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Cross Diagonal Cover Problem

Permanent link to this puzzle: mscroggs.co.uk/puzzles/135
Draw with an \(m\times n\) rectangle, split into unit squares. Starting in the top left corner, move at 45° across the rectangle. When you reach the side, bounce off. Continue until you reach another corner of the rectangle:
How many squares will be coloured in when the process ends?

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If you enjoyed this puzzle, check out Sunday Afternoon Maths LX,
puzzles about area, or a random puzzle.
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