Sender: Norm
Subject: Three daughters question
Date: Tue, 16 Feb 1999 17:49:46 -0600

I recently received a beat up copy of the three daughters question. I have only some of the question. It ends after the statement "the oldest one looks....... It does not finish. Is there any chance that someone can finish it off for me? Was the answer included?

Norm

Hi Norm

Two women meet after many years and have the following conversation.

 Question: "How old are your three daughters?" Answer: "The product of their ages is 36." Question: "But that is not enough information." Answer: "Well, the sum of their ages is the same number as the post office box that we shared at college". Question: "But that is still not enough information." Answer: "The oldest one looks like me." Question: "Oh, now I know their ages."

What are the ages of the daughters?

Try it! AFTER you have tried you can look at a solution.

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## Solution

First list the possible ages for the three daughters. Since the product of the ages is 36 = 2232 list all triples of positive integers whose product is 36.

1, 1, 361, 1, 3636
1, 2, 2x321, 2, 1821
1, 2x3, 2x31, 6, 613
1, 22, 321, 4, 914
1, 223, 31, 12, 316
2, 2, 322, 2, 913
2, 2x3, 32, 6, 311
22, 3, 34, 3, 310

The sum of the ages is the post office box number which both women know and yet the post office box number does not completely determine the ages. Thus it must be that there are at least two options that have the post office box numerr as their sum. Looking at the table the post office number must be 13 and the ages are either 1, 6 and 6 or 2, 2 and 9. The final statement implies that there is a unique eldest daughter so the ages must be 2, 2 and 9.

Cheers
Rick and Harley

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