Task 1. We have two jugs, one holds exactly 3 liters, and the other holds exactly 5 liters. Can we measure exactly 4 liters using the two jugs?
Solution. First, we fill the 3-liter jug and pour it into the 5-liter jug, leaving room for 2 more liters. Then, we fill the 3-liter jug again and use it to fill the 5-liter jug, which means that 1 liter will remain in the 3-liter jug. We empty the full 5-liter jug and pour the 1 liter from the 3-liter jug into it. Finally, we fill the 3-liter jug for the third time and pour it into the 5-liter jug, which already has 1 liter. This way, the 5-liter jug now has exactly 4 liters.