MathDB
ASU 091 All Soviet Union MO 1967 499 white castles and 1 black king

Source:

June 20, 2019
combinatoricsChessboard

Problem Statement

"KING-THE SUICIDER" Given a chess-board 1000×10001000\times 1000, 499499 white castles and a black king. Prove that it does not matter neither the initial situation nor the way white plays, but the king can always enter under the check in a finite number of moves.