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Today our professor presented us with a puzzle of interest called The 'eating apple' problem (I have no idea what is it called formally though). The rules are

  • There are three compartments, in which each compartment contains 3, 5, and 7 apples respectively.
  • Two players, or 'eaters', will eat n apples in turns, until all apples are eaten. (n>0, n not necessarily 1)
  • The last player to empty the compartments will be declared the loser.
  • Each player can eat from at most one compartment at a time.

After trial and error with my friends, I have discovered that the person who starts the game will have an advantage, if not even a total dominance over the other player, but how can I prove this? As a cs student, I'm not a math geek at all, so a little help to where I can start would be appreciated.

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Have you tried thinking about what would happen if you had one compartment? Then two? Then maybe one apple in the third compartment etc –  Mark Bennet Apr 10 '12 at 6:12
Related: math.stackexchange.com/questions/52130/the-game-of-nim and math.stackexchange.com/questions/33468/a-nim-game-variant. The first is not exact dupe, but can be considered minor variant, I suppose. The second is just related. –  Aryabhata Apr 10 '12 at 6:16
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1 Answer

up vote 2 down vote accepted

This is the classic game/variant of NIM. The wiki has a good description on the winning strategies.

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