The Mutilated Chessboard 



If you think you know everything about this already, you might want to head over to The Mutilated Chessboard Revisited ... 
Something not often mentioned is that cutting off two adjacent corners leaves the remaining squares coverable, and it takes 31 dominoes. It's not hard  pretty much the first attempt will succeed.
So here's the classic problem:
One of the key characteristics of mathematicians and puzzlers is that they don't simply give up, they try to prove that it's impossible. 
So that's the question  when two opposite corners have been removed from the chessboard, is it possible to cover it completely and exactly with dominoes?
Or can you prove that it's impossible?
If you've seen this, or if you solve it, or if you simply want to know more, you might like to visit this page:
There we find that there's more going on than most people think.
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Quotation from Tim BernersLee 