# Alice's daughters

Alicia is the mother of four daughters. The oldest is four years older than the second, which is four years older than the third, which is four years older than the fourth who is half as old as the oldest.

How old is the youngest daughter?

#### Solution

We can do some tests with concrete quantities. We know that we can calculate the ages of the sisters from the oldest, subtracting four years.

If the older sister had 30 years, for example, the second would be 26, the third, 22 and the fourth would be 18, that is, four years less than the third, eight less than the second and twelve years less than the oldest.

Unfortunately, in this example, the little girl is not half as old as the oldest, so it does not work for us as a solution, but it does provide us with very valuable information: the little sister is always twelve years younger than the oldest.

We can also try to calculate it the other way around, the age of the oldest from that of the little one. Thus, if the little girl was eight years old, the oldest would be 16, because she must be twice as old.

Unfortunately, in this example, the little girl is not twelve years younger than the oldest, if not eight years less, since for the oldest to be twice as old, the difference in years must coincide with the age of the little one. the little girl must be 12 years old, the largest 24, the second 20 and the third 16.