1. A person has 12 pints of wine in a barrel (pint - an old French unit of volume, 1 pint ≈ 0.568 liters) and wants to give away half of the wine, but does not have a 6-pint container. However, there are two empty containers with capacities of 8 pints and 5 pints. How can one use them to measure out exactly 6 pints of wine?

This is the most famous problem of its kind; it is known as Poisson's problem. The famous French mathematician, mechanician, and physicist Siméon Denis Poisson (1781-1840) solved it in his youth and later said that it was precisely this problem that inspired him to become a mathematician.
$\triangle$ The solution to the problem can be written as follows:

| Vessel with a capacity of 8 pints | 0 | 8 | 3 | 3 | 0 | 8 | 6 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Vessel with a capacity of 5 pints | 0 | 0 | 5 | 0 | 3 | 3 | 5 | 0 |

This should be understood as follows. Initially, both vessels are empty (first column). We fill the vessel with a capacity of 8 pints (second column), then we fill the vessel with a capacity of 5 pints from it (third column), then we pour these 5 pints from the smaller vessel into a barrel that already contains 12 pints (fourth column), then we transfer 3 pints of wine from the vessel with a capacity of 8 pints to the vessel with a capacity of 5 pints (fifth column), and so on until the larger of the two vessels contains 6 pints of wine.

Try to solve the problem differently, by first filling the vessel with a capacity of 5 pints. Will the solution be shorter?

Another method for solving such problems - using graphs - is discussed in the reference [16].