3. On the board is written a three-digit number **8. A trio of students guessed the properties of this number.

Zoran: All its digits are even and it has an even number of different prime divisors.

Daniel: It is divisible by 9 and is the square of some natural number.

Nikola: It is less than 400 and 13 times the square of some natural number.

It turned out that each of them guessed only one property of the number. Which digits are in the places of the asterisks?
Solution. The number written on the board has the digit 8 in the units place, so it cannot be a square of a natural number. Therefore, Daniel's statement that the number is divisible by 9 is correct. According to this, it is one of the following numbers: $109,198,288,378,468,558,648,738,828,918$. From Nikola's statement, it follows that these can be numbers less than 400 or the number 468, since $468=13 \cdot 36$. We factorize the remaining numbers:

$$
\begin{gathered}
108=2 \cdot 2 \cdot 3 \cdot 3 \cdot 3,198=2 \cdot 3 \cdot 3 \cdot 11,288=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \\
378=2 \cdot 3 \cdot 3 \cdot 3 \cdot 7,468=2 \cdot 2 \cdot 3 \cdot 3 \cdot 13
\end{gathered}
$$

We see that only one of the properties mentioned by Bojan are satisfied by the numbers 108 (an even number of distinct factors) and 468 (all digits are even).

The number written on the board is one of the numbers 108 or 468.