2.86 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.
(China Junior High School Mathematics League, 1986)
[Solution] $\because$ When $a=0$, the equation $||x-2|-1|=0$ has two solutions $x=1,3$, $\therefore$ (A) is not correct.
$\because$ When $a=1$, we have $|1 x-2|-1|=1$,
which means $|x-2|=2$ or $|x-2|=0$, yielding three solutions $x=0,2,4$. Therefore, the correct choice is $(B)$.