Coin Problem?

Question

A coin game requires:1. Ten coins in one pile.2. That each player takes one, two, or four coins from the pile at alternate turns.3. That the player who takes the last coin loses.I. When Austin and Brooks play, Austin goes first and Brooks goes second.II. Each player always makes a move that allows him to win when possible; if there is no way for him to win, then he always makes a move that allows a tie when possible.Must one of the two men win? If so, which one?

Answer 1

Austin will always win if he take 4 on his first turn despite how many Brooks takes on his turn.



~6 remaining after Austin's turn~

Brooks takes 1

Austin take 4

Brooks is left with the last one

Brooks take 2

Austin take 3

Brooks is left with the last one

Brookes also take 4

Austin take 1

Brooks is once again left with the last one