Problem

Source: INMO 2024/2

Tags: combinatorics



All the squares of a $2024 \times 2024$ board are coloured white. In one move, Mohit can select one row or column whose every square is white, choose exactly $1000$ squares in that row or column, and colour all of them red. Find maximum number of squares Mohit can colour in a finite number of moves. $\quad$ Proposed by Pranjal Srivastava