## Task 2 - 230812

Determine all three-digit natural numbers $n$ with the following properties:

(1) The cross sum of $n$ is 17.

(2) If you multiply the first digit (i.e., the hundreds digit) of $n$ by 4, you get a two-digit number, which is exactly the number formed by the last two digits of $n$.
From (2) it follows:

For the hundreds digit of the sought number $n$, only $3, 4, \ldots, 9$ are possible, and for $n$ subsequently only the numbers $312; 416; 520; 624; 728; 832; 936$.

The corresponding digit sums are: $6; 11; 7; 12; 17; 13; 18$.

It is evident from this that only the number 728 satisfies both conditions (1), (2).