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Possible values of determinant of 0-1 matrices

Source: 2021 Simon Marais, A3

November 2, 2021
matrixdeterminantlinear algebra

Problem Statement

Let M\mathcal{M} be the set of all 2021×20212021 \times 2021 matrices with at most two entries in each row equal to 11 and all other entries equal to 00. Determine the size of the set {det⁡A:A∈M}\{ \det A : A \in M \}. Here det⁡A\det A denotes the determinant of the matrix AA.
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