A man knocks on the door of a house, and tells the woman who
answers that he is doing a survey on the need for school places for
children. He asks if there are any children living at that address, and
the woman tells him that there are three.
He then enquires the ages of the children, and the woman - who is fed
up with being questioned by bureaucrats - tells him that their ages,
when multiplied together, gives 36.
The man says that this is not enough information, so the woman tells
him that their ages, when added, gives the number of the house next
door.
The man looks at the next door house number, but after thinking for a
moment, says that he still has insufficient information.
The woman says that the last thing she will say is that the eldest child is
not at home.
"Ah!" says the man, who then writes down the ages of the children on
his clipboard.
What are the ages of the children ?