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The three daughters (Posted on 2002-10-31) Difficulty: 3 of 5
A man in my neighbourhood has three daughters. One day when I asked their ages he said:

"The product of their ages is 36".

When I still couldn't find their ages he said:

"Ok. I'll give you another clue: the sum of their ages is same as the number of my house".

I knew the number but still couldn't calculate their ages. So the man gave me a last hint, he said:

"My eldest daughter lives upstairs".

Finally I was able to find their ages. Can you?

  Submitted by maverick    
Rating: 3.4118 (17 votes)
Solution: (Hide)
First, we find the prime factorization of 36:

36 = 1 * 2 * 2 * 3 * 3

Now, find all groupings of these factors into 3 numbers (and their sums):

  • 36 = 1 * 2 * 18 (21)
  • 36 = 1 * 3 * 12 (16)
  • 36 = 1 * 4 * 9 (14)
  • 36 = 1 * 6 * 6 (13)
  • 36 = 2 * 2 * 9 (13)
  • 36 = 2 * 3 * 6 (11)
  • 36 = 3 * 3 * 4 (10)

    If I knew the sum of the daughters' ages, and that didn't help me, it means that the sum must have been 13. (Any other sum would yield a unique solution, but 13 is repeated twice in the list.)

    The last bit of information seems pretty useless, but it let me know that there exists an eldest daughter. Of the two combinations adding up to 13, (1,6,6) and (2,2,9), the first one has two older daughters of the same age. The fact that there is an eldest daugher means that the daughers' ages MUST be 2, 2 and 9.

  • Comments: ( You must be logged in to post comments.)
      Subject Author Date
    SolutionPuzzle SolutionK Sengupta2007-10-15 05:13:42
    SolutionThe solutionjoshua2006-08-26 10:53:32
    Some ThoughtsNo SubjectStephen Ticsay2005-04-16 14:55:25
    not to nitpick, but...yocko2005-03-09 23:14:15
    impressive3llis2005-01-13 08:50:13
    re: HELP!maggie2004-11-02 18:40:20
    The Three DaughtersRavi Raja2003-01-05 19:32:58
    I enjoyed this one......cges2002-12-05 08:29:33
    can't be solveddrew2002-12-04 12:52:16
    re: HELP!levik2002-11-06 10:12:43
    SimpleJames Mitchell Ullman2002-11-06 07:10:11
    HELP!Lucia Lawson2002-11-05 12:33:25
    Solutionsolutiondanny2002-11-04 14:16:19
    Solutionyiannis2002-11-01 00:46:16
    Solution"missing" information.TomM2002-10-31 21:24:24
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