N-Queens Puzzle Generator

What this generator does

Places one queen per row by backtracking, trying columns in a random order so different runs produce different solutions, then re-checks the finished placement for shared columns and shared diagonals. At ten queens or fewer it also enumerates every solution to report the exact total.

How to use this tool

1. Choose a board size and generate a placement.
2. Check it yourself: no two queens share a row, column or diagonal.
3. Read the total number of solutions and compare across sizes.
4. Try 6x6, which has fewer solutions than 5x5 despite the larger board.

Understanding the controls

Board size

Between 4 and 10. There is no solution at all on a 2x2 or 3x3 board, and above ten the exhaustive count becomes slow.

Seed

Any word reproduces exactly the same placement, so the same puzzle can be set and marked later.

Common use cases

• Teaching backtracking with a problem that has a countable answer
• Chess puzzles and classroom starters with a verified solution
• Demonstrating that solution counts do not grow smoothly with board size
• Test instances for a constraint-solving implementation
• Setting the same placement twice from a seed

How this generator works

Only one queen can sit in each row, so the search works row by row and only ever chooses a column — which reduces the problem from placing pieces on 64 squares to choosing 8 numbers. A column is rejected if any earlier queen shares it, or if the difference in columns equals the difference in rows, which is exactly what sharing a diagonal means. The counting pass uses the same rule without the randomisation.

Randomness and fairness

The column order is randomised so each run finds a different solution; the placement is then verified. A seed reproduces the same solution exactly and is therefore explicitly not cryptographically secure. Without a seed the browser's cryptographically secure generator is used.

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

Limitations and good to know

• Boards from 4x4 to 10x10; the exhaustive solution count is what limits the upper end.
• Solutions related by rotation or reflection are counted separately, which is the standard convention.
• One solution is shown at a time rather than all of them.
• No difficulty rating — every size is equally easy for the solver, however hard it is by hand.
• Placements are not stored between visits; seed one you want again.

Privacy and your data

The placement and the solution count are computed in your browser. Nothing about the board or your seed is transmitted or kept.