# The age of three daughters



## Marcelo Branco (Aug 5, 2012)

Two mathematicians meet and one of them:
- How old are your three daughters?

- The product of their age is 36

- Okay, but I need more information ...

The father, pointing to a house on the street, responds:
- The sum of the ages is equal to the number of that house.

- Hmm ... still can not know precisely how old they were ...

- The oldest dance ballet.

- Now I know how old they were, thank you!

You also know?

M.


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## drsarao (Aug 6, 2012)

Marcelo Branco said:


> Two mathematicians meet and one of them:
> - How old are your three daughters?
> 
> - The product of their age is 36
> ...



Should be "Oldest is a ballet dancer"


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## Al Chara (Aug 6, 2012)

The daughters' ages are 2, 2, and 9.


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## drsarao (Aug 6, 2012)

Disregarding my "correction", if we take Marc's statement literally *"The oldest dance ballet."* (the verb 'dance' here is pleural!)
Then the answer would be 1, 6, 6!!

Over to Marc.


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## Al Chara (Aug 6, 2012)

drsarao said:


> Disregarding my "correction", if we take Marc's statement literally *"The oldest dance ballet."* (the verb 'dance' here is pleural!)
> Then the answer would be 1, 6, 6!!
> 
> Over to Marc.



I read this as the oldest daughter dances ballet, which would make the answer 2, 2, 9.  If its the oldest daughters dance ballet, then you are right, the ages are 1, 6, 6.


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## Jonmo1 (Aug 6, 2012)

Marcelo Branco said:


> *The sum of the ages is equal to the number of that house.
> *



We also need to know the number of that house..

Answer could be
1 1 36
1 2 18
1 3 12
2 3 6


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## JamesW (Aug 6, 2012)

Can someone explain the ballet relevance?


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## Al Chara (Aug 6, 2012)

jonmo1 said:


> We also need to know the number of that house..
> 
> Answer could be
> 1 1 36
> ...



Not necessarily, we have to assume that the mathematician knows the number of the house.  So if the house number clue wasn't enough, then the sum of the ages must be ambigous, hence the only acceptable answers are 1, 6, 6 or 2, 2, 9.


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## Jonmo1 (Aug 6, 2012)

Al Chara said:


> Not necessarily, we have to assume that the mathematician knows the number of the house. So if the house number clue wasn't enough, then the sum of the ages must be ambigous, hence the only acceptable answers are 1, 6, 6 or 2, 2, 9.



Just because the house number wasn't enough information, doesn't mean it is not critical to the correct answer once more information was provided....

What is the point of adding the sentence about the house number to the riddle, if it is not part of the solution?


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## TinaP (Aug 6, 2012)

JamesW said:


> Can someone explain the ballet relevance?


Ballet is a red herring.  It could also be, "The oldest play piano."  The true hint comes from the use of the noun, oldest, and the verb, dance.  The oldest generally refers to a single person.  However the verb, dance, implies that there are two, otherwise it would be dance*s*.  Because of this, the ages would be 6, 6, and 1.


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## barry houdini (Aug 6, 2012)

JamesW said:


> Can someone explain the ballet relevance?



ballet itself isn't relevant, just that he refers to "the oldest" - the implication being that the ages must be 9, 2 and 2 rather than 6, 6 and 1 where there is no "oldest" (although I presume one of the 6 year olds must be older than the other, even if they are twins!)


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## barry houdini (Aug 6, 2012)

jonmo1 said:


> What is the point of adding the sentence about the house number to the riddle, if it is not part of the solution?



It is part of the solution, because it tells you that the sum of the ages is a number that can be achieved more than one way (within the first constraint that the product should be 36). You don't need to know what the number is (although it can only be 13)


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## Jonmo1 (Aug 6, 2012)

barry houdini said:


> It is part of the solution, because it tells you that the sum of the ages is a number that can be achieved more than one way (within the first constraint that the product should be 36). You don't need to know what the number is (although it can only be 13)



OK, I get that now thanks.

But I think the answer should be 6 6 1, not 9 2 2
Because of the senctence
The oldest dance ballet.
Either way you read 6 6 1 and 9 2 2, there is most likely a set of twins.
We must assume it is NOT a typo (untill otherwise corrected by the poster)
And the word dance is meant to be plural.
It seems gramatically correct to me, to refer to a set of twins as your oldest.
So the oldest is the set of 6 year old twins.


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## barry houdini (Aug 6, 2012)

Now I re-read it I think you're right Jonmo!.......[as per drsarao's answer also]


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## Norie (Aug 6, 2012)

Why 13?


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## Jonmo1 (Aug 6, 2012)

Norie said:


> Why 13?


Because 13 is the only possible number that is the SUM of 3 numbers, where there are multiple possible 3 numbers whose product are 36.

Any number other than 13, would have been enough information to solve the riddle without knowing the oldest dance ballet.


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## barry houdini (Aug 6, 2012)

There are 8 possible solutions for ages that multiply to 36 (I think). That's 

1 1 36, 
1 2 18, 
1 3 12, 
1 4 9,
2 2 9,
1 6 6,
2 3 6,
4 3 3

....and out of those only 2 add up to the same total (2 2 9 and 1 6 6 sum to 13) so if the mathematician still can't know what the ages are once he knows the house number then it must be 13 because that's the only number that wouldn't point to a specific solution


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## Marcelo Branco (Aug 6, 2012)

Hello friends,

Very sorry about my bad english...

My intention was to say: The oldest *dances* ballet.

So 9,2 and 2 are the correct answers

M.


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## drsarao (Aug 6, 2012)

Marc at last owns up! 2-2-9.
Quite a lot of traffic it generated.
I must shamelessly admit that I got the logic (though not the solution) from worldwideweb,
Cheers!
Marc, come up with another. It makes the forum interesting.
Moderator(s) may consider starting a separate Thread Group titled Quizzes. (Preferably, but not necessarily related to Excel).


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## schielrn (Aug 8, 2012)

drsarao said:


> Marc at last owns up! 2-2-9.
> Quite a lot of traffic it generated.
> I must shamelessly admit that I got the logic (though not the solution) from worldwideweb,
> Cheers!
> ...



Here are a lot of brain teasers:

http://www.mrexcel.com/forum/showthread.php?436925-Brain-Teasers&highlight=riddle


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