There are six children in the family. Five of them are respectively 2, 6, 8, 12, and 14 years older than the youngest, and the age of each child is a prime number.

How old is the youngest?
Can the age of the youngest child be an even number?

## Solution

The age of the youngest child cannot be an even number, as otherwise the ages of the older children would not be prime numbers. It cannot end in $1,3,7,9$ - otherwise the age of one of the older children would be divisible by 5. The only prime number that meets these conditions is 5. Checking shows that if the age of the youngest child is 5 years, the ages of all the older ones will be expressed as prime numbers.

## Answer

5 years.