1. (48th Slovenian Mathematical Olympiad) Find all three-digit numbers that satisfy the following condition: the number is equal to 30 times the sum of its digits.
1. Consider the number $\overline{x y z}$, satisfying $100 x+10 y+z=30(x+y+z)$.

If an integer is a multiple of 30, then its last digit must be 0, so the digit $z$ must be 0. Therefore, we have $100 x+10 y=30(x+y)$, which simplifies to $10 x+y=3(x+y)$.
Thus, we have $7 x=2 y$.
Since $x, y$ are both single-digit numbers, the only possibility is $x=2, y=7$, so there is only one three-digit number that is 30 times the sum of its digits, and this number is 270.