The Census Taker
During the recent census, a man told the census-maker that he had three children. When asked their ages, he replied, "The product of their ages is 72. The sum of their ages is the same as my house number."

The census-taker ran to the door and looked at the house number. "I still can't tell," she complained.

The man replied, "Oh, that's right. I forgot to tell you that the oldest one likes chocolate pudding."

The census-maker promptly wrote down the ages of the three children.

How old are the children?

Here are the facts of the problem:

There are three children. Let's label them a, b, and c.

The product of their ages is 72. Therefore, a x b x c = 72.

The sum of their ages is the same as the house number. Therefore, a + b + c = x.

First, let's list the possibilities of a x b x c = 72.

The most strange part of this problem for me was the statement from the man informing the census taker that his oldest child likes chocolate pudding. My initial thought was, "What in the world does that have to do with anything???"

Clearly, the census taker knows the man's house number. The information that he/she is looking for are the ages of the man's children. We can see in the chart that the only sum that has more than one combination of mutipliers is 14.

This is where that odd statement comes in!! The two combinations in question are 8, 3, and 3, and 6, 6, and 2. Because the man stated that he indeed has an oldest child, this rules out 6, 6, and 2 because there are two "eldest" in these ages. Therefore, the man must have one 8 year old, and two 3 year olds.

 

Now wasn't that cool??!! :-D

Reference: Dr. Jim Wilson's EMAT 6600 Page

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