Two old men...

  1. Two old men....

    Two old men were talking on the porch.

    The first old man says: "I have three daughters. The sum of their ages is equal to the same number as this house's address (we don't know the number, but these two old men do). The product of their ages is 36."

    The second old man thought for a moment and says: "That's not enough information."

    The first old man says: "My oldest daughter has green eyes."

    Then second old man figured out the ages of the first old man's daughters.

    What are the ages of the first old man's daughters?
     
  2. jcsd
  3. Ooooh, I like this one.
    Got it.
     
  4. marcus

    marcus 23,959
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    I aint too proud to say the answer

    2, 2, 9
     
  5. marcus

    marcus 23,959
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    the ambiguity (which forced him to say a sentence indicating that
    the oldest was one person and not twins) is the possibility of

    1,6,6

    but it cant be that because the oldest has green eyes so it has to be

    2,2,9
     
  6. arildno

    arildno 12,015
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    Unacceptable, unless we are talking about siamese twins :wink:
    If one of the twins are born prior to the other, we certainly may say that that twin is the oldest

    EDIT:
    (D**n, I forgot about caesarian(?) birth..)
     
  7. It is either 2, 3 and 6 or 2, 2 and 9.

    As the oldest daughter has green eyes you can assume that the oldest and next oldest are not twins, otherwise it would have been oldest daughters.

    The Bob (2004 ©)
     
  8. marcus

    marcus 23,959
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    The Bob, I already gave the 2,2,9 answer
    and I am sticking with that.

    I do not think that what you suggest (2,3,6) is a possible answer

    I think that because the second man said "that's not enough information"

    the point is that if the housenumber had been 11 then he would not have asked for more information because there is no ambiguity: there's only one possible answer (2,3,6 is the only set of positive integers that work)

    so we know that the housenumber was NOT 11

    the only thing left is for it to be 13
    because this has ambiguity----1,6,6 and 2,2,9----and makes a
    reason for him to say "that's not enough information"

    at that point he is told that one single daughter is the oldest and he knows it is 2,2,9
     
  9. I know. I believe I was repeating it. Sorry. :redface:

    Point made. I did only spend about 2 minutes in my head doing it. Sorry.

    The Bob (2004 ©)
     
  10. marcus

    marcus 23,959
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    no problemo The Bob!
    BTW I cannot reconstruct from memory a wellknown puzzler about the
    3 people and the smudge on the forehead
    or someone is wearing a funny hat and they are supposed
    to deduce who. Maybe I always avoided getting acquainted
    with this problem because I found it taunting. Can you remember or reconstruct it?
     
  11. People who have twins or triplets still consider the first born, the oldest, even if they are all the same age. Could they be 12 year old triplets? 3x12? The sum of the age would be the same as the product.
     
  12. Couldn't you just ask how old the daughters are? :rolleyes:
     
  13. Math Is Hard

    Math Is Hard 4,915
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    I don't understand why there are two OLD men talking when the daughters are so young. Is this just to throw you off track? And what does the address of the house have to do with it?
     
  14. marcus

    marcus 23,959
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    Mathis, there can be some pretty spry old men
    Lets change the subject shall we
     
  15. lol... yea, males can continue to procreate well into their 70s.
     
  16. I remember my thread about hats where there are 4 people and they must deduce what colour hat they have on. I don't think I know what you mean really.

    The Bob (2004 ©)
     
  17. Math Is Hard

    Math Is Hard 4,915
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    hehehehehe... but what about the house address? Just a distraction?
     
  18. BobG

    BobG 2,339
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    I know these two guys. They live on 1313 Mockingbird Lane. (That actually makes a little more sense if you happen to know the first guy has twin daughters - he's used to looking at doubles of the same thing).

    Both of these guys are old, but the second is old to the point of senility, which is why he's having trouble remembering the ages of his own granddaughters.
     
  19. marcus

    marcus 23,959
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    Mathis I think you see that we are just fooling around here and should really change the subject of conversation. But just to respond to your question:

    no Mathis, the house address is an essential part of the problem
    It could have been rephrased by saying that First whispers to the other what the sum of the ages is. the important thing is they both know the sum (even tho we do not)

    The information we start with is
    A. the ages are whole numbers (assumed)
    B. the ages multiply to make 36
    C. Even though Second O.M. knows the sum, he still cannot deduce
    the ages and has to ask for more info.

    from this one can deduce that the sum is NOT 11
    because if it were then he would be able to say 2,3,6
    THERE ARE NO OTHER 3 NUMBERS THAT ADD UP TO 11 and multiply to 36.

    Also we can deduce the sum is not 10 (he didnt whisper "ten" to his friend) because then the ages would have to be 3,3,4.

    Also we can deduce that he didnt whisper "38"
    because then the unique possible answer would be 1,1,36

    So, mathis, it is as if we can eavesdrop on what he whispers
    We also know he didnt whisper "21" for the sum because then
    the immediate inference is 1,2,18
    And he didnt whisper "16" because then Second O.M. would deduce 1,3,12

    So the only thing he can have whispered was "13" because for sum of 13
    there are two possibilities 2,2,9 and 1,6,6.
    So that is why Second OM said "tell me more information"

    You can check that 13 is the only possible whole number besides what we already excluded. :surprise:
     
  20. Math Is Hard

    Math Is Hard 4,915
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    OK, I see what you're saying. It's really only important that both men have knowledge of the sum of the ages of the three daughters, and since both know the house address number, then we can conclude that they do.
     
  21. ehhhh probably 64
     
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