Home > Combinatorics, IMO, Problem Solving > 2×1 tilling of a square board

## 2×1 tilling of a square board

Suppose that a $n\times n$ board is filled with $2 \times 1$ rectangles in such a way that only one unit square remains uncovered. Moreover, any two such small rectangles do not form a $2\times 2$ square. Prove that the free square is situated at the center of the board.