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MathNet 2018-part-01 — 181 problems (EN–VI) Question 122

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 122

Three $n \times n$ squares form the figure $\Phi$ on the checkered plane as

Question illustration

shown in the picture. (Neighbouring squares touch along a segment of length $1$.)
Find all $n \gt 1$ for which the figure $\Phi$ can be covered with $1 \times 3$ and $3 \times 1$ tiles without overlapping.