MathDB

For real numbers

a_1, a_2, \ldots, a_{200}

, we consider the value

S = a_1a_2 + a_2a_3 + \ldots + a_{199}a_{200} + a_{200}a_1

. In one operation, you can change the sign of any number (that is, change

a_i

-a_i

), and then calculate the value of

S

for the new numbers again. What is the smallest number of operations needed to always be able to make

S

nonnegative?
Proposed by Oleksii Masalitin

Problem Statement