How to play Number Regions
Write a number in every square so that each region of joined, equal numbers has exactly that many squares. Also known as Region sizes, Polyomino numbers.
The rules
- Every square must contain a number.
- Squares with the same number that share a side are part of one region.
- A region’s size equals its number: a region of 4s has exactly four squares.
- Two regions of the same size can’t share a side.
Playing Number Regions on Puzzle Solvers
- Choose the biggest region, a size and a difficulty, then press New Puzzle.
- Tap a square and a number on the pad (or type it). Quickest of all: drag from a number to copy it across neighbouring squares.
- Regions that are the right size light up; regions that are too big, or boxed in too small, show in red.
- Hint explains the next square — complete regions, the only way a region can grow, and sizes that don’t fit.
Using the Number Regions solver
- Choose the size, type the given numbers (or press Sample).
- Press Solve and step through: complete regions, the only way out, sizes that can’t fit, and what-ifs.
A worked example
A 3 sits in a corner with a 1 beside it. The 1 is already complete, so the 3 can only grow along the edge.
It needs two more squares and has one way out, then one again — so the next two squares along the edge are 3s, and the region is closed.
Strategies
- Close finished regions. When a region reaches its size, none of its neighbours can have the same number.
- Only one way out. If a region still needs squares and has just one free neighbour, it must grow there.
- Small gaps. A gap of two empty squares surrounded by finished regions can only be a 2 (or two 1s).
- Don’t merge. Placing a 3 next to another region of 3 would join them into one too-big region.
- Count the room. A 5 needs five squares it can reach — if there isn’t room, it can’t go there.
Common mistakes
- Letting two regions of the same number touch.
- Leaving a square without a number.
- Growing a region past its size.
Where it comes from
Region-size puzzles of this kind were first published by the Japanese puzzle company Nikoli and have spread to puzzle magazines worldwide.
Frequently asked questions
Can a number appear in several regions?
Yes — there can be many regions of 3, as long as no two of them touch along a side.
Is there always one answer?
Yes — every puzzle here is checked to have exactly one solution.
Why is there a biggest region option?
It sets the largest region in the puzzle, which also keeps puzzles a sensible size to solve.
How do I solve one from a book?
Open the Number Regions Solver, type the numbers and press Solve.
Keep going
- Play Number Regionsa fresh puzzle every time
- Number Regions Solverstep by step, every move explained
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