Question 76
Let $n \ge 5$ be a positive integer. There are $n$ stars with values 1 to $n$, respectively. Anya and Becky play a game. Before the game starts, Anya place the $n$ stars in a row by whatever order she wishes. Then, starting from Becky, each player takes the left-most or right-most star in the row. After all the stars have been taken, the player with the highest total value of stars wins; if their total values are the same, then the game ends in draw. Find all $n$ such that Becky has a winning strategy.