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exactly 225 rectangles with odd sides in m x n grid

Source: New Zealand NZMOC Camp Selection Problems 2017 p5

September 19, 2021
rectanglecombinatoricscombinatorial geometry

Problem Statement

Find all pairs (m,n)(m, n) of positive integers such that the m×nm \times n grid contains exactly 225225 rectangles whose side lengths are odd and whose edges lie on the lines of the grid.
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