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by dmurray
1675 days ago
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Yes, by induction. Suppose the total number of squares is 2n. Remove any domino that doesn't disconnect the board, and reduce to the problem for 2n - 2. Alternative proof: no, by example. Consider the shape made up by the X's in XXX
.X.
.X.
XXX
(All maths proofs should be presented alongside a proof of the opposite result, to allow the reader to judge which one is likely to have slipped something past you. My favourite presentation following this rule is Mental Poker [0] by the authors of RSA.)[0] https://people.csail.mit.edu/rivest/pubs/SRA81.pdf |
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