Rose and Kylie are playing a game. Here are the rules：  1. There are $$14$$ marbles placed in a row.  2. The players take turns removing either $1$ or $2$ marbles each turn.  3. Whoever picks the last marble wins the game.  Rose starts first and is followed by Kylie. To ensure her victory, how many marbles must Rose take away in the first turn? 
Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy
If there are n marbles in total, the first player has a winning strategy for all $$n$$ that is not a multiple of $$3$$. For $$n$$ being a multiple of $$3$$, the second player can always win, regardless of what strategy the first player plays.  $$14\div (1+2)=4 \textbackslash{} \text{R} 2$$ Rose should take away the remainder, i.e. two marbles, to make herself the second player when there is a multiple of $3$ marbles left. 