$33 \cdot 27$ For every real number $x$, let $[x]$ denote the greatest integer not exceeding $x$. If first-class mail costs 6 cents per ounce (or fraction thereof), then the first-class postage in cents for a letter weighing $W$ ounces is given by the formula
(A) $6 W$.
(B) $6[W]$.
(C) $6([W]-1)$.
(D) $6([W]+1)$.
(E) $-6[-W]$.
(22nd American High School Mathematics Examination, 1970)
[Solution] The postage calculation involves another function $L(x)$, which represents the smallest integer not less than $x$. Now we prove that $L(x)=-[-x]$.
If we set $x=n+\alpha, n$ as an integer, $0 \leqslant \alpha<1$. Then $[x]=n, \quad$ and $\quad L(x)=\left\{\begin{array}{ll}n, & \text { if } \alpha=0 ; \\ n+1, & \text { if } \alpha \neq 0 .\end{array}\right.$
When $-x=-n-\alpha$,
$[-x]=\left\{\begin{array}{ll}-n, & \text { if } \alpha=0 ; \\ -n-1, & \text { if } \alpha \neq 0 .\end{array}\right.$
That is, $-[-x]=\left\{\begin{array}{ll}n, & \text { if } \alpha=0 ｝ \\{n+1,} &{\text { if } \alpha \neq 0 .}\end{array}\right.$
Therefore, $6 L(W)=-6[-W]$.
Hence, the answer is $(E)$.