**A. 402.** Two players play the following game: Let *n* be a fixed integer greater than 1. Starting from number *k*=2, each player has two possible moves: either replace the number *k* by *k*+1 or by 2*k*. The player who is forced to write a number greater than *n* loses the game. Which player has a winning strategy for which *n*?

*Vojtech Jarnik Competition,*Ostrava, 2006

(5 points)