chess piece domination puzzles
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README.md

chessdom

Please try out the live example here. Pages in this repo are intended to help explore the mathematical chess concepts of domination (covering) and independence (unguarding). In the mathematical chess problem of domination, you are tasked with finding an arrangement of several pieces of the same type so that every square on the board is reachable in a single move by at least one of the pieces. In the problem of independence, your goal is to place the maximum number of pieces of the same type so that none of the pieces lie in the path of another.

On the Explorer page, you can experiment by placing pieces on boards of different sizes. When using this page, you are not restricted to use only pieces of the same type.

explorer example

On the Puzzles page, you can attempt to solve a number of mathematical chess puzzles involving domination and independence. For example:

explorer example

puzzles

Information on mathematical chess puzzles can be obtained from many sources online. My primary source was John J. Watkins book Across the Board (2004, Princeton University Press).

Puzzle definitions are generated by running the puzzles.py Python script in the build directory.

[chessdom/build]$ python puzzles.py 
-------------------------------------------
Generating Chess Puzzle Data.
 --- creating file ../data/puzzles.json
 --- done

This script generates the puzzles.json script, which contains puzzles in this format:

{
  "name": "8 queens on 8x8",
  "size": 8,
  "cover": "true",
  "unguard": "true",
  "pieces": [
    {
      "name": "queen",
      "count": 8
    }
  ]
}

The puzzle above is the classic "8 queens" problem, one of the more difficult problems in the set.