MathDB

On the board we write a series of

n

numbers, where

n \geq 40

, and each one of them is equal to either

1

-1

, such that the following conditions both hold:
(i) The sum of every

40

consecutive numbers is equal to

0

. (ii) The sum of every

42

consecutive numbers is not equal to

0

.
We denote by

S_n

the sum of the

n

numbers of the board. Find the maximum possible value of

S_n

for all possible values of

n

3