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BALTIC-WAY 2005 Problem 9

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A rectangle is divided into 200×3200 \times 3 unit squares. Prove that the number of ways of splitting this rectangle into rectangles of size 1×21 \times 2 is divisible by 3 .

Dataset text NuminaMath olympiads. Quoted with source.

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N_{6k+2} \equiv 0 \pmod{3}

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