$35 \cdot 21$ In a box, there are many pieces of wood, which are red, white, and blue. The number of blue pieces is at least half the number of white pieces and at most one-third the number of red pieces. The sum of the number of white and blue pieces is at least 55. The minimum number of red pieces is
(A) 24.
(B) 33.
(C) 45.
(D) 54.
(E) 57
(22nd American High School Mathematics Examination, 1971)
[Solution] Let $w, b$ and $r$ represent the number of white, blue, and red wood chips, respectively. Then $w \leqslant 2 b$, and $3 b \leqslant r$. It is also known that $w+b \geqslant 55$, so $2 b+b=3 b \geqslant 55$.
Since $b$ is an integer, then $b \geqslant 19$,
thus $r \geqslant 3 b \geqslant 57$. The minimum number of red wood chips is 57.
Therefore, the answer is $(E)$.