 2, 2, 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, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 9, 3, 9, 0, 0, 0], [0, 2, 9, 0, 0, 0, 0, 0, 2, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 ... | 3,030 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,570 | [
"<note1>\n<description>First, identify the background by frequency: the color that occupies most cells is usually unchanged. Everything else is a candidate “seed” color that the transformation acts on. This reduces the problem to deciding which seed(s) matter and how they change.</description>\n<example>Imagine a 7... | [{"input": [[3, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, ... | [{"input": [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [5, 1, 1, 1, 1], [1, 1, 1, 1, 1], [5, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [5, 1, 1, 1, 1], [1, 2, 1, 2, 1]], "output": [[1, 1, 1, 5, 5], [1, 5, 5, 1, 1], [5, 1, 1, 5, 5], [1, 5, 5, 1, 1], [5, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 5, 5], [1, 5, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 1 1 5 5
1 5 5 1 1
5 1 1 5 5
1 5 5 1 1
5 1 1 1 1
1 1 1 1 1
1 1 1 5 5
1 5 5 1 1
5 1 1 1 1
1 2 1 2 1
``` | 3,866 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,690 | [
"<note1>\n<description>Look for the large contiguous filled rectangle that is not the background. That rectangle is usually the object to be transformed and is easy to identify because it is a single color occupying a rectangular block.</description>\n<example>Imagine a grid with a single solid blue rectangle and a... | [{"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, 4, 4, 4, 4, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 5], [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]... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0
0 5 8 9 3 8 0 0
0 5 8 9 3 8 0 0
0 5 8 9 3 8 0 0
0 5 8 9 3 8 0 0
0 5 8 9 3 8 0 0
0 5 8 9 3 8 0 0
0 5 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 0 0
0 0 8 9 3 8 ... | 3,986 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,346 | [
"<note1>\n<description>Spot the background by frequency: the color that fills most of the grid is usually the background. Treat any cell with a different color as a foreground pixel and record its coordinates (row, column). This reduces the problem to a small set of meaningful points to analyze.</description>\n<exa... | [{"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,... | [{"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, 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, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
7 8 1
7 6 2
1 4 4
``` | 3,642 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,594 | [
"<note1>\n<description>Look for a full row or full column that is entirely one color (the background). Such a uniform line usually serves as a deliberate divider and is not part of the pattern to keep. Treat that line as a separator rather than content.</description>\n<example>Imagine a grid where row 6 is every ce... | [{"input": [[4, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5], [4, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 5], [5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 4, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 5, 5, 5, 5, 5, 4, 5, 4... | [{"input": [[2, 9, 0, 3, 3, 6, 1, 1, 1, 6, 3, 1, 4], [7, 1, 6, 0, 3, 1, 1, 1, 9, 9, 1, 1, 1], [2, 4, 6, 3, 6, 1, 1, 1, 1, 1, 1, 6, 4], [2, 1, 8, 3, 4, 1, 1, 1, 1, 8, 3, 0, 1], [1, 8, 8, 8, 0, 7, 1, 1, 0, 8, 1, 1, 7], [3, 2, 4, 8, 9, 4, 1, 3, 2, 4, 0, 1, 6], [8, 1, 8, 1, 0, 1, 1, 1, 1, 1, 0, 1, 6], [1, 1, 9, 0, 1, 1, 1,... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
2 9 0 3 3 6
7 1 6 0 3 1
2 4 6 3 6 1
2 1 8 3 4 1
1 8 8 8 0 7
3 2 4 8 9 4
8 1 8 1 0 1
1 1 9 0 1 1
8 9 3 7 9 9
1 1 3 9 1 3
1 2 8 1 2 7
``` | 2,890 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,203 | [
"<note1>\n<description>Look for a single non-background color that consistently forms identical hollow rectangular frames in every example. Treat that color as the object to analyze rather than the background. Recognizing repeated frames simplifies the rest of the transformation.</description>\n<example>Imagine a g... | [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 1, 8, 8, 8, 1, 8... | [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8... | arc 2 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
8 8 8 8 8 6 8 8 6 8 8 8 8 8 8
8 8 8 8 8 6 1 1 1 1 1 8 8 8 8
8 8 8 8 8 6 1 8 6 8 1 8 8 8 8
6 6 6 6 6 6 1 6 6 6 1 6 6 6 6
8 8 8 8 8 6 1 8 6 8 1 8 8 8 8
8 8 8 8 8 6 1 1 1 1 1 8 8 8 8
8 8 8 8 8 6 8 8 6 8 8 8 8 8 8
8 8 8 8 8 6 8 8 6 8 8 8 8 8 8
8 8 8 8 8 6 8 8 6 8 8 8 8 8 8
8 8 8 1 1 1 1 1 6 8 8 8 8 8 8
8 8 8 1 8 6 8 1 ... | 2,499 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,364 | [
"<note1>\n<description>Look for a single color that appears many times and forms a compact, contiguous region in the input. That color is usually the one being transformed or the anchor for the output.</description>\n<example>Imagine a grid where color A appears in a single block while other colors are scattered. C... | [{"input": [[1, 1, 1, 1, 6, 4, 3], [6, 2, 6, 4, 3, 4, 9], [4, 9, 1, 1, 9, 9, 5], [3, 4, 5, 6, 5, 9, 9], [9, 1, 9, 9, 1, 4, 3], [4, 3, 5, 4, 4, 6, 3], [1, 9, 4, 9, 3, 2, 4], [9, 9, 3, 1, 6, 6, 5]], "output": [[9, 4, 1, 3, 6, 5, 2], [9, 4, 1, 3, 6, 5, 2], [9, 4, 1, 3, 6, 5, 0], [9, 4, 1, 3, 6, 5, 0], [9, 4, 1, 3, 6, 5, 0... | [{"input": [[4, 4], [4, 2], [4, 5], [4, 1], [4, 4], [5, 1], [1, 2], [1, 4], [4, 2], [5, 1], [4, 1], [5, 5], [4, 4], [1, 5], [1, 1], [5, 1], [5, 4], [4, 4], [1, 5], [5, 1], [2, 4]], "output": [[4, 1, 5, 2], [4, 1, 5, 2], [4, 1, 5, 2], [4, 1, 5, 2], [4, 1, 5, 0], [4, 1, 5, 0], [4, 1, 5, 0], [4, 1, 5, 0], [4, 1, 5, 0], [4... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
4 1 5 2
4 1 5 2
4 1 5 2
4 1 5 2
4 1 5 0
4 1 5 0
4 1 5 0
4 1 5 0
4 1 5 0
4 1 5 0
4 1 0 0
4 1 0 0
4 0 0 0
4 0 0 0
4 0 0 0
4 0 0 0
``` | 1,660 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,836 | [
"<note1>\n<description>Compare entire rows between input and output: if every output row equals some input row (possibly after a simple rearrangement), the transformation is a row-level permutation rather than a pixel-by-pixel recoloring. This narrows the problem to finding which input row corresponds to which outp... | [{"input": [[6, 9, 8, 5, 6, 7, 9, 4], [3, 3, 7, 7, 9, 7, 5, 6], [7, 1, 6, 5, 8, 7, 4, 1], [8, 2, 7, 7, 3, 7, 1, 3], [8, 3, 3, 3, 8, 4, 5, 8], [9, 8, 9, 7, 4, 4, 3, 9], [7, 8, 5, 6, 6, 8, 5, 8], [9, 1, 8, 8, 4, 4, 5, 1]], "output": [[9, 7, 6, 5, 8, 9, 6, 4], [5, 7, 9, 7, 7, 3, 3, 4], [4, 7, 8, 5, 6, 1, 7, 4], [1, 7, 3, ... | [{"input": [[6, 5, 3, 6, 9, 5, 9, 1, 5], [6, 5, 6, 5, 6, 9, 9, 7, 8], [6, 6, 6, 8, 9, 4, 1, 7, 7], [7, 6, 5, 1, 2, 6, 9, 2, 3], [8, 7, 1, 7, 4, 8, 3, 5, 8], [7, 2, 6, 3, 3, 9, 7, 8, 3], [8, 4, 1, 3, 2, 8, 8, 9, 6], [7, 9, 4, 1, 6, 1, 4, 5, 2], [5, 2, 8, 1, 2, 4, 7, 1, 4]], "output": [[1, 9, 5, 9, 6, 3, 5, 6, 5], [7, 9,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 9 5 9 6 3 5 6 5
7 9 9 6 5 6 5 6 5
7 1 4 9 8 6 6 6 5
2 9 6 2 1 5 6 7 5
5 3 8 4 7 1 7 8 5
8 7 9 3 3 6 2 7 5
9 8 8 2 3 1 4 8 5
5 4 1 6 1 4 9 7 5
1 7 4 2 1 8 2 5 5
``` | 1,132 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,442 | [
"<note1>\n<description>Check the dimensions first: the output's width equals the input's height and its height equals the input's width. That tells you the output is a transposed grid and you should treat the input as a list of column-vectors to analyze.</description>\n<example>If an input is 5 rows by 3 columns, t... | [{"input": [[9, 1, 7, 7, 5, 6, 9, 7, 5, 2, 4, 1, 1, 5], [5, 2, 5, 6, 4, 5, 9, 4, 1, 4, 9, 5, 2, 9], [9, 9, 5, 2, 1, 4, 4, 6, 2, 8, 2, 4, 4, 9], [2, 5, 5, 9, 8, 5, 9, 5, 2, 2, 4, 6, 8, 4], [5, 5, 9, 5, 9, 9, 5, 7, 1, 9, 1, 5, 7, 9]], "output": [[5, 9, 4, 2, 1, 7, 6, 8], [5, 9, 4, 2, 1, 7, 6, 8], [5, 9, 4, 2, 1, 7, 6, 8]... | [{"input": [[8, 3, 5, 2, 5, 8, 2, 2, 3, 9, 3, 3, 8, 8, 6, 6, 5, 8, 2, 3, 8, 6], [2, 3, 5, 5, 5, 4, 4, 5, 5, 5, 3, 6, 8, 9, 5, 8, 1, 4, 8, 3, 6, 1], [2, 1, 4, 6, 1, 2, 8, 8, 3, 6, 9, 8, 5, 5, 5, 2, 2, 5, 2, 3, 6, 2], [5, 8, 3, 1, 8, 3, 3, 3, 9, 3, 3, 5, 2, 6, 2, 6, 5, 6, 5, 4, 8, 6], [2, 5, 5, 3, 6, 2, 1, 3, 3, 2, 2, 4,... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
5 2 3 8 6 1 4 9
5 2 3 8 6 1 4 9
5 2 3 8 6 1 4 9
5 2 3 8 6 1 4 9
5 2 3 8 6 1 4 9
5 2 3 8 6 1 4 9
5 2 3 8 6 1 4 0
5 2 3 8 6 1 4 0
5 2 3 8 6 1 4 0
5 2 3 8 6 1 4 0
5 2 3 8 6 1 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 0 0
5 2 3 8 6 0 ... | 1,738 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,424 | [
"<note1>\n<description>Find the background color first: the color that fills most of the grid. Everything that is not that color is a candidate object to be moved or repositioned. Identifying the background makes it easy to treat isolated pixels and small shapes the same way.</description>\n<example>Imagine a 7×7 g... | [{"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 9, 2, 2, 2, 2, 2, 6, 2, 2, 2], [2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2], ... | [{"input": [[6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6], [6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 1 7 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 8 2 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
``` | 1,720 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,098 | [
"<note1>\n<description>Look for concentric rectangular bands: many tasks use a frame of one color, a second color inside it, and a third color inside that. When you see three or more distinct colors arranged in nested rectangular outlines, treat each color as a layer and label them by their distance from the outer ... | [{"input": [[3, 3, 3, 3, 3, 3, 3, 3], [3, 6, 6, 6, 6, 6, 6, 3], [3, 6, 3, 3, 3, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, 3], [3, 6, 3, 5, 5, 3, 6, ... | [{"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3], [3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3], [3, 7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 3], [3, 7, 3, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 3, 7, 3], [3, 7, 3, 1, 9, 1, 1, 1, 1, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1
1 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3 1
1 3 7 3 3 3 3 3 3 3 3 3 3 3 3 7 3 1
1 3 7 3 1 1 1 1 1 1 1 1 1 1 3 7 3 1
1 3 7 3 1 9 9 9 9 9 9 9 9 1 3 7 3 1
1 3 7 3 1 9 9 9 9 9 9 9 9 1 3 7 3 1
1 3 7 3 1 1 1 1 1 1 1 1 1 1 3 7 3 1
1 3 7 3 3 3 3 3 3 3 3 3 3 3 ... | 2,394 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,802 | [
"<note1>\n<description>Look for the background: the color that fills most cells and forms a continuous outer border. This color is typically what gets removed in the transformation, so isolating it helps reduce noise and focus on the meaningful region.</description>\n<example>Imagine a 7×7 grid where every cell is ... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 2, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, ... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7,... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
3 6 0 0 0 0 0 0 0 0 0
6 0 5 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0 0 0
0 6 0 0 0 0 8 8 3 0 0
3 6 1 1 1 8 3 0 0 0 0
6 3 1 0 0 6 3 8 8 0 0
3 6 3 1 1 1 5 6 8 0 0
5 5 3 5 8 3 0 6 0 0 0
6 5 3 0 1 0 5 5 3 0 6
5 6 1 0 1 0 0 3 0 1 0
5 6 3 1 6 3 5 6 0 0 0
6 6 8 5 6 0 3 0 0 0 0
3 3 3 6 1 6 1 0 0 0 0
``` | 3,098 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,166 | [
"<note1>\n<description>Start by listing every non-background connected component and recording its color, bounding box (top, bottom, left, right), and size. Knowing these basic properties lets you compare how each object is treated in the outputs.</description>\n<example>Imagine a grid with three colored blobs: one... | [{"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, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 6, 6, 0, 0, 0, 0, 0], [3, 3, 2, 0, 2, 2, 3, 3, 3, ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 2 2 0 0 0 0
0 0 0 0 2 2 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
``` | 1,462 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,374 | [
"<note1>\n<description>Identify the two anchor pixels of interest: the task uses exactly two non-background cells in the input. Those two coordinates are the reference points for the transformation and should be treated as fixed.</description>\n<example>For instance, if a 7×7 grid contains a single green pixel at (... | [{"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, 4, 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, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [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... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 3 3 3 3 3 3 3 3
0 0 0 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 3
``` | 1,670 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,128 | [
"<note1>\n<description>Find the background: the color that fills most cells. Treat any other color as a marker (an object) to be preserved. This separation clarifies which pixels are candidates for change and which must remain unchanged.</description>\n<example>Imagine a 7×7 grid where 42 cells are color A and two ... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, ... | [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 7, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9,... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 4 9 4 9 4 9 4 9
9 9 9 7 9 9 9 9 9
``` | 2,424 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,734 | [
"<note1>\n<description>Spot the anchor: one color in the input appears as a single pixel in every example. That isolated pixel is the origin of the transformation and will be the center of a filled shape in the output.</description>\n<example>Imagine a 6×6 grid where color A appears exactly once at (2,3). In the ou... | [{"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, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 2, ... | [{"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, 2, 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], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 2 0 0 0 0 0 0 0 0
0 0 0 0 0 0 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 0 0 0 0 0 0 0 0 2 0 0 0 0
0 0 0 0 0 0 0 0 0 0 2 0 0 0
1 0 0 0 3 0 0 0 0 0 0 2 0 0
0 0 0 3 2 0 0 0 0 0 0 0 2 0
0 0 3 0 0 2 0 0 0 0 0 0 0 2
0 3 0 0 ... | 3,030 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,976 | [
"<note1>\n<description>Look for a single color that is rare or unique in the input; such a color often acts as a marker or seed for a larger transformation. When one color appears only a few times or is the only color not present in the majority of the grid, treat it as a candidate to drive the change.</description... | [{"input": [[7, 3, 1, 2, 3, 5, 7, 6, 7, 1, 6, 7, 7, 6, 2, 3, 2, 1, 7, 5, 7, 5, 2, 3, 5, 6, 2, 3, 6], [6, 1, 5, 3, 3, 6, 7, 5, 5, 7, 6, 5, 5, 1, 5, 5, 5, 6, 5, 7, 7, 5, 2, 7, 6, 5, 5, 3, 2], [1, 2, 2, 6, 3, 6, 5, 5, 6, 3, 2, 5, 6, 3, 6, 2, 6, 1, 2, 2, 7, 7, 1, 2, 3, 3, 3, 7, 7], [2, 7, 5, 2, 7, 6, 5, 1, 2, 1, 7, 7, 3, 5... | [{"input": [[1, 0, 8, 1, 4, 4, 7, 0, 4, 8, 8, 1, 0, 7, 1, 7, 1], [0, 8, 8, 4, 0, 8, 8, 1, 4, 1, 7, 0, 1, 8, 8, 0, 8], [1, 0, 4, 0, 0, 1, 4, 8, 7, 1, 7, 1, 0, 8, 8, 8, 8], [8, 4, 1, 8, 7, 0, 1, 7, 1, 8, 8, 1, 1, 1, 1, 4, 7], [1, 8, 8, 7, 7, 1, 7, 8, 8, 1, 7, 4, 0, 1, 7, 7, 1], [0, 7, 1, 1, 8, 7, 4, 0, 8, 8, 1, 1, 0, 8, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
1 0 2 1 4 4 7 0 4 8 8 1 0 7 2 7 1
0 8 8 2 0 8 8 1 4 1 7 0 1 2 8 0 8
1 0 4 0 2 1 4 8 7 1 7 1 2 8 8 8 8
8 4 1 8 7 2 1 7 1 8 8 2 1 1 1 4 7
1 8 8 7 7 1 2 8 8 1 2 4 0 1 7 7 1
0 7 1 1 8 7 4 2 8 2 1 1 0 8 7 8 7
4 0 4 1 7 1 1 8 2 4 8 4 0 7 8 8 7
8 1 1 7 8 4 4 2 7 2 4 7 8 0 4 4 4
4 0 0 7 7 4 2 1 7 8 2 7 4 7 7 7 1
8 8 4 1 8 ... | 2,272 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,702 | [
"<note1>\n<description>Look for small, repeated local structures: many ARC tasks use a small motif (e.g., a 3×3 block) that is repeated across the grid. Recognizing that motif is the first step because the transformation usually applies the same local rule everywhere.</description>\n<example>Imagine a grid mostly f... | [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 3, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 2, 9, ... | [{"input": [[7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[4, 8, 4, 7, 7, 7, 7, 7, 7, 7, 7, 1, 2, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}] | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
4 8 4 7 7 7 7 7 7 7 7 1 2 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7
``` | 2,998 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,286 | [
"<note1>\n<description>First separate the grid into connected components and treat each as an independent object. Many ARC tasks recolor whole objects rather than altering individual pixels, so identifying components is the natural first step.</description>\n<example>Imagine a grid with three separated blobs of dif... | [{"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, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 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, 2, 2, 2, 0, 0, 0], [0, 0, 0, 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, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 1 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 4 0 0 0 0 0 0 0
0 0 0 0 ... | 2,582 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,286 | [
"<note1>\n<description>Look for a one-to-one mapping between input colors and output colors: the same input color in different places becomes the same output color everywhere. If you can pair each input color with its corresponding output color consistently across examples, you have a global recoloring rule rather ... | [{"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, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 4, 4, 3, 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,... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 4, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 4, 6, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 4, 1, 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], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 0 0 0 6 6 0 0 0
0 0 0 0 1 1 0 0 0 6 6 0 0 0
0 0 0 0 1 1 0 0 0 6 6 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 2 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 0 0 0 0 0 0 0 2 2 0 0 0 0
0 0 0 0 ... | 2,582 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,956 | [
"<note1>\n<description>Look for the single color that appears as a compact, solid square: its bounding box will have equal width and height and will contain only that color. This compact square is the likely target for the transformation.</description>\n<example>Imagine a grid with many colored blobs but one small ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 2, 2, 2, 2, 2, 2, 0, 0, 0], [0, 2, 2, 8, 8, 8, 2, 0, 0, 0], [0, 2, 2, 8, 8, 8, 2, 0, 0, 0], [0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, ... | arc 1 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 6
6 6 6
6 6 6
``` | 3,252 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,378 | [
"<note1>\n<description>Compare input and output to find the preserved region: often the output keeps the original rows and columns unchanged and only adds new rows/columns. Identifying that preserved block tells you where the transformation is applied relative to the whole grid.</description>\n<example>If a 3×3 inp... | [{"input": [[0, 0, 0, 0, 0], [6, 0, 6, 6, 6], [0, 6, 0, 6, 0], [0, 0, 6, 6, 6]], "output": [[0, 0, 0, 0, 0], [6, 0, 6, 6, 6], [0, 6, 0, 6, 0], [0, 0, 6, 6, 6], [0, 0, 6, 6, 6], [0, 6, 0, 6, 0], [6, 0, 6, 6, 6], [0, 0, 0, 0, 0]]}, {"input": [[0, 7, 0, 0], [7, 0, 0, 7], [7, 0, 7, 7], [7, 0, 7, 7], [7, 7, 7, 0]], "output"... | [{"input": [[6, 6, 0], [0, 0, 6], [0, 6, 6]], "output": [[6, 6, 0], [0, 0, 6], [0, 6, 6], [0, 6, 6], [0, 0, 6], [6, 6, 0]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 0
0 0 6
0 6 6
0 6 6
0 0 6
6 6 0
``` | 674 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,552 | [
"<note1>\n<description>Isolate the anchor: find the unique non-background color and its minimal bounding rectangle. The bounding rectangle (top, bottom, left, right) is the key reference for all subsequent steps because the transformation is driven by that object's geometry.</description>\n<example>If you see a sin... | [{"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, 2, 2, 0], [0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0]], "output": [[0, 3, 3, 3, 3, 3, 3], [0, 0, 3, 3, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0], [0, 3, 3, 3, 3, 3, 0], [0, 3, 3, 3, 3, 3, 0], [0, 3, 3, 3, 3, 3, 3]]}, {"input": [[0, 0, ... | [{"input": [[0, 0, 0, 0, 0], [0, 0, 2, 2, 0], [0, 0, 2, 2, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]], "output": [[0, 3, 3, 3, 3], [0, 0, 3, 3, 0], [0, 3, 3, 3, 0], [0, 3, 3, 3, 3], [0, 3, 3, 3, 3]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 3 3 3 3
0 0 3 3 0
0 3 3 3 0
0 3 3 3 3
0 3 3 3 3
``` | 848 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,836 | [
"<note1>\n<description>Look for a mirror relationship between left and right halves: many tasks place the same colored pixels in the mirrored column positions. This is a horizontal reflection of the whole grid rather than a rotation or vertical flip.</description>\n<example>Imagine a 5×3 input where the left column... | [{"input": [[1, 0, 8, 0, 0, 0, 0, 0], [0, 1, 0, 8, 0, 0, 0, 0], [2, 0, 0, 3, 0, 0, 0, 0], [8, 4, 3, 0, 0, 0, 0, 0], [1, 1, 1, 4, 0, 0, 0, 0], [0, 2, 0, 8, 0, 0, 0, 0], [1, 4, 1, 0, 0, 0, 0, 0], [0, 8, 0, 1, 0, 0, 0, 0]], "output": [[1, 0, 8, 0, 0, 8, 0, 1], [0, 1, 0, 8, 8, 0, 1, 0], [2, 0, 0, 3, 3, 0, 0, 2], [8, 4, 3, ... | [{"input": [[8, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 8, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0], [1, 3, 1, 0, 0, 0, 0, 0, 0], [0, 4, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 8, 0, 0, 0, 0, 0, 0]], "output": [[8, 0, 0, 0, 0, 0, 0, 0, 8], [0, 2,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
8 0 0 0 0 0 0 0 8
0 2 0 8 0 8 0 2 0
0 0 2 0 0 0 2 0 0
0 3 0 0 0 0 0 3 0
0 0 2 2 0 2 2 0 0
1 3 1 0 0 0 1 3 1
0 4 3 0 0 0 3 4 0
0 0 0 0 0 0 0 0 0
2 0 8 0 0 0 8 0 2
``` | 1,132 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,098 | [
"<note1>\n<description>Check whether the output is a uniform tiling of the input: if every output block is an exact copy of the input, the transformation is a simple scaling (each input cell becomes a block of the same size). This reduces the problem to understanding how the input itself was created.</description>\... | [{"input": [[5, 1], [5, 1]], "output": [[5, 1, 1, 5], [5, 1, 1, 5], [5, 1, 1, 5], [5, 1, 1, 5]]}, {"input": [[5, 2], [5, 2]], "output": [[5, 2, 2, 5], [5, 2, 2, 5], [5, 2, 2, 5], [5, 2, 2, 5]]}, {"input": [[6, 2], [6, 2]], "output": [[6, 2, 2, 6], [6, 2, 2, 6], [6, 2, 2, 6], [6, 2, 2, 6]]}] | [{"input": [[4, 3], [4, 3]], "output": [[4, 3, 3, 4], [4, 3, 3, 4], [4, 3, 3, 4], [4, 3, 3, 4]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
4 3 3 4
4 3 3 4
4 3 3 4
4 3 3 4
``` | 394 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,604 | [
"<note1>\n<description>Start by looking for repeated substructures: many ARC tasks use a small motif (a 2×2 block or a 3×3 block) that appears multiple times in the input. Identifying that motif reduces the problem to counting how many copies exist.</description>\n<example>Imagine a grid where every 2×2 window cont... | [{"input": [[3, 8, 4, 4, 8, 7, 7, 8, 5, 8, 7, 7, 7, 7, 7, 8, 5, 8, 7, 7, 8, 4, 4, 8, 3], [7, 4, 7, 7, 7, 7, 8, 7, 7, 2, 7, 0, 0, 0, 7, 2, 7, 7, 8, 7, 7, 7, 7, 4, 7], [2, 7, 5, 7, 7, 5, 0, 8, 2, 5, 7, 2, 8, 2, 7, 5, 2, 8, 0, 5, 7, 7, 5, 7, 2], [7, 0, 7, 7, 3, 0, 2, 8, 7, 7, 2, 7, 7, 7, 2, 7, 7, 8, 2, 0, 3, 7, 7, 0, 7], ... | [{"input": [[7, 7, 0, 7, 7, 7, 4, 7], [7, 4, 7, 8, 0, 8, 4, 7], [8, 4, 7, 8, 7, 7, 0, 7], [8, 4, 7, 4, 4, 7, 4, 8], [0, 0, 7, 4, 4, 7, 8, 0], [0, 0, 4, 7, 0, 4, 4, 0], [0, 4, 4, 7, 7, 4, 8, 7], [0, 0, 0, 8, 0, 8, 7, 0], [0, 0, 8, 4, 4, 8, 8, 0], [7, 8, 4, 4, 4, 4, 8, 7], [7, 7, 7, 0, 0, 8, 7, 7], [8, 7, 0, 7, 0, 0, 7, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
7
``` | 1,900 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,254 | [
"<note1>\n<description>Find the anchor: one color that appears in a single row or column and is not the background. That color usually serves as the axis or pivot for the transformation (it is not the dominant background color).</description>\n<example>Imagine a grid where every cell is blue except for a thin verti... | [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8... | [{"input": [[7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 1], [7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 1], [7, 7, 7, 7, 7, 1], [7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7], [7, 2, 7, 2, 7, 7]], "output": [[7, 7, 1, 1, 7, 7], [7, 7, 7, 7, 1, 1], [1, 1, 7, 7, 7, 7], [1, 1, 1, 1, 7, 7], [7, 7, 1, 1, 1, 1], [7, 7, 7, 7, 1, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
7 7 1 1 7 7
7 7 7 7 1 1
1 1 7 7 7 7
1 1 1 1 7 7
7 7 1 1 1 1
7 7 7 7 1 1
7 7 7 7 7 7
7 7 7 7 7 7
7 2 7 2 7 7
``` | 3,550 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,974 | [
"<note1>\n<description>Look first at the overall size change: if the output has exactly twice the rows and twice the columns, the transformation is likely a 2×2 tiling (four identical subgrids). This reduces the problem to finding one representative tile and then repeating it.</description>\n<example>Imagine an inp... | [{"input": [[2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [2, 1, 2, 2, 2], [2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [2, 1, 2, 1, 2], [2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [1, 2, 2, 2, 2], [2, 1, 2, 2, 2], [2, 2, 2, 2, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 8, 2, 2, 8, 2, 8, 2, ... | [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5], ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 8 9 8 9 9 9 ... | 2,270 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,354 | [
"<note1>\n<description>First separate the meaningful objects from the background. Treat each contiguous group of non-background cells as an object and compute its bounding box so you can reason about its height and width independently of its color or exact coordinates.</description>\n<example>Imagine a 6×6 grid wit... | [{"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], [8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 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, 6, 6, 6, 0], [0, 0, 0, 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, 9, 9, 9, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 9, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0
2
2
2
2
``` | 1,650 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,586 | [
"<note1>\n<description>Look for a full-height or full-width column (or row) whose value is constant down (or across) the grid; such a uniform line usually acts as a deliberate divider. When present, it cleanly separates the grid into two subgrids and is the first thing to identify before any other transformation.</... | [{"input": [[7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0], [7, 0, 7, 0, 7, 0, 7, 7, 7, 7, 4, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0]], "output": [[0, 0, 0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 8, 0, 0, 0, 0, 0, 0]]}, {"i... | [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 4, 4, 0, 0, 4, 0, 0, 4, 0, 0], [7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 5, 0, 0, 4, 4, 4, 0, 4, 4, 0, 0], [7, 7, 7, 7, 7, 0, 7, 7, 0, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], [7, 7, 0, 0, 7, 7, 7, 0, 7, 7, 5, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0], [0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 0, 0, 4, 0, 4,... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 8 8 0 0 0 8 0 0
8 0 0 0 0 0 0 0 0 0
0 8 0 0 0 0 0 0 0 8
``` | 2,882 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,546 | [
"<note1>\n<description>Separate background from foreground by frequency: the color that fills most cells is usually the background and the remaining colors form the pattern to transform. This reduces the task to working with a small set of meaningful pixels instead of the whole grid.</description>\n<example>Imagine... | [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, ... | [{"input": [[3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 4, 5], [3, 3, 3, 5, 5, 5], [3, 3, 3... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
3 3 3 3 5 4
3 3 3 3 4 5
3 3 3 5 5 5
3 3 3 3 5 4
3 3 3 3 4 5
3 3 3 5 5 5
3 3 3 3 5 4
3 3 3 3 4 5
3 3 3 5 5 5
3 3 3 3 5 4
3 3 3 3 4 5
3 3 3 5 5 5
3 3 3 3 5 4
3 3 3 3 4 5
3 3 3 5 5 5
3 3 3 3 5 4
3 3 3 3 4 5
3 3 3 5 5 5
3 3 3 3 5 4
``` | 3,842 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,142 | [
"<note1>\n<description>Look first for an integer scale factor: the output is often an integer multiple of the input in both width and height. If the output dimensions are exact multiples of the input dimensions, that multiple is the natural candidate for how the input was enlarged.</description>\n<example>For insta... | [{"input": [[0, 9, 9, 9, 0], [9, 9, 9, 0, 0]], "output": [[0, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 0], [9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0], [0, 9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 9, 9, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0... | [{"input": [[0, 0], [5, 0], [0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 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, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0 0
5 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 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
``` | 2,438 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,248 | [
"<note1>\n<description>Check for a simple size reduction: the output is exactly one row shorter than the input. This suggests the transformation is built from an n×n input and an n×(n−1) output, so focus on how an n×n block was used to produce each row of the smaller grid.</description>\n<example>Imagine a 3×3 inpu... | [{"input": [[1, 3, 1, 4, 4], [1, 4, 4, 4, 2], [1, 1, 3, 2, 4], [4, 1, 4, 4, 2]], "output": [[3, 2, 3, 1, 1], [4, 3, 1, 1, 1], [3, 2, 4, 1, 3], [0, 0, 0, 0, 0]]}, {"input": [[4, 4, 3, 2], [3, 4, 1, 4], [1, 2, 2, 1], [2, 4, 1, 2], [1, 1, 3, 2]], "output": [[1, 1, 2, 4], [1, 2, 1, 3], [4, 4, 3, 3], [0, 0, 0, 0], [0, 0, 0,... | [{"input": [[1, 1, 2], [1, 2, 4], [1, 3, 2]], "output": [[3, 3, 4], [1, 3, 4], [2, 4, 3]]}] | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
3 3 4
1 3 4
2 4 3
``` | 544 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 1,800 | [
"<note1>\n<description>Look for a single color that appears as vertical bands (same column indices across many rows). These bands act as separators: they partition the grid into independent blocks and simplify the problem to analyzing each block separately.</description>\n<example>Imagine a grid where column 5 and ... | [{"input": [[7, 7, 4, 7, 8, 6, 7, 7, 8, 7, 7, 6, 5, 7, 7, 9, 7], [7, 7, 4, 4, 8, 6, 2, 2, 8, 3, 3, 6, 5, 5, 7, 9, 7], [2, 2, 4, 7, 8, 6, 7, 2, 8, 3, 7, 6, 7, 5, 0, 9, 9], [7, 7, 4, 4, 8, 6, 2, 2, 8, 3, 3, 6, 5, 5, 0, 7, 9], [7, 7, 4, 7, 8, 6, 7, 7, 8, 7, 7, 6, 5, 7, 0, 7, 9]], "output": [[7, 7, 8, 9, 7], [7, 7, 8, 9, 7... | [{"input": [[4, 4, 9, 9, 7, 6, 8, 8, 7, 7, 7, 6, 2, 2, 7, 7, 7], [4, 7, 9, 9, 7, 6, 7, 8, 7, 7, 7, 6, 7, 2, 7, 9, 9], [4, 4, 7, 7, 2, 6, 8, 8, 7, 9, 9, 6, 2, 2, 5, 7, 9], [7, 4, 7, 7, 2, 6, 8, 7, 2, 7, 9, 6, 7, 2, 7, 9, 9], [4, 4, 7, 7, 2, 6, 8, 8, 7, 9, 9, 6, 2, 2, 7, 7, 7]], "output": [[4, 4, 7, 7, 7], [4, 7, 7, 9, 9... | arc 2 | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
4 4 7 7 7
4 7 7 9 9
4 4 7 7 9
7 4 2 9 9
4 4 7 7 7
``` | 1,096 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 4,592 | [
"<note1>\n<description>Look for a full row or full column made of the same color that runs uninterrupted across the grid. This continuous line is usually a deliberate divider and is the key to splitting the image into two comparable regions.</description>\n<example>Imagine a grid where column 5 is entirely green fr... | [{"input": [[4, 4, 8, 4, 8, 4, 8, 4, 8, 8, 4, 4, 2, 9, 9, 8, 8, 8, 9, 9, 8, 8, 9, 9, 9], [4, 4, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 2, 8, 8, 8, 8, 8, 9, 9, 8, 9, 9, 9, 9], [4, 8, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 2, 8, 8, 8, 9, 8, 9, 8, 9, 8, 9, 9, 8], [8, 4, 4, 8, 4, 4, 4, 8, 8, 4, 4, 4, 2, 9, 9, 8, 8, 9, 9, 8, 9, 8, 8, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ... | 3,888 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,370 | [
"<note1>\n<description>Look for a contiguous, single-color horizontal band that occupies the grid's extreme left or extreme right columns. Such a band is a strong candidate because it is visually continuous across many rows and is often the anchor for the transformation.</description>\n<example>Imagine a 6×6 grid w... | [{"input": [[0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 9, 0, 9, 0], [0, 0, 9, 0, 0, 0, 9, 0, 9, 0], [0, 0, 0, 0, 0, 0, 9, 9, 9, 0], [4, 4, 4, 4, 0, 9, 9, 9, 9, 1], [4, 4, 4, 4, 0, 0, 0, 1, 1, 1], [4, 4, 4, 4, 0, 0, 9, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 1... | [{"input": [[0, 0, 0, 0, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2], [9, 0, 0, 0, 0, 0, 0, 2, 2, 2], [2, 0, 9, 9, 9, 9, 0, 0, 9, 0], [0, 0, 0, 9, 9, 9, 0, 0, 2, 2], [0, 0, 0, 9, 9, 2, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 9 9 9 9 0
0 0 0 0 0 0 9 9 9 0
0 0 0 0 0 0 9 2 2 2
0 0 0 0 0 0 0 2 2 2
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
``` | 1,666 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 3,734 | [
"<note1>\n<description>Look for a single, isolated colored pixel (a lone cell of a non-background color). In many ARC tasks this solitary pixel is the anchor or trigger for the transformation.</description>\n<example>Imagine a grid that contains one green pixel surrounded by black. That single green pixel is not pa... | [{"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, ... | [{"input": [[0, 0, 0, 0, 0, 3, 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, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 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], ... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
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 2 2 0 0 0 0 0 0 0
0 0 0 0 0 2 2 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 0 0 0 0
0 0 0 0 ... | 3,030 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,174 | [
"<note1>\n<description>Look for the single non-background color that forms a compact, rectangular region. This color is usually the only one that changes from input to output and is treated as the object to transform.</description>\n<example>Imagine a mostly gray grid with a solid red rectangle somewhere inside. Th... | [{"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "ou... | [{"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 4, 4, 4, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5,... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 4 4 4 5 5 5
5 5 5 4 4 4 5 5 5
5 5 5 4 4 4 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5
``` | 1,470 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,370 | [
"<note1>\n<description>Look for repeated objects: many ARC tasks use the same small motif repeated in different places. Identifying that motif reduces the problem to how one instance is transformed rather than many unrelated pixels.</description>\n<example>Imagine a grid with several identical 3‑pixel L‑shapes in d... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 4, 0, 0, 0], [0, 4, 0, 0, 0, 4, 0, 0, 0, 0], [4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 5, 0], [0, 0, 5, 5, 5, 0, 0, 5, 5, 5], [0, 0, 0, 5, 0, 0, 0, 0, 5, 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, 5, 0, 0, 0], [0, 0, 0, 0, 0, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0... | barc_heavy | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
0 0 0 0 0 0 0 0 0 0
0 5 0 5 0 0 0 0 5 0
0 0 5 5 5 0 0 5 5 5
0 0 0 5 0 0 0 0 5 0
0 0 0 0 5 0 0 0 0 0
0 0 0 0 0 5 0 0 0 0
0 0 0 0 0 0 5 0 0 0
0 0 0 0 0 5 5 5 0 0
0 0 0 0 0 0 5 0 5 0
0 0 0 0 0 0 0 0 0 5
``` | 1,666 |
<|im_start|>user
Developer: # ARC HINT GENERATOR
## Role & Goal
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your task is to generate a concise, actionable hint for a user who is struggling with an ARC problem. Analyze the problem and its correct solution to produce a single standalone, targeted h... | 2,324 | [
"<note1>\n<description>Look for a single non-background color that consistently appears across the examples and is the only color that changes in the outputs. When one color dominates the input and the output is uniform, that color is usually the source of the transformation.</description>\n<example>Imagine a grid ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0], ... | [{"input": [[0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], [6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, ... | rearc | You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan... | ```
6 6 6 6 6 6 6 6 6 6 6 6 6 6
``` | 1,620 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.