An octahedron has a volume $V$; what is its surface area $F$?
The volume of an octahedron:

$$
V=\frac{a^{3}}{3} \sqrt{2}
$$

from which

$$
a=\sqrt[3]{\frac{3 V \sqrt{2}}{2}}
$$

$$
F=2 a^{2} \sqrt{3}
$$

Substituting (2) into (3), we get:

$$
F=\sqrt{3} \sqrt[3]{36 V^{2}}
$$

Emil Geiszt. High School VII. grade, Györ

The problem was solved by: Bernát Friedmann, S.-A.-Ujhely; István Szabó, Debrecen; Ervin Hofbauer, Nándor Kántor, Mihály Krausz, Pál István Langheim, and Gyula Pósch, Budapest; Leó Goldberger and Béla Grünhut, Pécs.