Question 81
Let $n$ be a positive integer such that $n \ge 4$. For every permutation $(s_1, s_2, \dots, s_n)$ of the numbers $1, 2, \dots, n$, we calculate the following expression and write the result on the board:
$$
1s_1 + 2s_2 + 3s_3 + \dots + ns_n
$$
In the end, how many distinct values will be written on the board?
$$
1s_1 + 2s_2 + 3s_3 + \dots + ns_n
$$
In the end, how many distinct values will be written on the board?