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        riddles >> hard >> How to solve 3 Daughters problem?
        
(Message started by: mebden on Jul 27^th, 2002, 11:29am)

Title: How to solve 3 Daughters problem?
Post by mebden on Jul 27^th, 2002, 11:29am

How do you solve the 3 daughters problem? I figure if the product of their ages is 72, there are 3 possible answers:

1 8 9
3 3 8
2 4 9

Eliminate the last one because it sums to 13, not a valid house number. But how does the information about the piano playing help narrow it down between the next two?

Thanks

Title: Re: How to solve 3 Daughters problem?
Post by Neil Sedaka on Jul 30^th, 2002, 7:23am

Try these (age 18 and above excluded) :

1 6 12 19
1 8 9 18
2 3 12 17
2 4 9 15
2 6 6 14
3 3 8 14
3 4 6 13
4 3 6 13

The fourth column is the sum of the ages.

As knowing that the sum was the same as the house number didn't help, we can assume that is because the house was 14, and there are 2 possible sets of ages with that product.

So 13 being invalid as a house number is both debateable and irrelavent (note that there are also two sets, but they are duplicates).

2,6,6 would only work, using the word 'oldest' from the final clue if we cared about twins' ages, which people usually don't.

3,3,8 does include twins, but oldest isn't misleading, because she is the only one of that age.

Title: Re: How to solve 3 Daughters problem?
Post by mebden on Jul 30^th, 2002, 7:29am

Thank you!

--Mark

Title: Re: How to solve 3 Daughters problem?
Post by Scott Kurth on Aug 3^rd, 2002, 7:35am

While I realize that Neil's solution meets the "intent" of the problem, this problem is actually still ambiguous (without getting into the notion of an "older" twin).

Consider the case where you have three daughters with the following birthdays:
Brittany: 01 January 1995
Tiffany: 01 November 1995
Sally: 01 April 1999

If the two gentlemen met last December, the daughters' ages would be 2 6 6 and 'Brittany' would be busily tickling the ivories....

Title: Re: How to solve 3 Daughters problem?
Post by mebden on Aug 6^th, 2002, 3:50am

Excellent point - this is an insoluble puzzle, thanks to the 2 6 6 possibility!
:-/

Title: Re: How to solve 3 Daughters problem?
Post by srn347 on Aug 28^th, 2007, 9:41pm

on 07/27/02 at 11:29:22, mebden wrote:

That sums to 15. Maybe if the oldest just learned how to play the piano, there is only one oldest.