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?
Label each person by row and column: the person in the first row, first column position is (R1,C1) the person to his right is (R1, C2). The person in back of (R1,C1) is (R2, C2), etc.
Person A is (Rar, Cac) and person B is (Rbr, Cbc) [Ideally the r and c should have been subscripts]
Consider person C = (Rar, Cbc). He is in the same row as A, and so must be shorter than A (who is the tallest person in his row)
Likewise, since he is the same column as B, he must be taller than B. Since A is taller than C, who in turn, is taller than B, A must be taller than B
This assumes that A and B are in different rows and different columns. If they are in the same row, then person C is person A , and the argument that person C is taller than person B still applies. If they are in the same column, then person C is Person B, and the argument that person A is taller than person C still applies. If they are in the same row and the same column, then they are the same person, and must be the same height.

Posted by TomM
on 20020708 17:11:20 