MathDB
L+2x2=3x3

Source: Rioplatense L-2 2022 #2

December 13, 2022
geometryrotationcombinatorics

Problem Statement

Let m,n≥2m,n\geq 2. One needs to cover the table m×nm \times n using only the following tiles: Tile 1 - A square 2×22 \times 2. Tile 2 - A L-shaped tile with five cells, in other words, the square 3×33 \times 3 without the upper right square 2×22 \times 2. Each tile 1 covers exactly 44 cells and each tile 2 covers exactly 55 cells. Rotation is allowed. Determine all pairs (m,n)(m,n), such that the covering is possible.

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