You shower every odd day and paint on even ones. So you paint on days 2, 4, 6, 8, etc., and shower on days 1, 3, 5, 7, etc. If you start on day 1 (a shower day), then you will be covered in paint on days 2, 4 and 6 (both even days) but clean on all other days (odd days). Therefore, there is no day when you are both covered in paint and clean at the same time.
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