$2 \cdot 68$ Given that $x_{1}, x_{2}, \cdots, x_{1990}$ is any permutation of $1,2, \cdots, 1990$, find the maximum value of the expression
$$
\|\cdots\| x_{1}-x_{2}\left|-x_{3}\right|-\cdots\left|-x_{1990}\right|
$$
[Solution] Note that for any non-negative integers $x, y, z$, we always have $|x-y| \leqslant \max \{x, y\}, \max \{\max \{x, y\}, z\} = \max \{x, y, z\}$. Therefore, for all $n=1,2, \cdots, 1990$, we have
$$
\|\cdots\| x_{1}-x_{2}\left|-x_{3}\right|-\cdots\left|-x_{n}\right| \leqslant \max \left\{x_{1}, x_{2}, \cdots, x_{n}\right\}.
$$

This implies that the value of (1) does not exceed 1990. However, because the parity of the value of (1) is the same as the parity of the sum
$$
x_{1}+x_{2}+\cdots+x_{1990}=1+2+\cdots+1990=995 \times 1991,
$$

it cannot be equal to 1990.
On the other hand, for any four consecutive natural numbers $n, n+1, n+2, n+3$, we have
$$
|||n-(n+2)|-(n+3)|-(n+1)|=0,
$$

so we have
$$
\begin{array}{l}
\quad|\cdots||| 2-4|-5|-3|\cdots|-(4 k+2)|-(4 k+4)|-(4 k+5) \mid \\
-(4 k+3)|\cdots|-1986|-1988|-1989|-1987|-1990|-1| \\
=1989.
\end{array}
$$

In summary, the maximum value of expression (1) is 1989.