6・76 Given $\left|x_{i}\right|<1, i=1,2, \cdots, n$. Also,
$$\left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right|=19+\left|x_{1}+x_{2}+\cdots+x_{n}\right|$$

What is the minimum value of the integer $n$?
［Solution］From the given, we have
$$\sum_{i=1}^{n}\left|x_{i}\right|-\left|\sum_{i=1}^{n} x_{i}\right| \leqslant \sum_{i=1}^{n}\left|x_{i}\right|19$$,
thus we have $\quad n \geqslant 20$.
On the other hand, when $n=20$, we take
$$x_{i}=\left\{\begin{array}{l}
\frac{19}{20}, 1 \leqslant i \leqslant 10 \\
-\frac{19}{20}, 11 \leqslant i \leqslant 20 .
\end{array}\right.$$

Then $x_{1}, x_{2}, \cdots, x_{20}$ satisfy all the conditions given in the problem.
In conclusion, the smallest integer $n$ is 20.