MathDB

Let

n \geq 5

be a positive integer. There are

n

stars with values

1

n

, respectively. Anya and Becky play a game. Before the game starts, Anya places the

n

stars in a row in 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 a draw. Find all

n

such that Becky has a winning strategy.
Proposed by Ho-Chien Chen

Problem Statement