## Task 2 - 300612

a) List all two-digit natural numbers where one of the digits is 4 less than the other!

b) Determine among these numbers all those that are divisible by their digit sum!

Hint: The digit sum of a natural number is the sum of its digits. For example, the number 24801 has a digit sum of 15 because $2+4+8+0+1=15$.
The following table contains in the first row exactly all the numbers sought in (a). In the second row, the cross sum of each of these numbers is given. In the third row, the answer to the question of whether the respective number is divisible by its cross sum is stated (j for yes, n for no). According to this, the numbers 40, 84, and 48 are exactly those sought in (b).

| Number | 40 | 51 | 15 | 62 | 26 | 73 | 37 | 84 | 48 | 95 | 59 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Cross Sum | 4 | 6 | 6 | 8 | 8 | 10 | 10 | 12 | 12 | 14 | 14 |
| Divisible? | j | n | n | n | n | n | n | j | j | n | n |