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