3. If the equation ||$x-2|-1|=a$ has three integer solutions for $x$, then the value of $a$ is
(A) 0 ;
(B) 1 ;
(C) 2 ;
(D) 3 .
3. (B)

Solve $\because$ when $a=0$, the equation $||x-2|-1|=0$ has two solutions $x=1,3$,
$\therefore$ (A) is not correct.
$\because$ when $a=1$, $||x-2|-1|=1$,
$\therefore|x-2|=2$ or $|x-2|=0$, which has three solutions $x=0,2,4$.
Also, $\because$ only one of (A), (B), (C), (D) is correct, so (B) should be chosen.