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Thread: Do You Know This Puzzle?

  1. #1
    Advanced User Renk's Avatar
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    Do You Know This Puzzle?

    Two different (integer) numbers are chosen between 1 and 100, their sum being something else than 100. To Sophia, their sum is given, and to Padme, their product. Then the following conversation happens:

    Padme: I don't know what these numbers are.

    Sophia: I knew you didn't.

    Padme: Now, I know these numbers.

    Sophia:Me too.

    .......
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  2. Who Said Thanks:

    anon (13.01.21)

  3. #2
    my brain hurts just by thinking about this
    here this might help
    http://www.cs.rug.nl/~grl/ds05/sumproduct.pdf
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  4. Who Said Thanks:

    sigduwksnsksis9283 (14.01.21) , Renk (14.01.21) , anon (13.01.21)

  5. #3
    Moderator anon's Avatar
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    Had never heard of it. School should teach us these things I mean, I never realized any positive integer can be expressed as a sum of powers of 2 until I started hacking savegame files...
    "Come visit sometime, okay? We'll always be here for you. We... we all love you."
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    nice puzzle. something for mathematics
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  7. #5
    Advanced User Renk's Avatar
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    I performed some searches. It is called "the impossible puzzle" and as several variants: See here (and here for solutions), and its first occurrence seems to have been proposed by H. Freudenthal in 1969.

    What is even more amazing is you can replace the number 100 in the puzzle's statement by any number between 65 and 1684, the puzzle continues to be a true puzzle (ie to have only one solution).... and this solution remains the same....I really think beyond 200 or 300 you really need some aid (computer assistance or highly trained brain and psycho-chemicals of some sorts).

    I wonder to see how something as subtle as "knowing that someone know I don't know" is able to bring sufficient information to solve a problem with a priori so many possibles cases.
    Last edited by Renk; 14.01.21 at 01:30.
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  8. #6
    Because both the sum and product have multiple solutions and by process of elimination you can find the numbers. But not instantly like those two did. Unless they are two computers talking to each other.
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  9. #7
    Advanced User Renk's Avatar
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    Quote Originally Posted by cirulilu View Post
    Because both the sum and product have multiple solutions and by process of elimination you can find the numbers. But not instantly like those two did. Unless they are two computers talking to each other.
    I agree, but my final remark was only about how subtle the information it suffices to get, to be able to make the elimination process works.
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  10. #8
    I've met few similar puzzle like this one before.
    one was like the one "To Know or not To Know" on this site.
    http://www.puzzlesite.nl/teasers/index_us.html
    lot easier this one

    But that kind of thing will never happen in real life. Without pen and paper or a calculator rarely who can do all that math.
    With few augmentation like hexa core brain, no problem.
    Last edited by cirulilu; 14.01.21 at 20:16.
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