Shikaku

Overview

Shikaku replaces a blank grid with a complete tiling of rectangles. Every rectangle must contain exactly one clue, and that clue gives its area in cells. A six could occupy a one-by-six strip, a two-by-three rectangle, or their rotations, depending on the space available. Rectangles cannot overlap and no cell may remain outside the partition. You do not fill a number sequence or place irregular pieces; the geometry is strictly rectangular. SonoTap hosts the open-source Rectangles implementation with a puzzle generator and adjustable board settings. The deceptively simple area rule becomes interesting where several clues compete for the same empty corner. Deducing which rectangle must own a hard-to-reach cell can be more useful than starting from the largest number. Because every cell belongs to exactly one rectangle, each placement also deletes territory from every rival clue.

How to Play

Drag from one corner of a proposed rectangle to the opposite corner to draw its outline. Include one clue and count both dimensions so their product equals that clue. A narrow rectangle still needs its full length, not merely a line joining two grid intersections. On a phone, keep the drag inside the intended starting and ending squares and use Undo to correct an inaccurate selection. Partition the entire grid into valid rectangles. Restart clears the current arrangement, while New produces another layout with the chosen settings. If a rectangle refuses to register, check that it contains no second clue and no already-claimed cells.

Tips & Strategy

List the factor pairs of a difficult clue before testing positions. A prime area can only form a one-cell-wide strip, which sharply limits its placement near borders and other clues. Every candidate rectangle must contain its own clue and exclude every other clue. Look for empty cells reachable by only one remaining candidate, then extend that rectangle enough to cover them. Avoid committing a convenient rectangle that leaves a thin empty pocket unreachable by any clue. Near the finish, inspect the whole grid for uncovered cells rather than stopping when all numbers seem enclosed.

Reading the Numbers

Clues sort themselves by flexibility. A 1 is already solved: a single cell, claimed immediately. Prime clues such as 2, 3, 5, 7 and 11 form only one-cell-wide strips, so the open question is direction and length, never shape. Composite clues offer more shapes but fewer escapes in crowded regions — a 6 can be one-by-six or two-by-three, yet if every two-row position swallows a neighbouring clue, the flat strip is forced. A 9 is either a three-by-three block or a nine-cell strip, and on a standard board the strip rarely fits, which makes 9 nearly as rigid as a prime.

A worked example: an empty corner cell sits far from every clue except a 6 positioned two columns away along the edge. The 6 could in principle be two-by-three, but any two-row rectangle reaching that corner would enclose a 4 clue beside it. The 6 must therefore lie flat as a one-by-six strip along the border, its direction fixed, and its far end immediately walls off the cells above it for other clues. One corner argument has placed an entire rectangle and narrowed everything around it.

Mistakes to Avoid

The most frequent error is drawing a rectangle whose area matches its clue but which quietly encloses a second clue — the area rule passes while the one-clue rule fails. The mirror image of that mistake is leaving orphan pockets: a single uncovered cell surrounded by finished rectangles can never be claimed, so check reachability before closing a region. Players also reach for the largest clue first, when the rigid primes and corner cells usually carry the forced moves. Finally, count cells rather than grid intersections; an off-by-one length ruins an otherwise sound rectangle.