A $0,1,4,5,7,9$ digits can form how many 4-digit numbers in which at least one digit is repeated?
If we subtract the number of groups starting with 0 $\left(V_{6}^{i, 3}\right)$ from the number of ismétléses (repetitive) fourth-class variations formed from the given 6 elements $\left(V_{6}^{i, 4}\right)$, we get the number of all 4-digit numbers that can be formed from the given digits. Among these, the number of numbers containing all different digits is similarly: $V_{6}^{4}-V_{5}^{3}$.

Thus, the number of 4-digit numbers that can be formed from the given digits, in which at least one digit is repeated:

$$
\begin{aligned}
& \left(V_{6}^{i, 4}-V_{6}^{i, 3}\right)-\left(V_{6}^{4}-V_{5}^{3}\right)=\left(6^{4}-6^{3}\right)-(6 \cdot 5 \cdot 4 \cdot 3-5 \cdot 4 \cdot 3)= \\
& \quad=6^{3}(6-1)-5 \cdot 4 \cdot 3(6-1)=5(216-60)=5 \cdot 156=780
\end{aligned}
$$

Roboz Ágnes (Bp. VI., Varga Katalin g. I. o. t.)