Two players, A and B, play a game on a board which is a rhombus of side n and angles of 60∘ and 120∘, divided into 2n2 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∘ 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. geometryrhombuscombinatorics unsolvedcombinatorics