Crossnumber Puzzle Generator

What this generator does

Fills a fixed grid with random digits, never starting an entry with 0, and gives every entry one true clue about itself. It then searches every filling the clues allow. While a second filling exists, it adds a clue that is true of the answer and false of that filling, and searches again. A puzzle is kept only when the search finishes with exactly one filling and a second search, built differently, agrees.

How to use this tool

1. Choose the grid and whether clues may compare two entries.
2. Press Make the puzzle. A seed repeats a puzzle exactly.
3. Print the puzzle and the answer, which come out on separate pages.

Understanding the controls

Grid

4 × 4 (eight entries) or 5 × 5 (twelve). Every entry is 2 to 4 digits long and every white square is in at least one entry.

Clues

Each number alone uses square, cube, prime, reads the same backwards, multiple of 3 to 12 and digit sum. Also between numbers adds clues such as 3 Down + 14, 1 Across × 3 and 1 Across with its digits reversed.

Seed

The same seed and settings make the same puzzle while the generator is unchanged. Not a secret.

Worked examples

A 2 × 2 worked by hand

1 Across a square; 1 Down a multiple of 7 whose digits add up to 5; 2 Down a multiple of 3; 3 Across a square. Of 14, 21, 28 … 98 only 14 has digits adding to 5, so 1 Down is 14. 1 Across is a square starting with 1: 16. 3 Across is a square starting with 4: 49. 2 Down is 69, a multiple of 3.

Solving tip

Start with the clue that allows fewest numbers. Two-digit squares are only 16, 25, 36, 49, 64 and 81, and a crossing digit often leaves one.

Common use cases

• A number-sense puzzle for a maths class or club: factors, squares, primes and digit sums
• A puzzle page for a newsletter, with the answer printed separately
• Practice in reasoning from crossings: a digit fixed in one entry narrows another

How this generator works

The first search places whole entries, always the one with the fewest values left, and after each placement it removes values that no longer fit a crossing square or a clue tying two entries. It has a limit of 200,000 steps; if it reaches the limit it has proved nothing, and the puzzle is thrown away. The second search, which is also the check shown on the page, reads only the printed grid and clues: it fills one square at a time in reading order and tests each entry as its digits arrive. It too has a limit, and a puzzle it cannot settle is thrown away. The clue numbers are found again from the grid, and every clue is re-tested against the answer with separate arithmetic.

Randomness and fairness

The digits and the choice of clues come from the browser's secure generator, or a seeded one when you type a seed. Seeds are deterministic, not cryptographic, and not a secret.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

• Entries read left to right and top to bottom; “reverse” means the digits written backwards.

Limitations and good to know

• Exactly one answer is proved only for the clues as printed, within the clue kinds listed; nothing is graded for difficulty.
• Fixed grid shapes: two at 4 × 4 and two at 5 × 5.
• Clue wording is formulaic, not the cryptic or story clues of published crossnumbers.

Common mistakes

Starting an entry with 0

No entry starts with 0, so 07 is never a two-digit answer.

Treating 1 as prime

1 is not a prime number; the smallest prime is 2.

Privacy and your data

Puzzles are made in your browser. With analytics consent, a count records how many entries a puzzle had; the seed and the puzzle are not sent.