## Task 1 - 290611

Peter wants to measure exactly 13 liters of milk from a jug that contains more than 13 liters. The exact capacity of the jug is unknown, and it is also unknown how much milk is exactly in the jug. In addition to the jug, there are exactly two more containers available. One has a capacity of exactly 5 liters, and the other has a capacity of exactly 17 liters.

(There are no markings or similar means to measure other quantities.)

Describe how Peter can measure exactly 13 liters of milk using only these tools!
Peter can proceed as follows:

He first fills the small container three times with 5 liters each and pours it into the large container. Since $3 \cdot 5=15$, the large container then contains exactly 15 liters; since $17-15=2$, exactly 2 liters of milk still fit into it. These 2 liters are poured from the small container, which is filled again, into the large container, so that now there are $5-2=3$ liters left in the small container.

After that, the large container is emptied back into the can, and the 3 liters are then poured into the large container. If 5 liters of milk are added twice more, the large container contains $3+2 \cdot 5=13$ exactly 13 liters of milk, as required.