Another "brain stretcher"

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borogovio

1
Keeping in line with teutonu's plan, here's another brain stretcher. I'd rate it as a little more difficult than teutonu's first one:

Two friends meet in the street after some time of not seeing each other, and start talking:
- You know, I've married and I have 3 daughters. The product of their ages equals 36, and the sum of their ages equals ... how curious, it's exactly the number of the building across the street !
- I don't have enough information
- You're right: the eldest plays the piano.

Question: how old are the daughters? (Of course, justified)

NOTE: The ages are taken in years, no months are counted
 
B

borogovio

1
So far we have 2 PERFECT answers: teutonu and lew498 - and 2 wrong ones.
Keep thinking folks !
 
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B

borogovio

1
Only 2 more answers - and they were wrong ones.

I'll let you some more time: tomorrow I'll post a hint, and the day after tomorrow, the solution.
 
B

borogovio

1
I mean the number the building shows - usually people use it in their snail mail. For example:
If they where in front of Mr. Tony Blair's office in London, the number of the building in front would be 10 ('10 Drowning Street' if I'm not wrong).
If they were in front of Mr. Bush's office in Washington, the number of the building in front would be 1600 ('1600 Pennsylvania Avenue').
Of course, it doesn't have to be an even number: could be odd or even.

I'll post a hint at about 10 pm GMT
 
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borogovio

1
Okay, here comes the hint: think about why the friend states that he doesn't have enough information, and what that implies.

Tomorrow I'll post the answer.
 
L

lifejokes

1
can it be that the friend states that he does not have enough information because he does not have enough information, and this implies that he does not have enough information?

wow.......sounds correct to me...............

anyway, what does the eldest daughter plays piano implies?
and are 2 of them twins? or are they triplets? (u know....such that their ages are the same integers)
 
B

borogovio

1
@ lifejokes:

Cannot be triplets, because then the product can't be equal to 36:

2 * 2 * 2 = 8
3 * 3 * 3 = 27
4 * 4 * 4 = 64
5 * 5 * 5 = 125 etc.

The solution will come at about 22 pm GMT (unless you want some more time, I'm something of a sadic :D)
 
B

borogovio

1
Okay, here comes the promised solution.

Let's start with the possible ages of the daughters. 36 can be obtained in 8 different ways:

36 * 1 * 1 = 36
18 * 2 * 1 = 36
12 * 3 * 1 = 36
9 * 4 * 1 = 36
9 * 2 * 2 = 36
6 * 6 * 1 = 36
6 * 3 * 2 = 36
4 * 3 * 3 = 36

Now we must consider the sums of their ages:

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

Now re-read the problem. When the father informs the friend that the product is ... and the sum is ... , you don't know what is the number of the building, but the friend positively knows it. Yet he isn't able to learn the ages of the daughters !
Suppose they were in front of number 38 : he surely wouldn't have any problem, as there is only one combination of ages (36, 1, 1) that satisfies both requirements. So it isn't 38. The same applies to 21, 16, 14, 11 and 10 : in each case there is only one possible solution.
The friend can't calculate the ages, though, if they are standing in front of number 13, because in this case there are 2 equally possible answers: 9,2,2 and 6,6,1. So he states that he hasn't got enough information. When the father makes the statement about the eldest playing the piano, it shows that there is an older one, which rules out the solution 6, 6, 1 (there is no 'eldest'), so it must be 9, 2, 2 ! :D :D

I have to say that I have got 2 correct answers, teutonu and lew498, and that those are the first ones in all the years (about 25) I've been presenting this problem to people. So chapeau to both of you - and don't be dissapointed if you didn't succeed: it's a hell of a problem! Of course, I didn't make it, either.

I've got several other problems - though not so devilish - if somebody dares ... like: What English word is pronounced differently when it is capitalized? An English verb that means something and the opposite?
 
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borogovio

1
Sorry, PC-GUY, but:

a) The question stated clearly that the answer had to be justified

b) The PM I got from you says:
... the answer: 3 x 3 x 4.
Click to expand...
which is not the correct answer

c) And I PM back to you:
Sorry, but the answer must be justified. I'm not telling you whether your answer is right or no, but it is incomplete to start with.

Why 3,3 and 4 is the correct answer and not any of the other possible, like:

36, 1, 1 or 6, 6 , 1 or 18, 2, 1

etc.

Whichever the right answer it has to be justified !
Click to expand...
 
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