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rectangles by lines // sides of rectangle (2017 Auckland MO J5)

Source:

November 14, 2021
combinatorial geometrycombinatoricsrectangle

Problem Statement

A rectangle ABCDABCD is given. On the side ABAB, n different points are chosen strictly between AA and BB. Similarly, mm different points are chosen on the side ADAD between AA and DD. Lines are drawn from the points parallel to the sides. How many rectangles are formed in this way?
An example of a particular rectangle ABCDABCD is shown with a shaded one rectangle that may be formed in this way. https://cdn.artofproblemsolving.com/attachments/e/4/f7a04300f0c846fb6418d12dc23f5c74b54242.png
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