February 23–March 2, 2010

Problem

Each of n numbers x1, x2, ..., xn is selected from the set {-1, 1}. Prove that if

x_1 x_2 x_3 x_4 + x_2 x_3 x_4 x_5 + ... + x_{n-1} x_{n} x_1 x_2 + x_{n} x_1 x_2 x_3 = 0,

Then n is a multiple of 4.

Solution

here

List of solvers

Joshua Lim, Lloyd Sakazaki, Peiyush Jain, Mukund Tirumalai, Mike Goodman, Bai Li, Dod Moshe, Congpa You (outside).

Bai Li wins the prize!