MathDB
Classical double-counting combo

Source: Bulgaria MO Regional round 2024, 11.4

February 13, 2024
combinatorics

Problem Statement

A board 2025×20252025 \times 2025 is filled with the numbers 1,2,,20251, 2, \ldots, 2025, each appearing exactly 20252025 times. Show that there is a row or column with at least 4545 distinct numbers.