38. Pete and Vasya take turns painting the edges of a 77-sided pyramid, one at a time. You can paint an edge that has not been painted yet, provided that all adjacent edges are not painted. The player who cannot make a move loses. Pete starts. Who among them can always win, regardless of how the opponent plays? (Edges are adjacent if they share a common vertex.)
- Answer: Vasya. We will divide the edges into pairs, matching each base edge with a lateral edge passing through the opposite vertex of the base. In response to Petya's first move, Vasya paints the second edge from the same pair. After this, only certain base edges can be painted, which are divided into two identical non-intersecting sets. On Petya's move in any of the sets, Vasya repeats it in the other set.

(A. Shapovalov)