Question 65
Given several coins arranged in a row, a legal move is to take either the first or the last coin. In the initial arrangement there are $n$ coins of arbitrary denominations. Ana and Maria make moves in succession. Ana starts by making 2 moves, then Maria makes 1 move, and the same repeats until all coins are taken away: 2 moves of Ana are followed by 1 move of Maria. (Only the last Ana's move can be taking 1 coin if there is a single coin left.) Ana's objective is to ensure at least $\frac{2}{3}$ of the total sum of the coins for herself. Determine if she can do this with certainty if a) $n=2013$; b) $n=2014$.