MathDB

Let

n \ge 2

. Ana and Beto play the following game: Ana chooses

2n

non-negative real numbers

x_1, x_2,\ldots , x_{2n}

(not necessarily different) whose total sum is

1

, and shows them to Beto. Then Beto arranges these numbers in a circle in the way she sees fit, calculates the product of each pair of adjacent numbers, and writes the maximum value of these products. Ana wants to maximize the number written by Beto, while Beto wants to minimize it. What number will be written if both play optimally?

Problem Statement