Question 184
Two players, $A$ and $B$ play the following game. On a $1 \times n$ board, where fields are labeled in order from $1$ to $n$, a coin is placed at position $k$. Players take turns moving the coin, with player $A$ starting first. Each player can move a coin one or two fields in either direction, with the restriction that the coin cannot move onto a field it had already occupied. The player unable to make a move loses. For which values of $(n, k)$ does which player have a winning strategy?