6. A cat and a mouse occupy the top right and bottom left cells respectively of an rectangular grid, where . Each second they both move diagonally one cell. For which pairs is it possible for the cat and the mouse to occupy the same cell at the same time?
Note: For every pair you must either prove that it is impossible for them to meet, or explain a sequence of moves that ends with both in the same cell.
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Maclaurin Mathematical Olympiad (2021)
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