MathDB

Two players,

A

and

B

, play a game on a board which is a rhombus of side

n

and angles of

60^{\circ}

and

120^{\circ}

, divided into

2n^2

equilateral triangles, as shown in the diagram for

n=4

A

uses a red token and

B

uses a blue token, which are initially placed in cells containing opposite corners of the board (the

60^{\circ}

ones). In turns, players move their token to a neighboring cell (sharing a side with the previous one). To win the game, a player must either place his token on the cell containing the other player's token, or get to the opposite corner to the one where he started. If

A

starts the game, determine which player has a winning strategy.

Problem Statement