How to solve Patches

How to solve Patches: techniques that work

Every clue is an area, and areas factor. A 7 can only ever be a 1×7 or 7×1 strip; a 4 might be 1×4, 4×1 or 2×2. Start with primes and large numbers — their shapes are the most constrained, and on small boards a 5 or 7 often has a single legal placement once you check what stays in bounds and avoids other clues.

Remember that each rectangle must contain exactly one clue. That cuts both ways: a candidate rectangle that would swallow two numbers is illegal, and a cell that can only be reached by one clue's possible rectangles must belong to that clue. Scanning for these "orphan cells" is the strongest move in the game.

Work the frontier. Once a rectangle is placed, the cells alongside it lose options, and neighbouring clues often collapse to a single shape. Solved regions propagate — Patches boards tend to fall in an accelerating cascade.

Common mistakes

Assuming a number sits inside its rectangle centrally or in a corner: the clue can be anywhere inside its rectangle. What matters is only that the rectangle contains it, stays in the grid, and overlaps nothing.

Forgetting the exhaustive rule: the rectangles must tile the whole board with no gaps. If two leftover cells can't be covered by any remaining clue, an earlier rectangle has the wrong shape.

From easy to hard

Bigger boards mean more composite numbers with several viable shapes, so you'll hold two or three candidate placements in mind at once. The factor-first habit (primes, then large composites) keeps hard boards manageable. Patches is our take on the Japanese classic Shikaku.