## Task 2 - 180522

Marie-Luise wants to specify a two-digit natural number $z$ that simultaneously meets the following conditions (1), (2), (3):

(1) The number $z$ is not divisible by 10.

(2) If the units digit of the number $z$ is increased by 4, the result is the tens digit of $z$.

(3) If the digits of $z$ are swapped, the resulting number is such that its triple is less than 100.

Determine all numbers $z$ that satisfy the given conditions!
If a number $z$ satisfies the given conditions, then:

The units digit is not 0 according to (1), and according to (2), it must be such that when increased by 4, the result is less than or equal to 9.

Therefore, the units digit is one of the digits 1, 2, 3, 4, 5, and for $z$, the possible options are at most $51, 62, 73, 84, 95$.

By swapping the digits, we get 15, 26, 37, 48, 59, and the triple of these numbers is $45, 78, 111, 144, 177$.

Therefore, only the numbers 51 and 62 can satisfy all conditions due to (3). The calculations already performed for these numbers show that these numbers indeed satisfy conditions (1), (2), and (3).