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ASU 565 Commonwealth of Independent States 1991 gnomons in mxn table

Source:

August 15, 2019
tablecombinatoricscombinatorial geometry

Problem Statement

An m×nm \times n rectangle is divided into mn unit squares by lines parallel to its sides. A gnomon is the figure of three unit squares formed by deleting one unit square from a 2×22 \times 2 square. For what m,nm, n can we divide the rectangle into gnomons so that no two gnomons form a rectangle and no vertex is in four gnomons?
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