$33 \cdot 26$ Let $[t]$ denote the greatest integer not exceeding $t$, where $t \geqslant 0$ and
$$
S=\left\{(x, y):(x-T)^{2}+y^{2} \leqslant T^{2} \text { where } T=t-[t]\right\} \text {. }
$$

Then we have
(A) For any $t$, the point $(0,0)$ does not belong to $S$.
(B) The area of $S$ is between 0 and $\pi$.
(C) For all $t \geqslant 5, S$ is contained in the first quadrant.
(D) For any $t$, the center of $S$ lies on the line $y=x$.
(E) None of the above statements is correct.
(24th American High School Mathematics Examination, 1973)
［Solution］When $t \geqslant 0$, $0 \leqslant t-[t] \leqslant 1$. That is, when $t \geqslant 0$, we always have $0 \leqslant T<1$. Therefore, $S$ is a circle with center $(T, 0)$ and radius $T$, its area is $\pi T^{2}(0 \leqslant T<1)$, which lies between 0 and $\pi$.
Hence, the correct choice is $(B)$.