3. Two buckets, a river, and an empty open barrel that holds about 200 liters of liquid are available. It is not allowed to pour from one bucket to another. Can 13 liters of water be measured in the barrel if the buckets have capacities of:
a) 7 liters and 11 liters,
b) 6 liters and 10 liters?
Solution. a) They can be measured. Namely, since $2 \cdot 11 - 3 \cdot 7 = 1$, it follows that $26 \cdot 11 - 39 \cdot 7 = 13$. This means we fill 11-liter containers 26 times and empty 7-liter containers 39 times, resulting in 13 liters.

b) It is not possible, because 13 is an odd number, while the capacity of each bucket is an even number.