Once I walked up a hill, and on the summit sat a very old man cross-legged, calmly taking the air and observing the view below. I asked him if he was alone and he said:
"No. I have five cousins who are coming up after me. What is interesting about them superficially is that if you take their ages, each one being a double-digit integer, between them they include all of the digits 0 to 9.
But if you look deeper you will see it is even more remarkable: each pair of integers within the set is not coprime, that means they have a greatest common divisor that is 2 or more."
"Very interesting indeed" I replied. "But what can I ask is the closest gap between the ages of your cousins?"
"4 years" he replied.
How old are the five cousins?