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Dominos Overwhelming

Source: Tournament of Towns Spring 2017 Junior-A

January 30, 2018
combinatoricsgeometryChessboardRussia

Problem Statement

1×21\times 2 dominoes are placed on an 8×88 \times 8 chessboard without overlapping. They may partially stick out from the chessboard but the center of each domino must be strictly inside the chessboard (not on its border). Place on the chessboard in such a way: a) at least 4040 dominoes, (3 points) b) at least 4141 dominoes, (3 points) c) more than 4141 dominoes. (6 points)
(Mikhail Evdokimov)
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