Mathematical Games

A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks. — Gian-Carlo Rota.

I maintain this page for the only reason that I love puzzles and mathematical games. This page lists the resources found on www. Any such list (on any subject) has to be inexhaustible, still I hope this is as useful to someone as it has been to me.

• Richard Kaye’s Minesweeper Pages — Several interesting results including NP-completeness of minesweeper, turing completeness of infinite minesweeper and several other interesting links.
• What is the smallest number of entries in a Sudoku puzzle that has a unique completion? and Mathemtics of SuDoku
• Ed Pegg Jr.’s Math Games
• The ever reliable, Ed Pegg Jr.’s MathPuzzle.com
• Eric Friedman’s Math Magic with a great Puzzle of the Month feature
• Ponder This! at IBM Research
• Games on Graphs
• “Cross-sums” a.k.a. Kakuro is Sudoku’s bigger (and harder) brother, mathematics of Kakuro (Kakuro has been proven to be in NP! The algorithm and tips on solving it) and Kakuro Strategies
• Mathematics of the Game of Life. Following is a two-part interview of John Conway himself in which he talks about the philosophy and math of the game.
  
  
• Prof. Eppstein’s Combinatorial Games page has huge a collection
• Prof. Berlekamp’s Combinatorial Games page has his research and links to the literature relating to Dots and Boxes, Go, Konane, Amazons, Clobber
• Dave Rusin’s page on abstract games
• Dots and Boxes – Players take turns joining two horizontally or vertically adjacent dots by a line. A player that completes the fourth side of a square (a box) colours that box and must play again. When all boxes have been coloured, the game ends and the player who has coloured more boxes wins. Other games at Prof. Tom Ferguson’s website.