Question 4
Suppose that $|x_i|\lt1$ for $i=1,$ $2,$ $\ldots,$ $n.$ Suppose further that
$$
\begin{aligned}&|x_1|+|x_2|+\cdots+|x_n|\\&=19+\bigl|x_1+x_2\\&\qquad+\cdots+x_n\bigr|.\end{aligned}
$$
What is the smallest possible value of $n?$
$$
\begin{aligned}&|x_1|+|x_2|+\cdots+|x_n|\\&=19+\bigl|x_1+x_2\\&\qquad+\cdots+x_n\bigr|.\end{aligned}
$$
What is the smallest possible value of $n?$