How to Play Shikaku

Shikaku (“divide into rectangles”) is a partition puzzle. Slice the grid into non-overlapping rectangles so that each rectangle contains exactly one clue cell, and each clue equals that rectangle's area.

The Puzzle

A 6×6 puzzle with 9 clues. Every cell will end up inside some rectangle. The clues — and only the clues — sit at the “heart” of each rectangle.

The Three Rules

Rule 1: Every cell belongs to exactly one rectangle

The rectangles tile the grid — no overlaps, no gaps.

Rule 2: Each rectangle contains exactly one clue cell

No clueless rectangles, no rectangles with two clues. Every clue anchors its own rectangle.

Rule 3: A rectangle's area equals its clue's number

A clue of 6 means an area-6 rectangle. The shape can be 1×6, 6×1, 2×3, or 3×2 — whichever fits the grid and doesn't contain any other clue.

Walkthrough

Step 1 — The 6 in the bottom-left

Clue 6 at row 4, column 1. Factorizations of 6: 1×6, 6×1, 2×3, 3×2. Rule out the impossible ones:

• 1×6 (horizontal in row 4): would span all 6 columns of row 4 — contains clues 3 (at col 4) and 2 (at col 6) → impossible.
• 6×1 (vertical in column 1): spans 6 rows, but column 1 only has 6 rows total. Would contain clue 4 (at row 1) and others → impossible.
• 3×2 (3 rows, 2 cols): every variant pulls in another clue (4 at row 2, or 6 at row 6).
• 2×3 (2 rows, 3 cols), positioned at rows 4-5, cols 1-3: contains only the 6 itself. ✓

Step 2 — The 4 in the top-left corner

Clue 4 at row 1, column 1. Factorizations: 1×4, 4×1, 2×2.

• 4×1 vertical: would span rows 1-4 of column 1 — contains clue 6 at row 4 → impossible.
• 2×2: would include row 2 column 2 (the other 4 clue) → impossible.
• 1×4 horizontal in row 1, cols 1-4: contains only the 4 itself. ✓

Step 3 — The 5 in the middle

Clue 5 at row 3, column 5. 5 is prime — only 1×5 and 5×1.

• 1×5 horizontal in row 3: any 5-wide slice of row 3 must include either column 1 or 2 (the only way to fit width 5 around column 5) — but row 3 column 2 holds clue 3 → impossible.
• 5×1 vertical in column 5: column 5 has only one clue (the 5 itself). 5 cells fit easily. ✓

Two vertical positions are possible (rows 1-5 or rows 2-6 in column 5). Other constraints — like the 2×3 rectangle below blocking certain rows — narrow it to the unique placement.

Step 4 — Cascade

From here, every remaining clue's rectangle is forced by the cells already claimed and by clue-conflict elimination. Continuing yields the unique partition:

Tips for Beginners

• Start with prime clues. 2, 3, 5, 7 each have only two possible shapes (1×n or n×1) — much easier to nail down.
• List factorizations. For each clue, write down every possible shape: 6 → {1×6, 6×1, 2×3, 3×2}, 12 → {1×12, 12×1, 2×6, 6×2, 3×4, 4×3}.
• Eliminate by clue conflict. Any candidate rectangle must contain exactly one clue. Reject any placement that would swallow a second clue.
• Eliminate by grid edge. A rectangle can't extend past the grid. Clues near the edges have fewer options.
• Eliminate by area conflict. Once you place a rectangle, those cells are no longer available. Other rectangles shrink in possibilities.

Ready to try one yourself? Hit the button below to play your first Shikaku.