# Sudoku Maker (4×4 to 16×16, with Answer Key)

> Printable sudokus with one solution, graded by the solving techniques needed. Make printable sudokus from 4 × 4 for young children to 16 × 16 for experts. Every puzzle is proven to have exactly one solution, its difficulty is graded by the techniques a person needs (singles, locked candidates, pairs, triples, X-wing), and answer-key pages follow. Up to six per page, as a true-size PDF.

Part of usefulweb.site (https://usefulweb.site/). Part of [Printshop](https://printshop.usefulweb.site/) (ownerApp: printshop). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://printshopsudoku.usefulweb.site/ (interactive tool at https://printshopsudoku.usefulweb.site/tool)
- JSON API: POST https://printshopsudoku.usefulweb.site/api/v1/calculate with a JSON object of inputs (schema: https://printshopsudoku.usefulweb.site/api/v1/tool)
- OpenAPI: https://printshopsudoku.usefulweb.site/openapi.json
- MCP (Streamable HTTP): https://printshopsudoku.usefulweb.site/mcp - tool `printshop_sudoku`

## Inputs
- size (select): Grid size
- difficulty (select): Difficulty
- count (integer): Number of sudokus
- perPage (select): Sudokus per page
- symmetric (boolean): Symmetric clues (180° rotation)
- seed (text): Seed - The same seed and settings always give the same puzzles. Change it for new ones.
- title (text): Title on the page (optional)
- answers (boolean): Answer-key pages
- header (boolean): Name and date line
- paper (select): Paper size
- orientation (select): Orientation

## Method
- A full grid is filled by a randomised depth-first search that always tries the cell with the fewest candidates. Clues are then removed in a seeded order (in pairs when symmetric); a removal is kept only when a counting solver still finds exactly one solution — a count that runs out of its node budget keeps the clue, so uniqueness is always proven.
- Difficulty: a logic solver applies techniques from simple to hard — naked and hidden singles (easy), locked candidates (medium), naked and hidden pairs, naked triples and X-wing (hard). The grade is the hardest technique it needed; “expert” puzzles are unique but need more (chains or trial and error). For easy and medium a removal is also undone when the puzzle would need harder techniques.
- Easy puzzles keep at least 45 % of the cells as clues, medium at least 32 %. Several digging orders are tried and the one that matches the requested level best is kept; the printed level is always the measured one.

## Limits
- Difficulty is measured by technique, not by solving time; people find different techniques hard. 16 × 16 grids have a time budget and may keep a few extra clues.