Imagine a "grid" of people: some number of people arranged in a number of rows and columns in a rectangular formation.

We designate person A as the shortest person in the group of the tallest people of each row. We then designate person B as the tallest person in the group of shortest people in each column.

Who is taller, A or B?

I'm not sure how to prove it but I am speculating that the A = B always. But I guess the reason would be the fact that the tallest of the short people are columns and the shortest of the tall people are rows which means that they can infact and always will be the same person.