Let's find two numbers whose sum, product, and quotient are the same.
Let $x$ and $y$ be the two sought numbers. Then

$$
\begin{gathered}
x y=\frac{x}{y}, \text { from which, if } x \lessgtr 0 . \\
y=\frac{1}{y}
\end{gathered}
$$

from which

$$
y= \pm 1
$$

Furthermore

$$
x \pm 1= \pm 1 \cdot x
$$

so $x$ has a finite value only if we consider the negative value of $y$, and thus

$$
x=\frac{1}{2}, y=-1
$$

(László Szántó, Pécs.)

Number of solutions: 25.