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!