Three thieves from the Ali Baba band found a treasure that contained a large amount of gold coins and jewels and decided to distribute it equally among the three without reporting the discovery to the head of the band.

The problem was that they could not agree with the cast, since everyone had different opinions when assessing the pieces found.

**Can you think of a way to distribute the loot satisfactorily for everyone?**

#### Solution

To distribute between three people A, B and C the method would be as follows:

Person A divides the spoils into three parts that he considers of equal value; let's call them 1, 2 and 3. Person A asks B and C to choose a part. The following three cases may occur:

Case 1:

B and C choose different parts (for example, 2 and 3).

Then A takes 1,

B takes 2,

C take 3

and the problem is solved.

Case 2:

B and C choose the same part (for example, 2).

Then A asks B and C to choose a second option. If B and C choose the same part (for example, 3),

then A takes 1,

B and C are distributed 2 and 3 according to the method of the two people

and the problem is solved.

Case 3:

B and C choose the same part (for example, 2).

Then A asks B and C to choose a second option. If B and C choose different parts (for example, B chooses 1 and C chooses 3),

then B and C divide 2 according to the method of the two people,

B and A share 1 according to the method of the two people,

C and A 3 are distributed according to the method of the two people

and the problem is solved.