Consider a $2023\times2023$ board split into unit squares.
Source: 2023 Junior Macedonian Mathematical Olympiad P5
October 6, 2023
combinatorics
Problem Statement
Consider a board split into unit squares. Two unit squares are called adjacent is they share at least one vertex. Mahler and Srecko play a game on this board. Initially, Mahler has one piece placed on the square marked M, and Srecko has a piece placed on the square marked by S (see the attachment). The players alternate moving their piece, following three rules:
1. A piece can only be moved to a unit square adjacent to the one it is placed on.
2. A piece cannot be placed on a unit square on which a piece has been placed before (once used, a unit square can never be used again).
3. A piece cannot be moved to a unit square adjacent to the square occupied by the opponent’s piece.
A player wins the game if his piece gets to the corner diagonally opposite to its starting position (i.e. Srecko moves to , Mahler moves to ) or if the opponent has to move but has no legal move. Mahler moves first. Which player has a winning strategy?