# Maze Maker (Rectangle, Hexagon, Round and Shapes)

> Printable mazes in squares, hexagons or circles, cut to a heart, star or your own shape. Make printable mazes with square or hexagon cells or round “theta” mazes, optionally cut to a heart, star, circle, diamond, triangle or a shape you draw with # signs. Choose the recursive backtracker (long corridors), Kruskal or Wilson (uniform random) algorithm, up to six mazes per page and answer keys with the solution path.

Part of usefulweb.app (https://usefulweb.app/). Part of [Printshop](https://printshop.usefulweb.app/) (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://printshopmaze.usefulweb.app/ (interactive tool at https://printshopmaze.usefulweb.app/tool)
- JSON API: POST https://printshopmaze.usefulweb.app/api/v1/calculate with a JSON object of inputs (schema: https://printshopmaze.usefulweb.app/api/v1/tool)
- OpenAPI: https://printshopmaze.usefulweb.app/openapi.json
- MCP (Streamable HTTP): https://printshopmaze.usefulweb.app/mcp - tool `printshop_maze`

## Inputs
- shape (select): Cells
- cols (integer): Columns
- rows (integer): Rows (rings for a round maze)
- mask (select): Outline
- maskText (textarea): Own shape (# = inside) - One text line per row; # marks a cell inside the maze. Columns and rows then come from the drawing.
- algorithm (select): Algorithm
- count (integer): Number of mazes
- perPage (select): Mazes per page
- 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
- Every shape is a graph of cells whose sides are either shared with a neighbour or part of the outer wall. Square and hexagon grids can be cut to an outline (tested at each cell centre); only the largest connected group of cells is kept. Round mazes have one centre cell and rings whose cell count doubles when cells get wider than two ring heights.
- The maze is a spanning tree of that graph, so exactly one path joins the entrance (top) and the exit (bottom, or the centre of a round maze). Recursive backtracker = randomised depth-first search (about 10 % dead ends); Kruskal = random walls removed with union–find (about 30 %); Wilson = loop-erased random walks, which pick every possible maze with the same probability.
- The solution is found by breadth-first search through the open passages and drawn through the cell centres and the middle of each passage.

## Limits
- Very large mazes on small paper get thin walls; check the PNG preview before printing many copies.