Consider the following
Two players are
presented with a pile of n cookies. Taking turns, each player must choose a
number between 1 and 4 and eat that many cookies, until there are no cookies
left. Whichever player did not eat the last cookie wins a lifetime supply of
cookies (a truly incredible reward indeed).
I highly encourage practicing this game with a
friend and a fresh batch of cookies.
1. Prove or disprove Vn
e Z+, P(n), where P(n): “The current player can guarantee a win if n = 5a for
some positive integer a.”
2. Suppose the pile
contains 24 cookies. If you wish to win the lifetime supply, is it better to go
first or second?
3. Briefly describe the
optimal strategy to win the game.
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