Question 135
On a blackboard we write in a line $n$ numbers, $n \ge 40$, each being equal to $1$ or $-1$, such that:
(i) The sum of every $40$ successive numbers is equal to $0$.
(ii) The sum of every $42$ successive numbers is not equal to $0$.
We denote by $\Sigma_n$ the sum of the $n$ numbers on the blackboard. Find the greatest possible value of $\Sigma_n$.
(i) The sum of every $40$ successive numbers is equal to $0$.
(ii) The sum of every $42$ successive numbers is not equal to $0$.
We denote by $\Sigma_n$ the sum of the $n$ numbers on the blackboard. Find the greatest possible value of $\Sigma_n$.