For how many elements is it true that the number of repetitive 3-class variations is 225 greater than the number of variations without repetition?
Let the number of sought elements be denoted by $n$. According to the problem,

$$
V_{n}^{i, 3} n=V_{n}^{3}+225
$$

Since $V_{n}^{i, 3}=n^{3}$ and $V_{n}^{3}=n(n-1)(n-2)$, we have

$$
n^{3}=n(n-1)(n-2)+225
$$

which means

$$
n^{3}=n^{3}-3 n^{2}+2 n+225
$$

or

$$
3 n^{2}-2 n-225=0
$$

from which

$$
n_{1}=9 \quad\left|n_{2}=-\frac{25}{3}\right|
$$

The root $n_{2}$ is meaningless in this case. Therefore, the statement is true for 9 elements.

Benedek Tomor (Györ, Révay g. II. o. t.)