MathDB

A rectangular piece of paper is divided into square cells by lines parallel to the sides of the rectangle.

n

(horizontal) rows of

m

cells have emerged and

m

(vertical) columns of

n

cells have also been formed. There is a number in each cell. Find the largest number in each of the

n

rows. The smallest maxima of those

n

rows is called

A

. We also look for the smallest number in each of the

m

columns. The largest minima of those

m

columns is called

B

. Prove that

A

is greater than or equal to

B

. Can you give a simple example where

A = B

Problem Statement