How to Solve Shikaku: A Beginner’s Guide for Adults
To solve Shikaku, divide the entire grid into rectangles so each rectangle contains exactly one number equal to its area in squares. Start with 1s (always a single cell), prime numbers (always a straight line), and corner clues — then let logic, not guessing, finish the rest.
What Is Shikaku?
If you have looked at a grid covered in scattered numbers and thought “I can see the numbers but I have no idea which rectangle goes where,” you are in exactly the right starting place. That confusion is common, and it dissolves quickly once the single core rule clicks.
Shikaku — also called Rectangles or Divide by Box in English — is a logic puzzle created by Yoshinao Anpuku, a mathematics student at Kyoto University, in 1989. It was published by the Japanese puzzle magazine Nikoli under the Japanese name 四角に切れ (Shikaku ni Kire), meaning “divide by box.” That origin is context; the puzzle itself asks for nothing more than careful observation and patient reasoning.
The setup is clean: a rectangular grid where some cells hold a number. Your job is to slice the whole grid into rectangular (or square) pieces. Each piece must contain exactly one number, and that number tells you the size of the piece — specifically, how many squares it covers. When every cell belongs to exactly one rectangle, and every rectangle matches its number, the puzzle is solved.
Quick vocabulary: a clue is any numbered cell. The area of a rectangle is simply the count of squares it contains — a 2×3 rectangle has an area of 6. There are no bulbs, no paths, no loops here — just careful cutting.
The Rules of Shikaku (in Plain English)
According to Wikipedia’s article on Shikaku, the rules reduce to four clean points.
- Divide the entire grid into rectangles and squares. Every single cell must belong to exactly one piece. No gaps, no overlaps.
- Each piece contains exactly one numbered clue. A piece with zero numbers or two numbers is not legal.
- The number equals the area of its rectangle. A cell marked “6” belongs to a rectangle that covers exactly 6 squares — it could be 1×6, 2×3, 3×2, or 6×1. Your job is to decide which shape fits the available space.
- Pieces cannot overlap. Once you assign a group of cells to one number, those cells are off-limits to every other number.
One reassuring detail: unlike many puzzles, you never need to guess. As the shikaku.ch solving guide notes, if you feel like you have to guess, it means there is a constraint you have not used yet. Every Shikaku grid with a unique solution can be cracked by logic alone.
Quick worked example: a cell marked “6” sits near the center. Its rectangle must cover exactly 6 squares. You sketch the candidates — 1×6, 2×3, 3×2, 6×1 — and check which fits without colliding with a neighbor clue or spilling off the grid. The surrounding context eliminates options until only one shape remains.
Where Do You Start? Begin with the 1s and the Corners
Those scattered numbers are not a guessing game. You can confirm every rectangle by logic — and the easiest place to start is staring right at you: a clue that leaves almost no room for debate.
Start with the 1s. A cell marked “1” is its own rectangle. It cannot reach any neighbor. The moment you see a 1, draw its tiny 1×1 box immediately and move on. Every confirmed piece simplifies the cells around it.
Look for small clues in tight spaces. A “2” can only be 1×2 or 2×1 — two cells wide in one direction. A “3” can only be 1×3 or 3×1. Small numbers form confirmed blocks quickly, and each confirmed block narrows what adjacent clues can do.
Prioritize corners and edges. A clue sitting in the corner of the grid cannot extend in two of the four possible directions — the grid simply ends there. A clue along an edge loses one direction entirely. The fewer directions a rectangle can stretch, the faster it resolves. The shikaku.ch guide puts it plainly: because the rectangle cannot extend beyond the edge, corner and border clues are among the most constrained — and therefore the most useful — starting moves.
A clue marked 1 is always a single square — confirm it immediately. Corner and edge clues have fewer directions to stretch, so they resolve fastest and give you the clearest first moves.
The Prime Trick: Why a 5 or 7 Must Be a Straight Line
This is the insight most beginners miss — and once you see it, it unlocks more moves faster than almost any other technique.
The core idea. A prime number has exactly two factors: 1 and itself. That means the only rectangles with a prime area are 1×N and N×1 — a single straight line of cells, either horizontal or vertical. A “5” cannot be a 2×? or a 3×? because neither divides 5 evenly. It must be 1×5 or 5×1.
Why that matters. Once you know a prime clue is a straight line, you have only two options to evaluate: horizontal or vertical. Look at the space available. If the grid edge or a neighboring clue blocks one direction, the other is confirmed immediately. A single glance at the surroundings settles the entire rectangle.
Common prime clues you will encounter: 2, 3, 5, 7, 11, 13. Each one is locked to a straight-line shape. Keep a mental note that 4 (2×2 or 1×4) and 6 (2×3 or 1×6) have more options — but 5 and 7 never do.
Worked example. A “5” sits two cells from the right edge of the grid. It cannot stretch five cells to the right — there is not enough room. So it must run vertically: 5×1, five cells tall. One check, one confirmed rectangle.
If a clue’s number is prime (2, 3, 5, 7, 11…), its rectangle must be 1×N or N×1 — a single row or column of cells. One wall or neighbor is usually enough to decide which direction.
Stuck? Find the Cell Only One Number Can Reach
Every solver reaches a point where nothing looks obvious. Three habits keep the grid moving.
1. Find the cell only one number can reach. Ask: which clue’s rectangle could possibly include this uncovered cell? If only one clue can reach it, that placement is confirmed — most useful late in the puzzle when open cells are few.
2. Watch for isolated cells. A cell surrounded by confirmed rectangles on all sides that no clue has claimed signals an earlier error, not a dead end. Retrace from the most recent move and reassess.
3. Check for overlapping candidates. When two clues compete for the same cell, use the size constraint to eliminate. Sizes are exact — a confirmed 1×4 block that excludes the contested cell means the other clue must own it.
If any cell in the grid cannot be reached by any remaining clue’s rectangle, there is an error somewhere above. An orphaned cell is the clearest signal to backtrack — not to guess forward.
Getting Better at Shikaku
The fastest path to fluency is smaller grids. A 5×5 Shikaku can be solved in a few minutes once the 1s-and-corners and prime-trick habits are in place. Work through several small grids before stepping up to 7×7 or 10×10.
Try one puzzle each day from an app, book, or free printable. The rules stay identical at every size; what grows is your ability to immediately spot the most constrained clue rather than reading left to right.
If you enjoy step-by-step logic, similar reasoning carries into how to solve Akari, how to solve Slitherlink, and how to solve Hashi. New to logic puzzles? How to get better at Sudoku is the most familiar entry point.
Shikaku is about shapes and area, not fast arithmetic — but if you enjoy quick number sense between logic sessions, Make 10 is a free browser puzzle that keeps that habit warm. It is not a Shikaku solver; it works on a different idea, connecting touching tiles so their values add up to ten.
Frequently Asked Questions
What is the goal of Shikaku?
Divide the entire grid into rectangular pieces so that each piece contains exactly one numbered clue, and the clue’s number equals the piece’s area in squares. The puzzle is solved when every cell belongs to exactly one rectangle, every rectangle holds exactly one number, and every area matches.
What does the number in a Shikaku cell mean?
It tells you the size — specifically the area — of the rectangle that must surround it. A “6” means the rectangle covering that clue must be exactly 6 squares large. It could be shaped 1×6, 2×3, 3×2, or 6×1 — the puzzle logic tells you which one fits.
Where should I start a Shikaku puzzle?
Start with the most constrained clues: a 1 (always a single square), prime numbers (always a straight line of cells), and clues in corners or along edges (fewer directions to stretch). Confirming these first pieces restricts the options for every surrounding clue.
Can one rectangle contain two numbers?
No. Each rectangle must contain exactly one clue. A rectangle holding two numbers is an illegal placement. If you find yourself with a rectangle covering two numbered cells, one of the surrounding placements needs to be revised.
Is Shikaku based on math or logic?
Mostly logic, with a small amount of factoring. You need to know the possible dimensions of a given area — a 6 can be 1×6, 2×3, 3×2, or 6×1 — and the prime insight (5 can only be 1×5 or 5×1) is the trickiest arithmetic involved. Beyond that, the skill is spatial: reading constraints, eliminating options, confirming placements. No fast mental math required.
More from the Make10s blog: how to solve Akari · how to solve Slitherlink · how to solve Hashi · how to get better at Sudoku · all posts
Sources: Wikipedia — Shikaku · shikaku.ch — Solving Guide
Just for fun — not medical advice.