Three individuals - $A$, $B$, and $C$ - inherited an annual annuity of 9000 crowns for 25 years. They agreed that each would enjoy the entire annuity alone until they had received their respective share. How long did each enjoy the annuity?
The value of all annuities today:

$$
t=\frac{9000}{e^{25}} \frac{e^{25}-1}{e-1}
$$

where $e$ is the known interest factor: $\left(1+\frac{p}{100}\right)$. One third of this amount goes to each. If $A$ enjoys the annuity for the first $x$ years, then

$$
\frac{9000}{e^{x}} \cdot \frac{e^{x}-1}{e-1}=\frac{3000}{e^{25}} \cdot \frac{e^{25}-1}{e-1}
$$

from which

$$
x=\frac{\log 3+25 \log e-\log \left[2 e^{25}+1\right]}{\log e}
$$

After $x$ years, $B$ enjoys the annuity for $y$ years; thus

$$
\frac{9000}{e^{y}} \cdot \frac{e^{y}-1}{e-1}=\frac{3000}{e^{25}} \cdot \frac{e^{25}-1}{e-1} e^{x}
$$

Finally, $C$ enjoys the remaining $z$ years:

$$
z=25-(x+y)
$$

Let $p=4 \%$, then:

$$
\begin{array}{lccccccc}
\mathrm{x} & = & 5 & \text { years } & 11 & \text { months } & 14 & \text { days, } \\
\mathrm{y} & = & 7 & " & 9 & " & 12 & " \\
\mathrm{z} & = & 11 & " & 3 & " & 4 & \text { " }
\end{array}
$$

(Szmodics Hildegárd, Kaposvár.)

The problem was also solved by: Bartók I., Enyedi B., Haar A., König D., Pintér M., Schmidl I., Tóbiás J. L.