## Task 1 - 120811

Determine all three-digit natural numbers $z$, each of which satisfies the following conditions:

(1) The cross sum of the number $z$ is 12

(2) The two-digit number formed from the tens and units digit (in that order) of the number $z$ is five times the one-digit number formed from the hundreds digit of $z$.
The hundreds digit of the sought number $z$ can only be one of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9.

If one determines the other two digits for each of these according to (2), one obtains exactly the numbers 105, 210, 315, 420, 525, 630, 735, 840, 945.

Of these, only the numbers 525 and 840 have a digit sum of 12, thus also fulfilling (1) and are therefore the only solutions to the problem.