Number Block Puzzle Generator
In a number block puzzle the numbers describe themselves. Fill every square so the grid splits into blocks of touching equal numbers, and each block holds exactly as many squares as the number written throughout it — a block of three is three 3s, and a 1 stands entirely alone. It follows that two blocks of the same size may never touch, because if they did they would be one block of the wrong size. Every grid here is checked to have one answer and no other.
What this generator does
Fills a grid with blocks that already obey the rule, then takes numbers away one at a time — keeping a removal only while a single answer survives.
How to use this tool
- Choose a grid size and the largest block you would like to meet.
- Print or copy the grid; the numbers already written are the ones you are given.
- Write a number in each empty square, growing every number into a block of its own size.
- Keep two blocks of equal size apart — touching would merge them into one block too large for its number.
- Show the answer to check the finished grid.
Understanding the controls
- Grid
- Five to seven squares a side. Seven is the ceiling, and it is a measured one rather than a preference.
- Largest block
- Blocks of up to four, or up to five. Larger blocks make a slower puzzle to build as well as a roomier one to solve, so blocks of five are offered up to six squares a side and blocks of four up to seven.
- Seed (optional)
- Type anything to rebuild the same puzzle later, which is how you reprint a page you have lost. The seed makes the result repeatable; it is not a password and gives no cryptographic strength.
Common use cases
- A number puzzle that needs no arithmetic at all, only counting
- A printable page for a puzzle club, a classroom or a newsletter
- A gentle way into region-splitting puzzles for a Sudoku solver
- A short puzzle for a break, at five squares a side
- Reprinting the identical grid later from its seed
How this generator works
The whole of this puzzle collapses into one sentence about the finished grid: every connected group of equal numbers holds exactly as many squares as the number in it. The rule against two equal blocks touching needs no separate statement, because two touching blocks of three are a single group of six 3s, which that sentence already rejects — so it is checked once rather than twice. Squares are settled in reading order. A group may never grow past the number written in it; the moment it can grow no further it must be exactly that size; and a group still short of its number is abandoned early unless enough unsettled squares remain within its reach, which is the difference between a grid built in a fraction of a second and one built in nineteen. Numbers are then removed one at a time and a removal is kept only while the puzzle still has a single answer, proved by a solver shown the printed numbers alone.
Randomness and fairness
The blocks, and the order the numbers are taken away in, come from your browser's cryptographic random source. A seed replaces that source with a repeatable one so the same puzzle comes back; a seeded puzzle is reproducible, not cryptographically strong, and it is not a secret.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- The grid stops at seven squares a side, and blocks of five stop at six a side — both measured limits.
- Difficulty is not graded. Whether the block sizes pin each other down early or leave a long stretch of guesswork-free but slow deduction is not something this measures.
- The two settings are checked as a pair, so not every combination on the page can be asked for.
- About half the squares keep their number; the puzzle is not stripped as bare as it could be, which would take far longer to build for a small gain.
Privacy and your data
The grid is filled, thinned and checked entirely in your browser. Nothing you type as a seed, and no puzzle made from it, leaves the device.
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- Slant Puzzle GeneratorPrints a Slant puzzle — one diagonal in every square, numbers counting the ends at each corner, and no closed loop — with exactly one answer.
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