26.2.1 * In a regular $2 n$-sided polygon, vertices are alternately colored red and black. Two players, A and B, take turns drawing diagonals whose endpoints are the same color, but these diagonals cannot intersect with any previously drawn diagonals by the same player. A starts first. The player who cannot draw a diagonal loses. Is A guaranteed to win or is B guaranteed to win?
Parse "B must win".
Consider a regular $2n$-gon $A_{1} A_{2} \cdots A_{2 n}$. The strategy is: When A draws the diagonal $A_{i} A_{j}$, B only needs to draw the diagonal $A_{i+1} A_{j+1}\left(A_{2 n+1}-A_{1}\right)$.
