Suppose that $mn$ people of a marching band are standing in a rectangular formation of $m$ rows and $n$ columns in such a way that in each row each person is taller than the one to his or her left. Suppose that the leader rearranges the people in each column in increasing order of height from front to back. Show that the rows are still arranged in increasing order of height from left to right.
EDIT: Thanks. I didn't know that this question was already here, only differently phrased.