Problem 4. Using the digits $a, b$ and $c$, all three-digit numbers with distinct digits are formed. The sum of all such numbers is 5328. Determine all possible values for the digits $a, b$ and $c$.
Solution. The given sum is $\overline{a b c}+\overline{a c b}+\overline{b c a}+\overline{b a c}+\overline{c a b}+\overline{c b a}=5328$, i.e., $2 \cdot 111 \cdot(a+b+c)=5328$. Thus, $a+b+c=24$. There is only one choice for the digits, which is $7,8,9$.