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Perpendicula, the magnificent princess of the rectangle, is admiring her magnificent new bathroom. It's rectangular of course; 10m wide and 20m long. It still needs tiling, though, and Perpendicula has ordered tiles of pure gold to mirror the dimensions of the bathroom: they are 1m wide and 2m long.
There is a problem though: water, milk and honey pipes need to be fitted in two diagonally opposed corners of the bathroom. This means that in each of these two corners a square area of 1m×1m has to remain untiled. Can the rest of the floor area be tiled without cutting any of the 2m×1m tiles?