# Thread: crypto thought crackme #6

1. ## 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. 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

3. 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!

4. Numbers don't rot13 well... let's use base64 to encode the solution instead
Code:
```QmVnaW4gd2l0aCAyXjEgPSAyLg0KDQoyICogNy8yID0gNy4NCjcgKiAxMC83ID0gMTAuDQoxMCAqIDEz
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NyA9IDEzMC4NCjEzMCAqIDEzLzEwID0gMTY5Lg0KDQooY2Fubm90IHByb2NlZWQpDQoNCg==```
I think that's the first part of the solution...

Code:
```SWYgd2UgYXNzdW1lIG4gaXMgaW5maW5pdGUsIHRoZW4gdGhlIHNlcXVlbmNlIGlzIGluZmluaXRlIChn
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biBzdHVmZiBNaWtlIDotKQ==```
Edit: Uh.. guess it would be nicer spread out!

Will

6. Cool little math puzzle.

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

Code:
```RmFzY2luYXRpbmcuIEl0IHBsYXlzIG9uIHRoZSBwYXJ0cyBvZiB0aGUgZnJhY3Rpb25zLg0KDQpG
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MA0KDQpUaGUgZmluYWwgcmVzdWx0IGFnYWluIDEzXm4=```
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.

7. 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:
Originally Posted by gabri3l
Fascinating. It plays on the parts of the fractions.
Yep.
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.
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.

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

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

Code:
```SSBzZWUgbm93IHRoYXQgbXkgbXVkZHkgcHJvb2Ygc3RlcHMgd2VyZSBjb3ZlcmluZyB1cCB0aGUgbWlz
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NS8xMQ0Kcz0zKjUqMl57bi0yfSwgZj0zMy8yMA0Kcz0zXjIqMTEqMl57bi00fSwgZj01LzExIA0Kcz0z
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Mi8zDQpzPTJeMyoxMywgZj03LzINCjIqMyAtPiAxM14yDQo9MTNeMw0KDQpCeSBsb29raW5nIGF0IHdo
YXQncyBoYXBwZW5pbmcgd2l0aCBhIHJldmVyc2VyJ3MgZXllLCB5b3UgY2FuIGRlc2NyaWJlIHRoZQ0K
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Z2xldG9uIDIgaW50byAxMyBpZiB0aGVyZSBpcyBvbmUNCnR1cm4gYWxsIDNzIGludG8gMnMNCnJlcGVh
dA0KDQpUYWJsZSBvZiByZXN1bHRzOg0KDQpuPTEsMiwzLDQsNSw2LDcNCnM9MTNeeA0KeD0xLDEsMiwx
LDIsMiwzDQoNClNvIHBzZXVkb2NvZGU6DQpyZXN1bHQ9MTMNCndoaWxlKG4+MSkNCglpZiBuIGlzIG9k
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SSByZWNvZ25pemUgdGhpcyBwYXR0ZXJuIGZyb20gZXhwZXJpZW5jZS4uLiBpdCdzIHVzZWQgdG8gY291
bnQgdGhlIHN1bSBvZiAxcyBpbg0KdGhlIGJpbmFyeSByZXByZXNlbnRhdGlvbiBvZiBuLiBJdCdzIHZl
cnkgc2ltaWxhciB0byBhIG1ldGhvZCB1c2VkIGZvcg0KZXhwb25lbnRhdGlvbiAocmVwZWF0ZWQgc3F1
YXJpbmcpLg0KDQpQcmVkaWN0aW9uczoNCg0Kbj04LDksMTAsMTEsMTIsMTMsMTQsMTUsMTYsMTcNCnM9
MTNeeA0KeD0xLDIsIDIsIDMsIDIsIDMsIDMsIDQsIDEsIDINCg0KSWYgc29tZW9uZSB3YW50cyB0byBw
cm9wZXJseSBwcm92ZSB0aGlzIGJlaGF2aW91ciBmcm9tIHRoZSBwcm9ibGVtIHRoZW4gSSdkIGJlDQpo
YXBweSB0byBzZWUgaXQsIGJ1dCBwcm9vZnMgbmV2ZXIgd2VyZSBteSBzdHJvbmcgcG9pbnQgOyk=```
Cheers,

Will

Edit: fixed a typo

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.

10. 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. More more more :-)

Code:
```QXJnaCB5ZXMsIElcJ2QgaGVhcmQgb2YgSGFtbWluZyBkaXN0YW5jZXMvd2VpZ2h0cy4gRm9yZ290IHRo
ZSB0ZXJtIDotKQ0KDQpIZXJlXCdzIG15IChmaXJzdCkgYXR0ZW1wdCBhdCB0aGUgbmV4dCBjaGFsbGVu
Z2UgKGNvcnJlY3RlZCBiZWxvdyk6DQoNCjcvOSAxMS80IDEvNiA1LzMgNS8yIDMvNyAyLzExDQoNClNh
bWUgdGVjaG5pcXVlIGFzIGJlZm9yZSwgaGFsdmUgbi9tLCBpZiB0aGVyZXMgb25lIGxlZnQgb3ZlciB0
aGVuIHRoZXJlXCdzIGEgMQ0KaW4gdGhhdCBwb3NpdGlvbiBvZiBuIChpZiB0aGVyZVwncyBhIDMpIG9y
IG0gKGlmIHRoZXJlXCdzIGEgMikuIDExIGFuZCA3IGFyZSB1c2VkDQphcyB0ZW1wb3JhcnkgcmVwcmVz
ZW50YXRpdmVzLiBJZiB0aGVyZVwncyBib3RoIGEgMiBhbmQgYSAzIGxlZnQgb3ZlciwgdGhlbiB3ZSBn
bw0KdG8gYSAxIGJlY2F1c2UgMSB4b3IgMSBpcyAwLiBJZiB0aGVyZVwncyBqdXN0IG9uZSBvciB0aGUg
b3RoZXIgYWZ0ZXIgdGhhdCwgd2UgZ28NCnRvIDUuIFRoZW4gd2UgcmVzZXQgYmFjayB0byB0aGUgM3Mg
YW5kIDJzLg0KDQpJIGhhdmVuXCd0IGNoZWNrZWQgdGhpcyBpbiBkZXRhaWwsIGJ1dCBJIHRoaW5rIHRo
ZSBpZGVhIGlzIGF0IGxlYXN0IHNvdW5kLg0KDQpFZGl0OiBvaCwgc2lsbHkgbWUsIHdlIG5lZWQgdGhl
IHN3aXRjaCBiaXQgdGhlcmUgZG9uXCd0IHdlLiBUaGlzIGlzIHdoeSBJIHNob3VsZA0KYmUgYXNsZWVw
ISBJXCdtIG5vdCBzdXJlIGlmIHRoaXMgaXMgdGhlIG1vc3QgZWZmaWNpZW50IHdheSBvZiBkb2luZyBp
dCwgYnV0IEkNCmhvcGUgaXRcJ3MgY2xlYXI6DQoNCjEzKjcvMTMqOSAxMyoxMS8xMyo0IDEzKjEvMTMq
NiAxMyo1LzEzKjMgMTMqNS8xMyoyIDEvMTMgMy83IDIvMTEgMTMqMi8yIDEzKjMvMyANCg0KUmlnaHQg
YXQgdGhlIHN0YXJ0LCB3ZSBwdXQgYSBmYWN0b3Igb2YgMTMgaW4gYXMgYSBzd2l0Y2gsIGludHJvZHVj
ZWQgYnkgdGhlDQpsYXN0IHR3byB0ZXJtcy4gVGhlIGZpcnN0IDUgZnJhY3Rpb25zIHdpbGwgdGhlbiB3
b3JrIGFzIEkgZGVzY3JpYmVkIGFib3ZlIGZvcg0Kb25lIGN5Y2xlLCB1bnRpbCB0aGVyZSBpcyBub3Ro
aW5nIGxlZnQgdG8gZG8uIFRoZW4gdGhlIDEvMTMgd2lsbCBkaXNhYmxlIHRoZQ0KMTMgc3dpdGNoLCB0
aGUgN3MvMTFzIHdpbGwgYmUgY29udmVydGVkIGJhY2sgaW50byAzcy8ycyBhbmQgdGhlIGN5Y2xlIHdp
bGwNCnJlcGVhdCBhcyBkZXNpcmVkLg==```
Edit is explained inside!

Will

12. wtbw:
Code:
```SXQgbG9va3MgbGlrZSB5b3UncmUgdHJ5aW5
nIHRvIHNvbHZlIDNebiAyXm0gLT4gNV5IVyhuIHhvciBtKSwgDQp3
aGljaCBpcyBhIHZlcnkgZGlmZmVyZW50IHRoaW5nIGZyb20gNV4obiB4b3
IgbSkuICBBbHNvLCBtdWx0aXBseWluZw0KdG9wIGFuZCBib3R0b20gb2
YgYSBmcmFjdGlvbiBieSB0aGUgc2FtZSB0aGluZyBkb2Vzbid0IGNoYW5nZSB0
aGUgZnJhY3Rpb24h```

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,

14. What a mission :-)

Code:
```QWgsIGJsb29keSBoZWxsLiBUaGUgZGlmZmVyZW5jZSBiZWluZyB0aGF0IHlvdSB3YW50IHRvIGRvdWJs
ZSB0aGUgY3VycmVudCBudW1iZXINCm9mIGZpdmVzIGVhY2ggdGltZSwgYmVmb3JlIGFkZGluZyBvbmUu
DQoNClRvIGZpeCB0aGUgZnJhY3Rpb24gcHJvYmxlbSBpcyBwcmV0dHkgc2ltcGxlOg0KDQoxMy8xNyAx
Nyo3LzEzKjkgMTcqMTEvMTMqNCAxNy8xMyo2IDE3KjUvMTMqMyAxNyo1LzEzKjIgMS8xMyAxLzE3IDMv
NyAyLzExDQoxMyoyLzIgMTMqMy8zIA0KDQpmaXhlcyB0aGUgcHJvYmxlbSB3aXRoIDEzcywgYnV0IHRo
ZW4gd2UgaGF2ZSBpdCBhZ2FpbiB3aXRoIHRoZSBsYXN0IHR3byB0ZXJtcy4NCg0KMi8xOSAzLzIzIDEz
LzE3IDE3KjcvMTMqOSAxNyoxMS8xMyo0IDE3LzEzKjYgMTcqNS8xMyozIDE3KjUvMTMqMiAxLzEzIDMv
NyAyLzExDQoxMyoxOS8yIDEzKjIzLzMgDQoNCg0KU28gbm93IHdlIGZpeCB0aGUgbGFjayBvZiBkb3Vi
bGluZy4NCg0KSGVyZVwncyB0aGUgcHNldWRvY29kZSBvZiB3aGF0IElcJ20gdHJ5aW5nIHRvIGFjaGll
dmU6DQoNCnJlc3VsdD0xDQp3aGlsZShtIG9yIG4pDQogIHJlc3VsdD1yZXN1bHReMg0KICBpZiBtIGlz
IG9kZCBhbmQgbiBpcyBvZGQNCiAgICBtPW0tMQ0KICAgIG49bi0xDQogIGVsc2UgaWYgbSBpcyBvZGQN
CiAgICBtPW0tMQ0KICAgIHJlc3VsdD1yZXN1bHQqNQ0KICBlbHNlIGlmIG4gaXMgb2RkDQogICAgbj1u
LTENCiAgICByZXN1bHQ9cmVzdWx0KjUNCiAgbT1tLzINCiAgbj1uLzINCg0KSVwnbSBnb2luZyB0byBz
dGFydCBmb3JtYXR0aW5nIHVwL2Rvd24gZm9yIGNsYXJpdHkuIFRoZSBpbmRlbnRhdGlvbiBkb2Vzblwn
dA0KYWZmZWN0IHByaW9yaXR5Lg0KDQoxOiAyLzE5DQoxOiAzLzIzDQoyOiAgIDI5LzMxDQoyOiAgICAg
MzEqMzcvMjkqNSAgDQoyOiAgIDEzLzI5DQoyOiAgIDUqNS8zNw0KICAgICAgDQozOiAgIDEzLzE3DQoz
OiAgICAgMTcqNy8xMyozKjMNCjM6ICAgICAxNyoxMS8xMyoyKjINCjQ6ICAgICAxNy8xMyoyKjMNCjQ6
ICAgICAxNyo1LzEzKjINCjQ6ICAgICAxNyo1LzEzKjMNCjU6ICAgMS8xMyAgDQo1OiAgIDMvNw0KNTog
ICAyLzExDQoNCjE6IDI5KjE5LzINCjE6IDI5KjIzLzMNCg0KDQpJdFwncyBzdGFydGluZyB0byBsb29r
IGEgYml0IGNvbXBsaWNhdGVkLCBzbyBsZXRcJ3MgcmV2aWV3Og0KDQojIFN0YWdlIDENCiMgVHVybiBv
biBhIHN3aXRjaCAoMjkpLCBhbGxvd2luZyB0aGUgZG91Ymxpbmcgcm91bmQgdG8gY29udGludWUuDQoj
IExlYXZlIG51bWJlciBvZiAycy8zcyBpbnRhY3QuDQoNCklmIHRoZXJlIGFyZSBhbnkgMnMsIHJlcGxh
Y2Ugb25lIHdpdGggMjkqMTkNCiAgSWYgbm90LCByZXBsYWNlIGEgMyB3aXRoIDI5KjIzDQogICAgSWYg
bmVpdGhlciwgdGhlbiB3ZVwncmUgZG9uZS4NClR1cm4gdGhlIDE5IG9yIDIzIGJhY2sgaW50byAyIG9y
IDMgcmVzcGVjdGl2ZWx5Lg0KDQojIFN0YWdlIDINCiMgRG91YmxlIHRoZSBudW1iZXIgb2YgZml2ZXMs
IGFuZCB0aGVuIGV4Y2hhbmdlIHRoZSAyOSBzd2l0Y2ggZm9yIHRoZSAxMyBzd2l0Y2gsIGFsbG93aW5n
IHRoZSBiaXQgcm91bmQgdG8gY29udGludWUuDQoNClR1cm4gYSA1IGludG8gYSAzNywgYW5kIHRoZSAy
OSBpbnRvIDMxLg0KVHVybiB0aGUgMzEgYmFjayBpbnRvIGEgMjkuDQpSZXBlYXQgdW50aWwgbm8gZml2
ZXMgcmVtYWluLg0KDQpUdXJuIHRoZSAyOSBpbnRvIGEgMTMuDQoNClJlcGxhY2UgYW55IDM3cyB3aXRo
IDUqNS4NCg0KIyBTdGFnZSAzDQojIEhhbHZlIG0vbjsgaWYgdGhlcmUgaXMgYSByZW1haW5kZXIsIHRo
ZXJlIGlzIGEgMSBpbiB0aGlzIHBvc2l0aW9uIG9mIHRoZSBiaW5hcnkgcmVwcmVzZW50YXRpb24uDQoN
CklmIHRoZXJlIGFyZSB0d28gM3MgKDMqMz05KSwgcmVwbGFjZSB3aXRoIDcuDQogIFJlcGVhdCB1bnRp
bCBlaXRoZXIgbm8gM3Mgb3Igb25seSBvbmUgMyByZW1haW5zLg0KSWYgdGhlcmUgYXJlIHR3byAycyAo
MioyPTQpLCByZXBsYWNlIHdpdGggMTEuDQogIFJlcGVhdCB1bnRpbCBlaXRoZXIgbm8gMnMgb3Igb25s
eSBvbmUgMiByZW1haW5zLg0KDQojIFN0YWdlIDQNCiMgU28gaWYgdGhlcmUgaXMgYSAxIGluIGJvdGgg
KDIgYW5kIDMgcmVtYWluZGVycyBwcmVzZW50KSBjYW5jZWwgaXQgb3V0LiBJZiBqdXN0IG9uZSBvZiB0
aGVtLCBhZGQgYSA1Lg0KDQpJZiB0aGVyZVwncyBhIDIgYW5kIGEgMyAoMiozKSwgcmVwbGFjZSB3aXRo
IDEuDQpJZiB0aGVyZVwncyBzdGlsbCBhIDIsIHJlcGxhY2Ugd2l0aCA1Lg0KICBJZiB0aGVyZVwncyBz
dGlsbCBhIDMsIHJlcGxhY2Ugd2l0aCA1Lg0KICANCiMgU3RhZ2UgNQ0KIyBUdXJuIG9mZiB0aGUgMTMg
c3dpdGNoIGFuZCBwdXQgMnMvM3MgYmFjay4NCg0KUmVwbGFjZSAxMyB3aXRoIDEuDQpSZXBsYWNlIGFu
eSA3cyB3aXRoIDNzLg0KUmVwbGFjZSBhbnkgMTFzIHdpdGggMnMuDQoNClRoZW4gdGhlIGVudGlyZSBw
cm9jZXNzIHJlcGVhdHMsIHVudGlsIHRoZXJlIGFyZSBubyAycyBvciAzcyByZW1haW5pbmcuDQoNCkhl
cmVcJ3MgYSBxdWljayB0YWJsZSBvZiByZWZlcmVuY2Ugb2Ygd2hhdCB0aGUgcHJpbWVzIGFyZSB1c2Vk
IGZvcjoNCg0KMjogc3RvcmVzIG0NCjM6IHN0b3JlcyBuDQo1OiByZXN1bHQNCjc6IHN0b3JlcyBuLzIg
dGVtcG9yYXJpbHkNCjExOiBzdG9yZXMgbS8yIHRlbXBvcmFyaWx5DQoxMzogc3dpdGNoIGZvciBzdGFn
ZXMgMy00DQoxNzogb3RoZXIgaGFsZiBvZiAxMyBzd2l0Y2gNCjE5OiB1c2VkIHRvIGFjdGl2YXRlIDI5
Y2g7IGhvbGRzIGEgMyB0ZW1wb3JhcmlseQ0KMjk6IHN3aXRjaCBmb3Igc3RhZ2UgMg0KMzE6IG90aGVy
IGhhbGYgb2Ygc3dpdGNoIGZvciBzdGFnZSAyDQozNzogc3RvcmVzIHJlc3VsdCBiZWZvcmUgKjI=```
Will

15. 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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