Question 58
The real numbers $x_1, x_2, \ldots, x_{1991}$ satisfy
$$
|x_1 - x_2| + |x_2 - x_3| + \ldots + |x_{1990} - x_{1991}| = 1991.
$$
What is the maximum possible value of
$$
|s_1 - s_2| + |s_2 - s_3| + \ldots + |s_{1990} - s_{1991}|,
$$
where $s_n = (x_1 + x_2 + \ldots + x_n)/n$?
$$
|x_1 - x_2| + |x_2 - x_3| + \ldots + |x_{1990} - x_{1991}| = 1991.
$$
What is the maximum possible value of
$$
|s_1 - s_2| + |s_2 - s_3| + \ldots + |s_{1990} - s_{1991}|,
$$
where $s_n = (x_1 + x_2 + \ldots + x_n)/n$?