Shikaku solving techniques

After learning how Shikaku works, think in candidate rectangles rather than trying to draw the final partition immediately.

Enumerate factor pairs

A clue’s area determines its possible dimensions. For 12, consider 1×12, 2×6, 3×4 and their rotations. Remove any placement that crosses the grid edge or includes another clue. This turns a visual hunch into a finite list.

Use candidate overlap

If every legal rectangle for a clue contains a particular cell, that cell belongs to the clue even before its complete boundary is known. This ownership can eliminate candidates for neighbouring numbers and reveal a forced shape.

Work from constrained boundaries

Corners limit both directions; edges limit one. Large clues also have fewer places to slide. Resolve clues with the smallest candidate lists first instead of automatically starting with the smallest number.

Inspect orphan cells and pockets

An uncovered cell must be reachable by some remaining clue’s legal rectangle. If only one clue can cover it, discard that clue’s candidates that miss it. Similarly, a pocket cut off by confirmed boundaries must have an area equal to the sum of the clues whose rectangles will fill it.

Test boundaries, not guesses

When two candidate rectangles compete, look at what each boundary would leave behind. A one-cell-wide bend cannot be tiled by rectangles crossing a fixed boundary. An enclosed region with no clue is impossible. These contradictions often decide between candidates without trial-and-error play.

Recount after every rectangle

A confirmed rectangle changes the candidate set of every nearby clue. Redraw those candidates and look for cells no longer coverable. Shikaku solutions often cascade from a single edge placement.

Try these ideas in the Great Patchwork or today’s daily Shikaku. See the Shikaku FAQ for controls and rules details.