## 1. British Hospital

In a British hospital, the following announcement can be read: "Surgeon $X$ and Nurse $Y$ have the pleasure of announcing their forthcoming marriage." Suppose that at the time the hospital was opened, the groom was as old as the bride is now, and that the product of the ages of the groom and the bride and the number of years the hospital has been in existence minus the age of the surgeon equals 1539. When was the hospital opened?
1. Let $x$ be the age (number of full years) of the surgeon (groom or bride), $y$ be the number of years of the paramedic (groom or bride), and $h$ be the number of years the hospital has been in existence.

The conditions of the problem can be written as the following two equations:

$$
\begin{gathered}
|x-y|=h \\
x(y h-1)=1539=3^{4} \cdot 19
\end{gathered}
$$

Since, by the context of the problem, $x$ is obviously greater than 9 and less than 171, there are four possible values for $x$: $19, 27, 57, 81$.

These correspond to four values of the expression ($y h - 1$): $81, 57, 27, 19$ and, therefore, four values for $y h$: 82, 58, 28, and 20.

But if $y h=82=2 \cdot 41$, then $y=41, \quad h=2$,

$$
\begin{array}{lll}
y h=58=2 \cdot 29 & y=29, & h=2 \\
y h=28=2^{2} \cdot 7, & y=28 & h=1 \\
y h=20=2^{2} \cdot 5, & y=20, & h=1 .
\end{array}
$$

We obtained these four solutions using only the second equation. If we also use the first equation ($|x-y|=h$), then only the second solution remains, i.e., $x=27, y=29$, and $h=2$.

Thus, the problem is about the marriage of a 29-year-old paramedic to a 27-year-old female surgeon, who work in a hospital that opened 2 years ago.