ELMO 2020 Problem 5

Let $m$ and $n$ be positive integers. Find the smallest positive integer $s$ for which there exists an $m \times n$ rectangular array of positive integers such that

• each row contains $n$ distinct consecutive integers in some order,
• each column contains $m$ distinct consecutive integers in some order, and
• each entry is less than or equal to $s$ .

Proposed by Ankan Bhattacharya.