$2 \cdot 88|||| x-1|-1|-1|-1|=0$ is an equation containing 4 layers of absolute value symbols. Then
(A) $0,2,4$ are all roots.
(B) $0,2,4$ are not roots at all.
(C) $0,2,4$ are not all roots.
(D) There are no roots other than $0,2,4$.
(2nd "Five Sheep Cup" Junior High School Mathematics Competition, 1990)
［Solution］From the given, we have
||$|x-1|-1|-1|=1$, that is, ||$x-1|-1|-1= \pm 1$,
which means $\square$ ||$x-1|-1|=0$ or 2, so $|x-1|-1=0$ or $\pm 2$, thus $|x-1|=1,-1$ or 3, solving this yields $x=0, \pm 2,4$. Therefore, the answer is $(A)$.