Problem

Source: Ukraine 1997

Tags: combinatorics proposed, combinatorics



There are $ n$ candidates on a table. Petrik and Mikola alternately take candies from the table according to the following rule. Petrik starts by taking one candy; then Mikola takes $ i$ candies, where $ i$ divides $ 2$, then Petrik takes $ j$ candies, where $ j$ divides $ 3$, and so on. The player who takes the last candy wins the game. Which player has a winning strategy?