2. Nikola thought of three different digits, different from zero. Martin wrote down all the two-digit numbers using these digits. The sum of all the numbers that Martin wrote down is equal to 231. Which digits did Nikola think of?
Solution. Let $a, b$, and $c$ be the three digits that Nikola has thought of. From these three digits, nine two-digit numbers can be written: $\overline{a a}, \overline{b b}$, $\overline{c c}, \overline{a b}, \overline{b a}, \overline{b c}, \overline{c b}, \overline{a c}, \overline{c a}$. Their sum is:

$$
\begin{aligned}
231= & (10 a+a)+(10 b+b)+(10 c+c)+(10 a+b)+(10 b+a)+ \\
& +(10 b+c)+(10 c+b)+(10 a+c)+(10 c+a) \\
= & 33 a+33 b+33 c \\
= & 33(a+b+c)
\end{aligned}
$$

From this, $a+b+c=7$. Given that the digits $a, b$, and $c$ are distinct, the digits that Nikola has thought of are 1, 2, 4, as there are no other possibilities.