Problem

Source: 2021 Taiwan TST Round 1 Mock Day 1 P1

Tags: combinatorics, Taiwan



There are $110$ guinea pigs for each of the $110$ species, arranging as a $110\times 110$ array. Find the maximum integer $n$ such that, no matter how the guinea pigs align, we can always find a column or a row of $110$ guinea pigs containing at least $n$ different species.