Problem

Source: XII International Festival of Young Mathematicians Sozopol 2023, Theme for 10-12 grade

Tags: combinatorics



A table has $3 000 000$ rows and $100$ columns, divided into unit squares. Each row contains the numbers from $1$ to $100$, each exactly once, and no two rows are the same. Above each column, the number of distinct entries in that column is written in red. Find the smallest possible sum of the red numbers.