$29 \cdot 3$ is a three-digit number composed of three different non-zero digits (decimal). When this number is divided by the sum of these three digits, the minimum value of the quotient is
(A) 9.7.
(B) 10.1.
(C) 10.5.
(D) 10.9.
(E) 20.5.
(23rd American High School Mathematics Examination, 1972)
[Solution] Let the units, tens, and hundreds digits be $U, T$, and $H$, respectively. Therefore, the minimum value of the quotient is
$$
\frac{U+10 T+100 H}{U+T+H}=1+\frac{9(T+11 H)}{U+T+H} .
$$

Regardless of the values of $T, H$, when $U=9$, the above expression is minimized.
Thus,
$$
\frac{T+11 H}{T+H+9}=1+\frac{10 H-9}{T+H+9} .
$$

Since $T \neq 9$, the value is minimized when $T=8, H=1$.
Therefore, the number is 189, and the minimum value of the quotient is $\frac{189}{18}=10.5$. Hence, the answer is $(C)$.