Problem #7

Given the m×n array of points whose first coordinates come from the set {1,2,...,m} and whose second coordinates come from the set {1,2,...,n}, what is the total number of lines determined by all pairs of these points? For example when m = 3 and n = 2, the figure below shows that there are 11 lines (3 vertical, 2 horizontal, 4 at a 45 degree angle, and 2 other diagonals).

The solution will be posted shortly.

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