4. A three-digit number, all digits of which are different and non-zero, will be called balanced if it is equal to the sum of all possible two-digit numbers formed from the different digits of this number. Find the smallest balanced number.
Answer: 132.

Solution: Let the desired number be of the form $\overline{a b c}$. Then it can be represented as the sum of six different two-digit numbers: $\overline{a b c}=\overline{a b}+\overline{b a}+\overline{a c}+\overline{c a}+\overline{b c}+\overline{c b}$.

From the last equality, we get $100 a+10 b+c=22 a+22 b+22 c$, then, combining like terms and dividing both sides of the equation by 2, we reduce it to the form $26 a=4 b+7 c$.

Next, let $a=1$. Clearly, if we get a balanced number starting with 1, it will be less than any number with $a \geq 2$. Then we have $4 b+7 c=26$. Since $c$ is not less than 1, $b$ does not exceed 4. For $b=4$, we immediately get a contradiction, and for $b=3$, we find $c=2$. The smallest balanced number is 132.

Grading criteria: Correct and justified solution - 7 points, only the correct answer with verification - 2 points, the equation in integers using the digits of the number is obtained - $\mathbf{1}$ point, the solution is incorrect or only the answer without verification - 0 points.