Answer to March 26, 2001 Problem

Contributed by Warren Buckner
Adapted from a problem in
Problem Solving A Handbook for Teachers by Krulik and Rudnick

The Two Professors Problem

 
Two Professors meet after many years. They had gone to school together, you know.

Prof. Wise asked Prof. Wink about her family and she said that she had a lovely husband [smile] and three lovely children.

"How old are the children?" asked Prof. Wise.

"Well," said Prof. Wink, "if we agree only to consider ages in nearest whole years, then the product of their ages is 36."

Seeing that his old friend was still her same pedantic self, Prof. Wise thought just briefly before saying "Well, clearly that is not enough information."

Prof. Wink then told Prof. Wise that the sum of her childern's ages was coincidentally the same as the address on Genius street where she used to defeat him regularly at the chess club.

Prof. Wise this time thought a bit longer but admitted that he was still stumped.

Prof. Wink then admitted that her oldest child much preferred Strawberry malts.

Prof. Wink felt quite self-satisfied...that is until Prof. Wise told her the ages of her children almost immediately.

How old were they?

 

Solution to Problem:

The ages of the three children are 2, 2, and 9.

After Prof. Wink told Prof. Wise that the sum of her childrens' ages was the same as the address on Genius street, Prof. Wise made a list of possible sums of three numbers (three children) that add to the number of the address and whose product was 36.

Since that still was not enough information, it meant that at least two sums were the same. In the table below are all the possible factors of 36 and their sums:

Factor Factor Factor Sum
1 1 36 38
1 2 18 21
1 3 12 16
1 4 9 14
1 6 6 13
2 2 9 13
2 3 6 11
3 3 4 10

From the table, we can conclude that the address of the chess club was 13 Genius Street. I thought about making that the question instead of the childrens' ages.
The final clue that "the oldest child much preferred Strawberry malts" gives the information that there is an oldest child.
Thus the only correct answer would have to be 2, 2, and 9 since the other sum of 13 (1, 6, and 6) does not yield an "oldest child." Of course, "strawberry malts" and "where they played chess" are not at all important and can be replaced by anything.


Correctly solved by:

1. Bob Hearn Winchester, Virginia
2. Walt Arrison Philadelphia, Pennsylvania
3. Keith Mealy Cincinnati, Ohio
4. George Gaither Winchester, Virginia
5. Chip Schweikarth Winchester, Virginia
6. David Powell Winchester, Virginia
7. Evelyne Stalzer New Jersey
8. Kirstine Wynn Winchester, Virginia
9. Erin McGinnis Winchester, Virginia