Question: Please show a full proof thanks! Two players are presented with a pile of n cookies. Taking turns, each player must choose a number between

Please show a full proof thanks!

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 rst or second? 3. Briey describe the optimal strategy to win the game

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