There are $13$ coins arranged in a circular fashion.
Andrew and Bill play a game with these rules:
- Andrew starts the game
- A player can remove $1$ or $2$ adjacent coins from the circle during his turn.
- The one who removes the last coin wins.
Assuming that both players are smart and play optimally, who wins?
An example is shown below:
The brown coin cannot be taken with the yellow or orange coins as it is not adjacent anymore. Similarly, one or both of the orange coins can be taken, but not with a yellow coin or the brown coin.
This puzzle is NOT the 20 coins on the table!