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 2002-07-08 17:11:20