## Task 4 - 040624

Fritz gives Heinz the following riddle:

"In our class, 26 students can ride a bike and 12 students can swim. Every student can do at least one of these. If you multiply the number of students by 5, the cross sum of this product is twice as large as the cross sum of the number of students. Additionally, the product is divisible by 6.

How many students are in the class?"
From the first statement, it follows that the class can have at least 26 and at most 38 students.

The last statement narrows this possibility down to the numbers 30 and 36. Of these numbers, only 30 fulfills all conditions.

Solutions of the II. Round 1964 taken from [5]

### 3.6 V. Olympiad 1965

### 3.6.1 I. Round 1965, Class 6