tiling-packing-divisibility
A geometric region must be covered or partitioned by pieces subject to area / divisibility constraints. The decisive observation is usually arithmetic: total area mod tile-area gives the minimum waste, or the constrained items must fit inside a small bounding rectangle.
How to solve
- Change grid_dimensions to 4x9 and reuse the same tile set — the mod-4 leftover shifts to a different value
- Replace 1x4 with 1x3 tiles to change divisor_d from 4 to 3
- For an extremal-configuration variant, ask for the MAXIMUM number of clean rows/cols instead of minimum
Sub-archetype mix (3)
Click a row to see member problems.
- rectangular-tiling-minimum-filler 50% (7)
A rectangle is tiled by two or more fixed piece sizes; the total area (mod the dominant tile area) forces the minimum number of filler or unit pieces, and the answer is the smallest achievable value consistent with both the arithmetic constraint and a valid geometric arrangement.
- piece-set-feasibility-elimination 29% (4)
A given inventory of distinct pieces (polyomino or brick shapes) must cover a target region; a coloring, size, or spatial argument identifies which target arrangement is impossible (or which piece combination is the only feasible one).
- divisibility-count-packing 21% (3)
Count how many items in a range satisfy a divisibility condition, then determine the minimum bounding dimensions (side length or row-plus-column sum) needed to contain all those items in a grid or square, verified by an explicit integer-solution or area argument.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 3 3
- Gr 4 5
- Gr 5 2