Hobby explorations of the n-queens puzzle: the flat board, the wrap-around ("doughnut") board, queens in 3-D cubes and higher dimensions, what the average solution looks like on large boards, and how many solutions there are.
Everything lives on the website: pieceofdiy.com/queens. This GitHub page only points there; the notes, results, scripts' outputs and interactive pictures are kept and updated on the site.
This is a hobby project, worked out with Claude (Anthropic's AI assistant) by someone who is not a professional mathematician. Nothing here has been peer reviewed. Please check every result before relying on it.
- The flat board
- The doughnut board
- Queens in a cube
- Higher dimensions
- Density maps: what the average solution looks like
- A chessboard lock (hobby build idea)
- Solution structure: big boards, pairs, balance and the swap web
Every result as a pre-registered question with its answer: results analysis and the question list.
- The queens constant measured: a Monte Carlo count on 128 x 128 and 256 x 256 boards gives e^C = 2.5595 +- 0.0022, siding with the computed 2.560 over the earlier 2.55 (a confirmation run fixed in advance). See A tour of the queens board.
- Why 14 x 14 stands out: three arithmetic gears decide which perfect structures exist on each board size, with the Lo Shu and magic squares. See Board sizes as trigrams.
- Seeing the puzzle
- Listening to a cloud
- When the solutions join up
- A tour of the queens board
- Board sizes as trigrams
- One dot per solution family
- Pulsing heatmap
- The web of small moves
- Solutions on a sphere
- Doughnut solutions on a sphere
- The semi-queen constant
- Board sizes as trigrams (dial)
Text under CC BY 4.0. Questions and corrections are welcome as issues here or through the site.