Question: Let (xi, yi, zi), i = 1, 2, 3, 4, 5, 6, 7, 8, 9, be a set of nine distinct points with integer coordinates

Let (xi, yi, zi), i = 1, 2, 3, 4, 5, 6, 7, 8, 9, be a set of nine distinct points with integer coordinates in xyz space. Show that the midpoint of at least one pair of these points has integer coordinates.

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