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3031 identical dominoes, in 3x 2021 chessboard missing 1 corner square

Source: 2021 Irish Mathematical Olympiad P4

May 30, 2021
combinatorial geometrycombinatoricsdominoes

Problem Statement

You have a 3×20213 \times 2021 chessboard from which one corner square has been removed. You also have a set of 30313031 identical dominoes, each of which can cover two adjacent chessboard squares. Let mm be the number of ways in which the chessboard can be covered with the dominoes, without gaps or overlaps. What is the remainder when mm is divided by 1919?
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