You play a game where two people take turns picking coins from a pile of coins and the person to take the last coin wins!

The rule is you can take up to $n$ coins where $n$ is the turn number.

So, for example, suppose Sue and Esmerelda are playing the game. The first person (Sue) can take 1 coin (not much of a choice there!). The second person to play (Esmerelda) can take 1 or 2 coins. The third person (Sue again) can take 1, 2 or 3 coins.

Suppose you are the first to move and there are 16 coins.

If both people play optimally, can you guarantee a win?

No
Yes

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If $t$ is the turn number, and $c$ is the number of coins in the pile, then the following recursive relation determines whether you will win or not ( $1=$ win, $0 =$ lose):

Solving, $W(1,16) = 1$ .

So, $\boxed{\text{yes}}$ you can win!