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Thread: logical puzzle II

  1. #1

    logical puzzle II

    ok, here's one from me...

    peter, simon and daniel are given the task to figure out two numbers. they get the following information: both numbers are between 1 and 1000 and whole numbers (no decimal numbers). peter is given the result of multiplying both numbers with each other (= the product), simon is given the sum of both numbers (= one number plus the other), and daniel is given the difference between both numbers (= one number minus the other).

    however, they must not share those pieces of information with each other. but all three guys are mathematical geniuses, they can do any number of calculations in their head instantly.

    then, the following conversation takes place:

    peter: i don't know the numbers.
    simon: you don't need to tell me that, because i knew that already.
    peter: in that case, i know both numbers now.
    simon: ok, i know them now too.
    daniel: i still don't know the numbers. i can only guess a number, which is probably one of the numbers we're looking for, but i don't know for sure.
    peter: i know which number you're talking about, but that one is wrong.
    daniel: ok, then i also know both numbers now.

    which are the two numbers?
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  2. #2
    AH.FM Addict Vicky Wood's Avatar
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    Quote Originally Posted by dfx View Post
    which are the two numbers?


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  3. #3
    www.defconrecordings.com Lazarus's Avatar
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    Quote Originally Posted by dfx View Post
    ok, here's one from me...

    peter, simon and daniel are given the task to figure out two numbers. they get the following information: both numbers are between 1 and 1000 and whole numbers (no decimal numbers). peter is given the result of multiplying both numbers with each other (= the product), simon is given the sum of both numbers (= one number plus the other), and daniel is given the difference between both numbers (= one number minus the other).

    however, they must not share those pieces of information with each other. but all three guys are mathematical geniuses, they can do any number of calculations in their head instantly.

    then, the following conversation takes place:

    peter: i don't know the numbers.
    simon: you don't need to tell me that, because i knew that already.
    peter: in that case, i know both numbers now.
    simon: ok, i know them now too.
    daniel: i still don't know the numbers. i can only guess a number, which is probably one of the numbers we're looking for, but i don't know for sure.
    peter: i know which number you're talking about, but that one is wrong.
    daniel: ok, then i also know both numbers now.

    which are the two numbers?
    Got the first one but Faustus beat me to it! Determined to get this one in time now....
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  4. #4
    good luck everyone
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  5. #5
    www.defconrecordings.com Lazarus's Avatar
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    OK, I'm going out on a limb, are the numbers 2 and 6?
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  6. #6
    Quote Originally Posted by Lazarus View Post
    OK, I'm going out on a limb, are the numbers 2 and 6?
    ehm, no. xDD
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  7. #7
    www.defconrecordings.com Lazarus's Avatar
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    Quote Originally Posted by dfx View Post
    ehm, no. xDD
    Damn you!
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  8. #8
    AH.FM Addict t4e's Avatar
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    *demands a truckload of headache medication from dfx
    Your signature contains too many lines and must be shortened.

  9. #9
    www.defconrecordings.com Lazarus's Avatar
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    4 and 13!

    If it's not I'm quitting
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  10. #10
    Quote Originally Posted by Lazarus View Post
    4 and 13!

    If it's not I'm quitting
    haha still no xDDDD

    you gonna make half a million posts now, one for each combination?

    how you getting those numbers anyway?
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  11. #11
    Quote Originally Posted by t4e View Post
    *demands a truckload of headache medication from dfx
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  12. #12
    AH.FM Addict Vicky Wood's Avatar
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    1 and 999
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  13. #13
    Quote Originally Posted by Victoria View Post
    1 and 999
    nice try, but also no
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  14. #14
    AH.FM Addict t4e's Avatar
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    Quote Originally Posted by Victoria View Post
    1 and 999


    i can share my medication with you
    Your signature contains too many lines and must be shortened.

  15. #15
    www.defconrecordings.com Lazarus's Avatar
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    Quote Originally Posted by dfx View Post
    haha still no xDDDD

    you gonna make half a million posts now, one for each combination?

    how you getting those numbers anyway?
    Well, so far as I can tell:

    The product has to be divisible by more than just two numbers, which also means it can't be a prime number. I'm sure the sum must be even, which means both numbers must either be odd or both even, however, for Peter to reach his conclusion, the product has to be divisible only by either two odd or two even numbers, which in turn suggests that both of the numbers have to be quite low (otherwise there'd be more ways that they'd be divisible).

    It's been 16 years since I took a maths class though so I'm a little rusty
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