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2019 Central American and Caribbean Mathematical Olympiad, P6

Source:

June 19, 2019
combinatoricstiles

Problem Statement

A triminó is a rectangular tile of 1×31\times 3. Is it possible to cover a 8×88\times8 chessboard using 2121 triminós, in such a way there remains exactly one 1×11\times 1 square without covering? In case the answer is in the affirmative, determine all the possible locations of such a unit square in the chessboard.
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