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I had been asked the following question:

n coins are placed on a line such that they touch each other. A move consists in taking either one coin, or two adjacent (touching) coins. Solve the standard version of the game.

There are 2 players. I've seen version of this solved, where if two coins were adjacent, then if chosen they must be taken together.

E.g. for n=4 coins, consider the following combination. Player 1 has made his move, and has taken coin 2. Player 2 then, has the following situation

1 0 3 4 (0 is the missing coin, taken by player 2),

We may either take 1 or (3,4). This is not the version I am asking about. In the version I'm considering, you can take either 1,3,4 or (3,4). I've been struggling with this for ages now, and I really can't come up with much, that would get me close to the answer. Any thoughts, for solving this game for all n? I would be thankful for any input! It seems very similar to the other version, however i can't get anywhere with this!

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  • $\begingroup$ (0) Welcome to Puzzling Stack Exchange. (1) Questions should be self-contained and self-sufficient. I don’t know the game you are talking about; just state all the rules. (2) The fact that you talking vaguely about two different games, and not precisely describing either of them, makes this question very difficult for us non-telepaths to understand. $\endgroup$
    – Peregrine Rook
    Feb 16, 2017 at 17:08

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This is the game of

Kayles

a discussion of whose theory can be found at the other end of that link. (I don't recall ever encountering the different version you describe where "if two coins were adjacent, then if chosen they must be taken together".)

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