A census-taker calls at a house. He asks the woman living there the ages of her three daughters.
The woman says,"If you multiply their ages the total is 72;if you add together their ages the total is same as the number on my front door,which you can see."
The census-taker says, "That is not enough information for me to calculate their ages."
The woman says, "Well,my eldest daughter has a cat with a wooden leg."
The census-taker replies, "Ah! Now I know their ages."
Find the sum of squares of the ages of the girls