Answer to November 9, 1998 Problem

The Winchester Census Problem
During the recent Winchester 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 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 apple pie -- a favorite dessert of many of the children here in the Shenandoah Valley."
The census-taker promptly wrote down the ages of the three children.

How old are they?

Solution:
The ages of the three children must be 3, 3, and 8, and the address is 14.
The following are the only combinations of three ages whose product is 72:
1st Child 2nd Child 3rd Child Sum of Ages
1 1 72 74
1 2 36 39
1 3 24 28
1 4 18 23
1 6 12 19
1 8 9 18
2 2 18 22
2 3 12 17
2 4 9 15
2 6 6 14
3 3 8 14
3 4 6 13

Except for two of the combinations, their sums are all different, so the census worker would have been able to determine the ages of the children if the address had been any of the different ones.
As she needed more information, however, the address must have been 14, a total shared by two combinations: 2, 6, 6, and 3, 3, 8. So when the father indicated that he had an oldest child, she eliminated the first possibility, which had two "oldest," leaving only 3, 3, and 8 as the answer.

Correctly solved by:

1. Thad Hughes Charlottesville, VA
2. Elizabeth Pleacher Cotter Centreville, VA
3. Barrett Waybright Winchester, VA
4. John Beavers Winchester, VA
5. Andrew Crosby Winchester, VA