Shikaku Puzzle

What is Shikaku?

Shikaku was invented in 1989 by Yoshinao Anpuku, a university student in Kyoto, and published by Nikoli — the same company that brought Sudoku, Kakuro, and Nurikabe to the world. The Japanese name is 四角に切れ (shikaku ni kire), which translates roughly to “cut into rectangles.” Nikoli has published more than 14 books of Shikaku puzzles since then.

Outside Japan, the puzzle goes by a few different names. The Guardian newspaper runs it daily as “Cellblocks.” Nikoli's own English name is “Divide by Box.” Some publishers just call it “Rectangles.” The rules are identical regardless of the label.

What makes Shikaku unusual among grid puzzles is the interaction model. Instead of toggling cell states or placing numbers, you draw rectangles. Click one corner, drag to the opposite corner, and the cells in between get claimed. It feels different from anything else in the category — more construction than deduction, even though the underlying logic is pure constraint satisfaction.

The two rules

Most grid puzzles have four to six rules. Shikaku has two:

1. Full coverage. Divide the entire grid into non-overlapping rectangles. Every cell belongs to exactly one rectangle. Squares count as rectangles.
2. Number = area. Each rectangle contains exactly one number, and that number equals the rectangle's area. A cell showing “8” belongs to a rectangle of 8 cells — maybe 2×4, maybe 1×8.

That's it. No connectivity constraints, no adjacency restrictions, no row or column uniqueness. All the difficulty comes from the combinatorics of factorization and spatial packing.

For solving techniques and worked examples, read the full strategy guide.

How to play

Drawing rectangles on the grid:

• Draw — click and drag from one corner to the opposite corner. On mobile, tap the first corner, then tap the second.
• Remove — right-click a rectangle (desktop) or long-press (mobile) to remove it. Or use undo.
• Show possibilities — click a numbered cell without dragging to see all valid rectangle placements for that number.

Each placed rectangle gets a distinct pastel color so you can tell them apart at a glance. Invalid placements — wrong area, multiple numbers inside, or overlaps — get flagged immediately. Keyboard shortcuts: arrow keys navigate, Enter starts/ends selection, Delete removes a rectangle.

A math puzzle in disguise

Nikoli calls Shikaku “a great math trainer for kids,” and the reason is built into the rules. Every number on the grid is a factoring problem: 12 can be 1×12, 2×6, or 3×4. You need to work out which factorization fits the available space. On a 5×5 easy grid, those decisions are straightforward. On a 15×15 Einstein grid, a clue like 30 could be 1×30, 2×15, 3×10, 5×6 — and you're working out which one is geometrically possible while adjacent numbers compete for the same cells.

That makes Shikaku a natural fit for classrooms. The multiplication practice is real but doesn't feel like homework, because the spatial reasoning keeps it from being rote. Parents and teachers looking for something beyond flashcards might find the easy grids useful — 5×5 with small numbers is challenging enough to be interesting without being frustrating.

Also known as

Shikaku has more aliases than most Nikoli puzzles. The Guardian newspaper publishes it daily as “Cellblocks.” Nikoli's official English name has changed over the years — first “Divide by Squares,” then “Divide by Box.” Some publishers use “Rectangles” as a generic descriptor. The puzzle community has mostly settled on “Shikaku” as the universal name, which is what we use here.

Difficulty levels

Key strategies at a glance

The easiest technique is forced placement: some numbers, especially in corners or along edges, can only form one valid rectangle. Place those first. Next, look at large numbers— a clue of 15 on a 15×15 grid can only be 1×15, 3×5, 5×3, or 15×1, and usually only one or two of those fit. They partition the grid into smaller regions that constrain everything else.

On harder puzzles, boundary propagation does the heavy lifting. Once you place a rectangle, the unclaimed cells around it become more constrained, often forcing the next placement. And when two numbers compete for the same space, elimination by contradictionresolves it: if one placement would make a neighbor impossible to satisfy, that placement is wrong.

Frequently asked questions

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