8. Let there be $n$ real numbers, satisfying $\left|x_{i}\right|<1(i=1, \cdots, n),\left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right| \geqslant 19+\mid x_{1}+\cdots$ $+x_{n}$ |. Then the minimum value of $n$ is $\qquad$.
8. We solve it in two steps. The first step is to estimate a precise lower bound for $n$.

From $\left|x_{i}\right|19$.
The second step is to conjecture that the minimum value of $n$ is 20. We construct an example to show that the problem has a solution when $n=20$. Take
$$
x_{i}=\left\{\begin{array}{ll}
0.95 & \text { (when } i \text { is odd). } \\
-0.95 & \text { (when } i \text { is even). }
\end{array}\right.
$$

Such $x_{i}(i=1, \cdots, 20)$ satisfy the conditions of the problem and the given inequality, thus the minimum value of $n$ is 20.