14-12 Choose any three-digit positive integer $N$ represented in decimal notation, with each three-digit number having an equal chance of being selected. The probability that $\log _{2} N$ is an integer is
(A) 0 .
(B) $\frac{3}{899}$.
(C) $\frac{1}{225}$.
(D) $\frac{1}{300}$.
(E) $\frac{1}{450}$.
(26th American High School Mathematics Examination, 1975)
[Solution] From 100 to 999 there are 900 three-digit numbers, among which there are three:
$$
128=2^{6}, 256=2^{7}, 512=2^{8}
$$

are powers of 2, and thus their logarithms to the base 2 are also integers.
Therefore, the required probability is $\quad \frac{3}{900}=\frac{1}{300}$. Hence, the answer is $(D)$.