puzzle Patel was out looking for a new apartment to rent. The landlord asks him if he has any pets.
Patel: "Three cats"
Landlord: "How old are they?"
Patel: "The product of their ages is 72."
Landlord: "What kind of answer is that!? I need more information."
Patel: "Sorry, that must have been unclear. The sum of the ages of my pets is the same as your house number."
Landlord: "Still not enough information, As we have only 20 houses in this society."
Patel: "My oldest cat is called Gypsy and sum of letters and her age is related as perfect square"
Landlord: "Okay, cool. Now that I know their ages, you can have the house."
What is the sum of the ages of Puzzle Patel's pets?