For numbering the pages of a larger work, 2184 digits were needed. How many pages does the work have?
For the numbering of the pages, 9 single-digit, 90 double-digit, and $x$ triple-digit numbers were needed. Therefore,

$$
9 \cdot 1 + 90 \cdot 2 + x \cdot 3 = 2184
$$

from which

$$
x = 665
$$

and thus the work consists of $9 + 90 + 665 = 764$ pages.

(Czukor Gábor, Budapest, high school student.)

Number of solutions: 33.