Posers and Puzzles

Posers and Puzzles

  1. Joined
    21 Jul '06
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    0
    23 Aug '06 03:463 edits
    Sherlock Holmes and Dr Watson, H and W, are told that two positive integers x and y have been chosen such that 1 < x < y and x + y < 100. H is given the value x + y and W is given the value xy. They then have the following conversation:

    W: I cannot determine the two numbers.
    H: I knew that.
    W: Now I can determine them.
    H: So can I.

    Given that Holmes' and Watson's logic is impeccable and that the above statements are all true, what are the two numbers?
  2. Standard membersonhouse
    Fast and Curious
    slatington, pa, usa
    Joined
    28 Dec '04
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    52874
    24 Aug '06 07:061 edit
    Originally posted by ThudanBlunder
    Sherlock Holmes and Dr Watson, H and W, are told that two positive integers x and y have been chosen such that 1 < x < y and x + y < 100. H is given the value x + y and W is given the value xy. They then have the following conversation:

    W: I cannot determine the two numbers.
    H: I knew that.
    W: Now I can determine them.
    H: So on's logic is impeccable and that the above statements are all true, what are the two numbers?
    Great problem, got a chuckle from me! No idea how to actually solve it!
    Ah, simultaneous equations.
  3. Standard memberXanthosNZ
    Cancerous Bus Crash
    p^2.sin(phi)
    Joined
    06 Sep '04
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    25076
    24 Aug '06 08:45
    Originally posted by sonhouse
    Great problem, got a chuckle from me! No idea how to actually solve it!
    Ah, simultaneous equations.
    The problem here isn't the simultaneous equations but the logical conditions that Holmes and Watson demonstrate. Holmes knows that Watson cannot solve the equations just based on the information he is given and once Watson knows that that is the case then he can solve the system. And once Holmes knows that Watson can now solve it so can he.
  4. Joined
    18 Aug '06
    Moves
    538
    24 Aug '06 09:02
    x=4; y=13
    I could explain it, but it'd take a while... 😉
  5. SubscriberBigDoggProblemonline
    Just...the Dogg
    bigdogghouse.com/RHP
    Joined
    26 Nov '04
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    123854
    24 Aug '06 21:26
    Originally posted by Kipyusha
    x=4; y=13
    I could explain it, but it'd take a while... 😉
    Explanation and lengthy discussion on this problem can be found in Thread 17714.
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