In Sweden, there is allegedly a very deep ground fissure or cave, into which if we drop a stone, we only hear the impact sound after $25 \mathrm{sec}$. How deep is the cave, if we also take into account the speed of sound?
Let the sought depth be $x$, the time interval between the stone being dropped and the sound arriving be $t$, and the speed of sound be $c$. According to the problem:

$$
t=\frac{x}{c}+\sqrt{\frac{2 x}{g}}
$$

from which

$$
x^{2}-2\left(c t+\frac{c^{2}}{g}\right) x+c^{2} t^{2}=0
$$

which gives:

$$
x=\frac{c}{g}\left(c+g t \pm \sqrt{c^{2}+2 g c t}\right)
$$

Since according to the first equation $\frac{x}{c}<t$, thus $x<c t$, the square root can only be taken with a negative sign; substituting the given values: $x=1867 \mathrm{~m}$.

(Thiringer Aurél, secondary school VII. grade, Sopron.)

The problem was also solved by: Bálint B., Bauss O., Eislitzer Gy., Fischer O., Freund A., Friedmann B., Geist E., Goldstein Zs., Grünhut B., Hofbauer E., Iványi B., Kántor N., Klein M., Kornis Ö., Kunsch M., Ländler D., Lichtenberg S., Manheim E., Riesz F., Schiffer H., Schneider B., Szabó I.