Nikoli Classic • Divide by Box
Shikaku (Divide by Rectangles)
Slice the grid into neat bento boxes! Every rectangle must contain exactly one number matching its total area, with zero gaps and zero overlaps.
Drafting Shikaku partitions...
Shikaku Rules & Fundamentals
Published by Nikoli, Shikaku blends prime factor geometry with spatial partitioning:
1. One Number Per BoxEvery rectangle must encompass exactly one number from the puzzle grid.
2. Area MatchThe width multiplied by the height of each rectangle must equal the value of its enclosed number.
3. Full TilingEvery square on the board must belong to one rectangle. No unoccupied squares may remain.
4. Rectangular GeometriesShapes must be orthogonal rectangles or squares. L-shapes or non-convex polygons are strictly prohibited.
Master Partitioning Theorems
- Prime Numbers ($2, 3, 5, 7$): A prime area has only one factor pair: $1 \times N$ or $N \times 1$. If a “5” sits with fewer than 5 squares available in one direction, it is forced to extend in the perpendicular axis!
- Corner Squares: Look at the 4 corners of the board. The square at $(0, 0)$ must be claimed by some rectangle. Often, only one nearby clue can reach the corner without capturing a second clue!
- Edge Blocks: A clue near the outer edge has constrained expansion options. If a “4” is 1 cell away from an edge, a $2 \times 2$ square can only fit in one orientation.
- Isolate 1s: Clues with “1” are instantly locked into solitary $1 \times 1$ squares. Draw them first to create solid barriers for other numbers!