Brain teaser Strategic choice... $X$ 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?

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*$X$ must not reach the state of $2\dots6$ coins left on the table at $Y$'s turn

*Otherwise, $Y$ can take $1\dots5$ coins (leaving $1$ coin on the table) and win

*So $X$ should take $4$ coins off the table, and leave $7$ coins on the table

*Then, however many coins $Y$ takes, $X$ can take the remaining coins minus $1$
