Best of the Web: the mutilated chessboard

The mutilated chessboard

Hi everyone,

John and I have admitted to spending way too much time following the Chess World Cup on the event's official website. It features live streaming with commentary by GMs, including Susan Polgar! There have been some pretty spectacular games, especially between gata Kamsky and Shakriyar Mamedyarov, and there's lots more to come. Watch it here! 

I also wanted to recommend chesstempo's latest creation, a fun feature called "Guess the move", in which you go through master games and try to guess the moves as you go along. They've developped a rating system of sorts and I must say I had a good time going through the two free games basic members get (ie with a free account you only have access to two games, but there are many more for Gold members). Hopefully this feature will become popular and make its way to other free websites soon!

If you have an interest in brain-teasers and maths (as I expect a lot of you do!), read on!

The mutilated chessboard

I've just started a book called "Fermat's Enigma", by Simon Singh. It tells the story of Fermat's Last Theorem, a problem which baffled mathematicians for over 350 years before it was finally solved in the 1990s by Andrew Wiles. Very interesting read if you're interested in the history of maths, but I'm not here to ramble about that. The reason I mention this book is because in the first chapter, the author introduces the concept of mathematical proof by using a chess-related problem, which I thought would be a nice change from my usual posts. 

A quick google search informs me that the problem goes back to Max Black's book Critical Thinking (1946), and was featured in Martin Gardner's famous column "Mathematical Games" in Scientific American.

Here is the problem statement:

Take out two diagonally opposite corner squares of a chess board (a1and h8 or a8 and h1). There are thus 62 squares remaining. Now suppose you have 31 dominoes of dimension 2 x 1 (aka 1 domino covers two squares), is it possible to cover the entire board using only the 31 dominoes provided? 

Of course, you can't cut dominoes or anything like that. The idea is simply to find out if it's possible to cover the board entirely with the remaining dominoes. If it is possible, then you must find an arrangement. If, after a few tries, you come to the conclusion it isn't possible, then try to prove it.

Good luck!

You can find the solution here or on Wikipedia.