[ Mathematical logic (miscellaneous).] [ Arithmetic. Mental arithmetic, etc. ]

This ancient problem was known even in Ancient Rome.

A wealthy senator, on his deathbed, left his wife pregnant. After the senator's death, it was discovered that his estate, worth 210 talents, was left with the following will: "In the event of the birth of a son, give the boy two-thirds of the estate (i.e., 140 talents), and the remaining one-third (i.e., 70 talents) to the mother; in the event of the birth of a daughter, give the girl one-third of the estate (i.e., 70 talents), and the remaining two-thirds (i.e., 140 talents) to the mother."

The senator's widow gave birth to twins - a boy and a girl. This possibility was not anticipated by the testator. How can the estate be divided among the three heirs in the best approximation to the conditions of the will?
Since it is impossible to fulfill all the testator's requirements, only a part of them will have to be fulfilled. Depending on which specific part we fulfill, one or another method of division will be adopted.

## Solution

Since it is impossible to fulfill all the testator's requirements, we will have to fulfill only a part of them. Depending on which specific part we fulfill, we will get one or another answer. There are many options. For example: 1) from the first condition of the will, it follows that the son should receive $2 / 3$ of the estate, and from the second condition, that the daughter should receive half of what the mother receives; 2) from the first condition of the will, it follows that the mother's share is half of the son's, and from the second condition, that this share is twice the daughter's; 3) in each condition, the mother's share is not less than $1 / 3$, while the son's share is four times the daughter's. Other options can also be proposed. This problem arose from practice. Such a case indeed occurred in Ancient Rome. There, the court divided the estate as proposed in the second option: the son received $4 / 7$ of the estate, the mother $2 / 7$, and the daughter $1 / 7$, i.e., 120 talents to the son, 60 to the mother, and 30 to the daughter.