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WhyThe Oldest Liked Strawberry Pudding...

Every math teacher (and perhaps even many students) have their favorite math problems. My personal choices for favorites seem to fluctuate daily (hourly?)...it is like facing a smorgasbord and you can eat only one item!

Nonetheless, the following problem regularly appears on my list of favorites, primarily because of not only all the neat memories regarding students attempts to solve it....but also the fact that its original version was created by George Polya.


The host at a party turned to a guest and said, "I have three daughters and I will tell you how old they are. The product of their ages is 72. The sum of their ages is my house number. How old is each?"

The guest rushed to the door, looked at the house number, and informed the host that he needed more information.

The host then added, :The oldest likes strawberry pudding." The guest then announced the ages of the three girls.

What are the ages of the three daughters? (All ages are whole numbers. It is possible that there may be twins.) Explain your answer.


A side note: With one group of university students, I had one student actually report that they had traveled down streets near the university, looking for particular house numbers...then inquiring whether or not the family in the house had three daughters...and if the oldest liked strawberry pudding. No lie!

 

Source: C. Greenes, R. Spungin, & J. M. Dombrowski, Problem-Mathics, 1977


Hint: Use each clue in sequence...make an organized list...and then, try to figure out what strawberry pudding has to do with anything, as it actually is very important!

 


Solution Commentary: Sorry...you are on your own. But, if you get desperate, you can find variations of this problem on-line (with detailed solutions).