Combinatorics pigeonhole principle with matrix

104 Views Asked by At

Let A be a 100 x 100 matrix such that every number from {1, 2, ... 100} shows in A exactly 100 times.

Prove that there's a row or a column with at least 10 different numbers.

The context is the Pigeonhole Principle.

EDIT: theres a solution to this questuion here: Prove that there exists a row or a column of the chessboard which contains at least √n distinct numbers.

but the problem is that I dont understand how to prove the part which is said to be "clearly

I couldn't solve it by myself, when trying every strategy I know for solving Pigeonhole problems.