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Chess in Flatland

April 11, 2011
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Professor Stewart's Hoard Of Mathematical Treasures by Ian Stewart

I have not yet begun to finish talking about different dimensions. And this will be the second time (but also not the last) I write about chess, because chess is a game of infinite dimensions.

A Math Puzzle

We play a two-dimensional form of chess in our three-dimensional world. But in the book Professor Stewart's Hoard of Mathematical Treasures, Ian Stewart proposes an interesting math puzzle, known as Chess in Flatland.

Take It Out of the Book and Into the World

Remember Flatland? I totally expounded on it here. It is a two-dimensional land populated by geometric shapes such as triangles, squares, and circles. They have their own version of chess, one-dimensional chess, which you can play at home.

How You Ask?

chess in Flatland
One-dimensional chess is played with three pieces to each side--a king, a knight and a rook. The pieces are set up on an eight-cell board in that order, with two empty cells ("squares," in regular chess) between them. The rules are pretty much the same as in standard chess. The king can move forward or backwards one cell. The knight can jump over other pieces, and moves two squares in either direction at a time. The rook can move across any number of empty cells, in either direction.

Checkmate, Stalemate

Checkmate occurs when a player's king is placed into check without means of escape (or without means of blocking), and stalemate occurs when a player cannot make any legal moves.

Do It Yourself

You can play flatland chess at home by placing your chess board at eye level and viewing it from the side! Only one row of squares and six pieces are needed to play this game, which is guaranteed to provide veritable minutes of entertainment! A game of flatland chess is as much fun as a rousing game of tic-tac-toe, and, really, works in kind of the same fashion. once you work out all the moves in flatland chess, it becomes impossible for you to lose if you start as white, kind of like how it is impossible to lose at tic-tac-toe if you go first (and if you know what you are doing).

 

Author Bio:

Josh Pearce was developed by IBM. On May 11, 1997, he won a six-game match by two wins to one with three draws against world champion Garry Kasparov.