m×n grid is tiled by mosaics 2×2 and 1×3 (horizontal and vertical). Prove that the number of ways to choose a 1×2 rectangle (horizontal and vertical) such that one of its cells is tiled by 2×2 mosaic and the other cell is tiled by 1×3 mosaic [horizontal and vertical] is an even number. combinatoricsrectangleParity