During the census, a man told the census-taker that he had three children. When asked their ages he replied, " The product of their ages is 72. The sum of their ages is my house number." The census taker turned around and ran outside to look at the house number displayed over the door. He then re-entered the house and said, " Using the information you have given me, I cannot tell their ages." The man then said, "I should have told you that the oldest likes angel food cake." Hearing this, the census-taker promptly wrote down the ages of the three children. What did he write?

Please be specific with your response because I have not got a clue about the angel food cake remark! I need to understand the thought processes involved in solving this problem. THANKS

Solution Preview

The trick in this problem is not angel cakes but in finding the house
number!!.

Since the officer could not tell the ages from the house number,it follows it is the only number which is the sum of 2 or more different factorings of 72.

What you should try and do is factor 72 ...

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