1. All real numbers $c$ that make the equation $|x-1|-|x-2|+2|x-3|=$ $c$ have exactly two solutions are $\qquad$ .
二、1. $c>3$ or $13$;
(2) When $1 \leqslant x3$, the original equation has exactly two solutions $\frac{5-c}{2}, \frac{5+c}{2}$;
When $1<c<3$, the original equation has exactly two solutions $\frac{7-c}{2}, \frac{5+c}{2}$.