## Task 4 - 040824

Peter is at a summer camp. He wants to buy soda for his group at 21 Pf per bottle and takes empty bottles with him.

With the refund money (30 Pf for each of the empty bottles), he wants to buy as many bottles of soda as possible. For each bottle, 30 Pf deposit must be paid again.

It turns out that he receives 6 fewer bottles than he handed in. Additionally, he gets some money back.

How many empty bottles did Peter take with him? (There is not just one solution.)
Peter has to pay for the content of the bottles he bought from the proceeds of the 6 bottles not returned. Since $180: 21=8 \frac{12}{21}$, he could have bought a maximum of 8 bottles.

1. Solution: Peter had 14 bottles and receives 12 Pf back.
2. Solution: Peter had 13 bottles and receives 33 Pf back.

If Peter had had 12 bottles, he could have bought 7 bottles, i.e., $(n-5)$ instead of just $(n-6)$, which contradicts the problem.

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

### 5.6.3 III. Round 1964, Class 8