Combinatorics - possibly pigeon hole, 100 by 100 matrix with numbers from 1 to 100

Question

We are given a $100$ by $100$ matrix. Each number from $\{1,2,...,100\}$ appears in the matrix exactly a $100$ times.

Show there is a column or a row with at least $10$ different numbers.

I'd like a small tip how to tackle this problem. I tried of thinking what are the pigeons and what are the holes. obviously there are 200 holes (100 rows and 100 columns). what are the pigeons?

Answer 1

Managed to solve it.

first, understand that each number appears in at least 20 different rows and columns (maximum is 101, minimum is 20). The most extreme and compact case, is that a number fills a $10$ by $10$ matrix, so that's 20 holes

But we have 100 different numbers, 100*20=2000. $\frac{2000}{200}=10$ and so there is a hole with at least 10 different numbers