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Covering a board with 1x2 horizontal dominoes and 3x1 vertical trominoes

Source: 2003 Junior Macedonian Mathematical Olympiad P5

June 29, 2021
combinatorics

Problem Statement

Is it possible to cover a 2003×20032003 \times 2003 chessboard (without overlap) using only horizontal 1×21 \times 2 dominoes and only vertical 3×13 \times 1 trominoes?
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