A number's cube is a five-digit number; the first digit is 4, the fifth is 6. Which number is this?
If the sought number is $n$, then

\[
\begin{aligned}
& 40000<n^{3}<50000 \\
& 34, \ldots<n<36, \ldots
\end{aligned}
\]

It follows that $n$ is either 35 or 36. Since the units digit of $n^{3}$ is 6, only $n=36$ is possible $\left(36^{3}=46656\right)$. Ozoróczy Sarolta (Szilágyi Erzsébet female high school, V. grade, Bp. I.)