The Case of The Mutilated Chessboard

Introduction

This is another Seven Days In article from six years ago when I was reading a number of books by the excellent Simon Singh, and this is the one below:

What the Theorem is and what the back cover of the books says:

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions

n 1963 a schoolboy browsing in his local library stumbled across the world's greatest mathematical problem: Fermat's Last Theorem, a puzzle that every child can understand but which has baffled mathematicians for over 300 years. Aged just ten, Andrew Wiles dreamed that he would crack it. Wiles's lifelong obsession with a seemingly simple challenge set by a long-dead Frenchman is an emotional tale of sacrifice and extraordinary determination. In the end, Wiles was forced to work in secrecy and isolation for seven years, harnessing all the power of modern maths to achieve his childhood dream. Many before him had tried and failed, including a 18-century philanderer who was killed in a duel. An 18-century Frenchwoman made a major breakthrough in solving the riddle, but she had to attend maths lectures at the Ecole Polytechnique disguised as a man since women were forbidden entry to the school. A remarkable story of human endeavour and intellectual brilliance over three centuries, Fermat's Last Theorem will fascinate both specialist and general readers.

The Case of The Mutilated Chessboard

Still not thirty pages into Simon Singh's "Fermat's Last Theorem" and he throws in another conceptual gem of a problem apparently first proposed by a guy called Max Black in his book "Critical Thinking" in 1946. It sounds like the title of an Agatha Christie or Sir Arthur Conan Doyle novel (who incidentally met up in Sky Arts' "Urban Myths" series here).

The Wikipedia entry for the Mutilated Chessboard problem is here but basically, it's this

"Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares?"

.. and basically, it is actually impossible because each domino must cover a black and a white square and the board is left with thirty of one colour and thirty-two of the other. There are conceptual solutions but you cannot solve it in reality. In the book, this was introduced when talking about the concept of mathematical theory against scientific theory.

Science always has doubt because it is based on observation whereas mathematics demands absolute proof and until that happens it's always just a theory.

So suitable music for this could be Elvis Costello's "Watching The Detectives" or something from "Chess" but I'm going for Jefferson Airplane's "White Rabbit" as it mentions a chessboard and it is such a perfect piece of music. Enjoy your Thursday everybody.

Conclusion:

This came up in my blog feed and I remember being incredibly fascinated with the book. Of course, this is another example of my fascination with numbers and if you have any similar inclinations get yourself a copy and dive in.

Seeing this has made me want to revisit the book and Simon Singh's other publications, although this is a fascinating pseudo-detective story as there was no crime but just a lost or forgotten explanation, and it was finally found.

There was no jeopardy but just the excitement of the journey to finally prove the theorem.

Thank you for reading.