Task 1 - 110931 Günter tells:

"I remember our school's six-digit phone number like this:

I write down our two-digit house number. Behind it, I write the cross sum of the house number and then add the sum of the last two digits written each time, until six digits stand. By the way, there is no one in the phone number of our school, and our house number is a number divisible by 3."

What is Günter's house number and what is the phone number of his school?
If the cross sum of the first two numbers were two-digit, it would be at most 18, and thus the telephone number would contain a 1, which is not possible. Therefore, the cross sum must be a single digit. Since the house number also must not contain a 1, the remaining possibilities for the house number are: $24, 27, 30, 33, 36, 42, 45, 54, 60, 63, 72, 90$ with the cross sums $6, 9, 3, 6, 9, 6, 9, 9, 6, 9, 9, 9$ respectively. In all cases except for $30, 33, 60$, and 90, the first digit of the next sum would be a 1, which is not allowed. For 33, it results in 336915, for 60 it results in 606612, and for 90 it results in 909918, which are not valid. Therefore, the house number is 30 and the telephone number is 303369.