Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How many children

  1. Aug 27, 2007 #1
    A man invites his friend to his house for a small chatter over some tea. There is a good number of children playing in the backyard, and upon seeing this, the guest asks his host whether all these children are his. The host gives him a brief "no" and tells him that the children belong to himself and three other families. The guest redoubles curiosity and asks to his host how many children he has. The host answers him: "Let's put it this way: the total number of children playing in the background is less than 18, with each family having a different number of children, mine being the largest. Also, the product of the number of children in each family happens to be my home number which you just saw when you arrived". The guest then scrambles on piece of paper for a bit and then looks up and says "I need more information. Does the family with the smallest number of children have more than one child?". As soon as the host answers, the guest is able to correctly tell how many children the latter has. All of this having been said, anyone can do the same on the basis of the information given above. How many children does the man in question have?
     
    Last edited: Aug 27, 2007
  2. jcsd
  3. Aug 27, 2007 #2
    He has 5 children.
    :smile:
     
  4. Aug 27, 2007 #3

    DaveC426913

    User Avatar
    Gold Member

    I'm missing a piece. I don't see why he couldn't have 6.
     
  5. Aug 27, 2007 #4
    And what would be the home number, in this case?
     
  6. Aug 27, 2007 #5

    DaveC426913

    User Avatar
    Gold Member

    Well, I didn't really know what that meant. Address? Phone number? My phone number is ten digits.
     
  7. Aug 27, 2007 #6
    Dave, it's important to remember the question the guest asks.
     
  8. Aug 27, 2007 #7

    DaveC426913

    User Avatar
    Gold Member

    Yes, the way I see it, that eliminates 9 out of 12 possibilites, narrowing it down to 3.
     
  9. Aug 27, 2007 #8
    It's definitly solvable :wink:
     
  10. Aug 27, 2007 #9

    DaveC426913

    User Avatar
    Gold Member

    Is this relevant? "my home number which you just saw when you arrived".
    I don't see how that provides any information for filtering. At least not a universal one. Perhaps it's Yankee-centric?
     
  11. Aug 27, 2007 #10
    Well, according to your calculations, how much is the product of the number of children in each family?
     
  12. Aug 27, 2007 #11

    DaveC426913

    User Avatar
    Gold Member

    Either 120 or 180 or 240.
     
  13. Aug 27, 2007 #12

    DaveC426913

    User Avatar
    Gold Member

    Hm. No, I'm definitely doing something wrong. Upon review, my notes reveal a plethora of answers. I'm missing several pieces.
     
  14. Aug 27, 2007 #13
    If it was 180, for instance, the numbers would have to be a combination of the factors
    2*2*3*3*5.
    Considering the possibility of a family with just 1 child, how many children would the other families have?
     
  15. Aug 27, 2007 #14

    DaveC426913

    User Avatar
    Gold Member

    2,3,5,6 works.
     
  16. Aug 27, 2007 #15
    No, it doesn't. Answer the post #13, and you will see why it doesn't work.
     
  17. Aug 27, 2007 #16

    DaveC426913

    User Avatar
    Gold Member

    If family A had just one child, then the possibilities are virtually limitless.
    1,2,3,4
    1,2,3,12
    1,4,5,7
    or anything in between
     
  18. Aug 27, 2007 #17

    DaveC426913

    User Avatar
    Gold Member

    The question here isn't whether it's solvable, the question is whether it's solvable without certain culture-centric conventions (such as certain values for a "home number").
     
  19. Aug 27, 2007 #18
    If the product is 180, and one family has one children, how many children would the other families have?
    For instance, 4,5,9 doesn't works, since the sum 1+4+5+9 > 18 ...

    Hint: reread the original question!:smile:
     
  20. Aug 27, 2007 #19
    Dave, your not concluding the most out of this part: "As soon as the host answers, the guest is able to correctly tell how many children the latter has."
     
  21. Aug 27, 2007 #20
    Forget the "home number". Consider it was just a number written in a piece of paper.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How many children
Loading...