Thursday, 24 May 2018

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 propsed 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?" 

Here's The Problem


... 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 and thirty two of the other. There are conceptual solutions but you cannot solve it in reality. Itn 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, Elvis Costello's "Watching The Detectives" , something from "Chess" but I'm going for Jefferson Airplane's "White Rabbit" as it mentions a chessnoard and it is sucjh a perfect piece of music. Enjoy your Thursday everybody.

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