TITLE: Brain teaser Strategic choice...
QUESTION [6 upvotes]: $X$ and $Y$ are playing a game. There are $11$ coins on the table and each player must pick up at least $1$ coin, but not more than $5$. The person picking up the last coin loses. $X$ starts. How many should he pick up to start to ensure a win no matter what strategy $Y$ employs?

REPLY [4 votes]: No matter what Y needs to be left with only $1$. Since the most someone can take is $5$ and the least someone can take is $1$ then in order to win, X needs to make sure he is picking when there are between $1+1=2$ and $1+5=6$ coins left. So to do this in the least amount of steps possible, X needs to start off by taking $4$ coins. Then there will be $7$ coins left. After Y's turn, there will be guaranteed between $2$ and $6$ coins left. Then X just needs to take $5$ coins and Y will be forced to take $1$ and X wins.