Question 59
Let $a_1, a_2, \dots, a_{100}$ be a permutation of numbers $1, 2, \dots, 100$. Denote by $N$ the number of different values of the sums
$$
\sum_{i=u}^{v} a_i, \quad \text{where} \quad 1 \le u \le v \le 100.
$$
Is it possible that $N \ge 2500$?
$$
\sum_{i=u}^{v} a_i, \quad \text{where} \quad 1 \le u \le v \le 100.
$$
Is it possible that $N \ge 2500$?