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Thread: crypto thought crackme #6

  1. #1
    הבּרוּ נשׂאי כּלי יהוה mike's Avatar
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    crypto thought crackme #6

    Not quite crypto, but still a fun little puzzle. Start with s=2^n. Then pick the first fraction f in the list such that sf is an integer. Repeat until there is no such fraction. What's the result?

    Code:
    33   5  13  1  2  10  7
    --, --, --, -, -, --, -
    20  11  10  5  3   7  2

  2. #2
    Hey

    I'm not sure if I totally get this game. My first answer was n=0, 'cause the list contains no integers. That seems a little silly, so I guess we have to start at n=1 (which forces us to pick the last fraction).

    The only problem is that you've missed out the 'inductive step'. What exactly does 'repeat' mean? if it means 'increment n' as I'd have guessed then we may be here for a long time, as (7/2)*2^n = 7*2^(n-1) which is integral for every n >= 1.

    Maybe somebody can clear this up for me.

    Regards
    Admiral

  3. #3
    הבּרוּ נשׂאי כּלי יהוה mike's Avatar
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    The assignment should be s[i]=s[i-1]*f[i-1] at each step, where f[i-1] is the first fraction in the list such that s[i-1]*f[i-1] is an integer.

    Assume n>4 for now. So the first steps go
    s=2^n, f=7/2
    s=7*2^{n-1}, f=10/7
    s=5*2^n, f=33/20
    s=3*11*2^{n-2}, f=5/11
    s=3*5*2^{n-2}, f=33/20
    s=3^2*11*2^{n-4}, f=5/11
    s=3^2*5*2^{n-4}, etc.

    P.S. If you have an answer, remember to ROT13 so others can still play!
    Last edited by mike; May 20th, 2006 at 18:30.

  4. #4
    Numbers don't rot13 well... let's use base64 to encode the solution instead
    Code:
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    I think that's the first part of the solution...

  5. #5
    I'll follow LLXX's example...

    Code:
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    Edit: Uh.. guess it would be nicer spread out!

    Will
    Last edited by wtbw; May 20th, 2006 at 20:28.

  6. #6
    Cool little math puzzle.

    Heres my proof:
    I am think it is correct so I use "proof" very lightly.

    Code:
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    I must warn you I say divide a few times when talking about the numerators and denominators but I mean multiply by the fractions, just didn't feel like going back and fixing it.
    Last edited by gabri3l; May 21st, 2006 at 03:46.
    To teach is to learn

  7. #7
    הבּרוּ נשׂאי כּלי יהוה mike's Avatar
    Join Date
    Mar 2001
    Posts
    491
    LLXX: You got the first three terms right. What's the pattern?
    wtbw: You got the first three terms, but messed up on n=4
    Code:
    s=2^n, f=7/2
    s=7*2^{n-1}, f=10/7
    s=5*2^n, f=33/20 
    s=3*11*2^{n-2}, f=5/11
    s=3*5*2^{n-2}, f=33/20
    s=3^2*11*2^{n-4}
    s=3^2*11, f=5/11 
    s=3^2*5, f=1/5
    s=3^2*11, f=2/3 <-- here, should be 3^2, not 3^2*11
    To avoid typos, why don't you write up some code to follow the algorithm, and then see what happens?

    gabri3l:
    Quote Originally Posted by gabri3l
    Fascinating. It plays on the parts of the fractions.
    Yep.
    Quote Originally Posted by gabri3l
    So we can predict that the next fraction we choose is 10/7.
    So our next equation is:
    (10/7)(7*2^(n-1))
    which is equal to
    10*2^(n-1)
    Yes, though it would probably be more useful to write 5*2^n.
    Quote Originally Posted by gabri3l
    Here we need to find a divisor for the product of 10 and 2.
    Our options have to be products of primes 2 and 5.

    2,5,10,20 are all options for the denominator.

    Here is where the options vary, we are going to examine each one to its conclusion.
    No, you have no options! There is only one fraction that you're allowed to pick at each stage. The only option you have is choosing n.
    First we will pick the simple 1/5
    You can only pick 1/5 if 33/20 doesn't work. And that always works if n>1.
    Last edited by mike; May 22nd, 2006 at 08:04.

  8. #8
    Ah, what a stupid mistake, sorry Mike.

    I see that there is a little more fun in this yet.

    Code:
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    YXBweSB0byBzZWUgaXQsIGJ1dCBwcm9vZnMgbmV2ZXIgd2VyZSBteSBzdHJvbmcgcG9pbnQgOyk=
    Cheers,

    Will

    Edit: fixed a typo
    Last edited by wtbw; May 22nd, 2006 at 09:21.

  9. #9
    ahh! I missed this part in the instructions:
    first fraction f in the list
    Man that would have made all that writing much easier. lol

    Thank god this wasn't a test because seems that little fact now changes everything. I would have failed.
    Last edited by gabri3l; May 22nd, 2006 at 10:50.
    To teach is to learn

  10. #10
    הבּרוּ נשׂאי כּלי יהוה mike's Avatar
    Join Date
    Mar 2001
    Posts
    491
    wtbw: You got it! The pseudocode itself is a proof, so you're good there. Here's some more info.
    Code:
    VGhlIGZ1bmN0aW9uIGdpdmVzIDEzXkhXKG4pLCB3aGVyZSBIVyhuKSBpcyB0aGUgSGFtbWluZyB3ZWlnaHQgb2YgbiwgdGhlIHN1bSBvZiBhbGwgdGhlIDEncyBpbiB0aGUgYmluYXJ5IGV4cGFuc2lvbi4=
    gabri3l: Yes, that rule makes all the difference, doesn't it?

    Next challenge for everyone:
    Code:
    R2l2ZW4gM15uMl5tLCBnaXZlIGEgbGlzdCBvZiBmcmFjdGlvbnMgc3VjaCB0aGF0IHRoZSBlbmQgcmVzdWx0IGlzIDVeKG4geG9yIG0p

  11. #11
    More more more :-)

    Code:
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    bGwNCnJlcGVhdCBhcyBkZXNpcmVkLg==
    Edit is explained inside!

    Will
    Last edited by wtbw; May 22nd, 2006 at 12:03.

  12. #12
    הבּרוּ נשׂאי כּלי יהוה mike's Avatar
    Join Date
    Mar 2001
    Posts
    491
    wtbw:
    Code:
    SXQgbG9va3MgbGlrZSB5b3UncmUgdHJ5aW5
    nIHRvIHNvbHZlIDNebiAyXm0gLT4gNV5IVyhuIHhvciBtKSwgDQp3
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    YgYSBmcmFjdGlvbiBieSB0aGUgc2FtZSB0aGluZyBkb2Vzbid0IGNoYW5nZSB0
    aGUgZnJhY3Rpb24h

  13. #13
    My apologies to wtbw for having overwritten his Post four times with my efforts at creating a second forum with the current database to practice in setting up the OllyForum, which will be appearing here shortly.

    I thought I had solved all the problem, but still had one last glitch which caused the database to, again, revert to the 05.23.06 backup and then be brought up again to the 05.24.06 backup. Unfortunately, when that backup was made, wtbw had not reposted his contribution, which he hopefully can post one last time without me screwing it up again.

    Our test forum is up and running with the 05.24.06 current forum backup and we are about to attempt importing the OllyForum, which Kayaker worked dilegently on to convert, then convert the conversion, and finally import into a working vBulletin forum. Now we attempt to import into a working copy of the current Forum and see how that works. If all goes smoothly, we will have it open very soon.

    Regards,
    JMI

  14. #14
    What a mission :-)

    Code:
    QWgsIGJsb29keSBoZWxsLiBUaGUgZGlmZmVyZW5jZSBiZWluZyB0aGF0IHlvdSB3YW50IHRvIGRvdWJs
    ZSB0aGUgY3VycmVudCBudW1iZXINCm9mIGZpdmVzIGVhY2ggdGltZSwgYmVmb3JlIGFkZGluZyBvbmUu
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    Will

  15. #15
    הבּרוּ נשׂאי כּלי יהוה mike's Avatar
    Join Date
    Mar 2001
    Posts
    491
    wtbw: Great! I hope you can see that the system is universal for computation. Can you come up with a systematic way to call a subroutine? That is, given your program, how could you use it in another program that may use those primes for something else?

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