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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Silver Puzzle Cards
[Puzzle] #243 Silver - Shuffled Part 2 (Read 1st Post!)
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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miamo_tutti
Boot

Joined: 06 Apr 2006
Posts: 50
Location: Colorado Springs, CO
Lilian wrote:
HELP Exclamation cos i'm a beginner at this crypto lark i need to ask the question if you get the right passkey would it generate the message right away or would i have to keep shuffling till it came up Question
*edit* also are we keeping the outer letters in or out of the equation


Well, if you had the right passkey, you would first shuffle the deck based on the passkey and then produce your keystream which would decrypt the message. Of course, the decrypted message might just be another passkey that has to be run through the whole process again or something like that. If that's the case though, we'd (seemingly) have no way of knowing it based on what's on the card, unless we're missing some coded instruction.

I've kind of abandoned the passkey route, though. You'd need a longish passkey to really shuffle the deck well, but we've had no luck with "If entropy wins outward looks should leave you cold." I believe the 108/128 letters must be the ciphertext because the perplexcity.com solve page shows a big text box for inputting the message, so I can't see anything else that would work as a good passkey.

For the record though, I like most tried anything I could think of--including individual key words, the disappearing letters and the ciphertext itself--as a passkey to no avail.

PostPosted: Mon Jun 12, 2006 6:09 pm
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manleym
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Joined: 26 Dec 2005
Posts: 197
Location: Norwich UK
Sh1ft wrote:
Anagram "seven" to "evens"?

Not much luck on the even 108 characters both zero based evens and 1 based evens. (Basically both even and odds.)


Just a last thought for the night before i switch off and watch a DVD, On the Seven/Evens Anagram, There is a poker game called 'Seven Card Stud' which i have not seen mentioned in the forum before.
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PostPosted: Mon Jun 12, 2006 6:55 pm
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kian
Boot

Joined: 16 Feb 2006
Posts: 24

 		A few observations
I've been thinking some about Information Entropy. Interestingly, the first block of five letters (EODMF) is in descending order according to frequency of letters in the English language. It also has the highest 0th order entropy value (according to Shannon's formula, where 0th order means each letter is independent of the others). That's assuming my calculations are correct. If I calculate the 0th order entropy of each block of five letters (and one block of three), I get the following in decreasing entropy order:
EODMF 1.1, SMMOS 1.04, BIOGI 1.02, NQHRS 1.01, ETKWY 0.99, XRUTH 0.96, ITHPJ 0.95, RAGXH 0.91, LJOTY 0.91, MVBAA 0.88, FJTAM 0.87, FHURG 0.87, HGFIB 0.84, IFULP 0.83, WEZFL 0.82, LFHWY 0.79, XIHGU 0.78, FUVMR 0.7, WXOVM 0.62, YNGYJ 0.61, XAWJU 0.59, WBBMC 0.53, LUL 0.52, YKZPL 0.47, LXCQY 0.47, KPGVV 0.41
I haven't played with 1-order, 2-order, etc. entropies. Not sure where to get the numbers. Also, a variation might be to try frequencies of letters in the character string itself.

Has it been noted that the entire string of letters has only one 'D' and two 'N's, much like the word "DJINN"?

PostPosted: Mon Jun 12, 2006 10:24 pm
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Sh1ft
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Joined: 12 Nov 2003
Posts: 110
Location: Salt Lake City, Utah

 		Kian, I dunno where you get your frequency information, but it's a well-known fact that the most frequently used letters in english is indeed:

ETAOIN SHRDLU

(See card 53. I suppose it should be noted that this does not apply to the frequency of the first letter of a word in english, that honor goes to "TAISO CMFPW" more here.)

However, the rest of your post is interesting, particularly concerning the D and the N.

However, frequency analysis was noted on the wiki.

Now, I don't mean to discourage you from trying to solve the card, quite the opposite. After all the thinly veiled hint in the Sentinel clearly stated that it would take a "fresh pair of eyes to reframe the problem" or similiar.

Good luck!

PostPosted: Tue Jun 13, 2006 3:21 am
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X/X
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Sh1ft wrote:
Kian, I dunno where you get your frequency information, but it's a well-known fact that the most frequently used letters in english is indeed:

ETAOIN SHRDLU

(See card 53. I suppose it should be noted that this does not apply to the frequency of the first letter of a word in english, that honor goes to "TAISO CMFPW" more here.)

However, the rest of your post is interesting, particularly concerning the D and the N.

However, frequency analysis was noted on the wiki.

Now, I don't mean to discourage you from trying to solve the card, quite the opposite. After all the thinly veiled hint in the Sentinel clearly stated that it would take a "fresh pair of eyes to reframe the problem" or similiar.

Good luck!


Maybe I'm taking you wrong, but you came off as rather condescending in this post. You missed out completely on what was being said. Kian was taking the letter groups found on the pack of cards and ordering them by their letter frequency as found when taken as a group. This is not mentioned in the wiki or in any of the 60+ pages here on unfiction. It is truly interesting work (whether it leads to anything or not) from a real contributor. So "I don't mean to discourage you from trying to solve this card", but please try to fully grasp an idea before dismissing it as "that's nice kid, now the adults have to get back to work actually solving this card..."

PostPosted: Tue Jun 13, 2006 8:40 am
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BBuck
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Joined: 13 Dec 2005
Posts: 184

 		I agree with X/X about tone (but wish people would sign in properly). Still, let's play nice and talk substance.

On this, I think Kian's ideas are all new. I read the comment about EODMF not that the letters are the five most frequent, but that they are in correct order: ie that E is more frequent than O, which is more frequent than D, which is more frequent than M, which is more frequent than F.

The Wiki on ETAOIN SHRDLU bears this out with the usual order defined as:

ETAOIN SHRDLU CMFWYP VBGKQJ XZ

PostPosted: Tue Jun 13, 2006 9:43 am
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arnezami
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Joined: 14 Apr 2006
Posts: 136

 		Re: A few observations
kian wrote:
I've been thinking some about Information Entropy. Interestingly, the first block of five letters (EODMF) is in descending order according to frequency of letters in the English language.


Thought this might be interesting:

There are 26^5 = 11.88 million possible 5 letter groups.

Of those only 65780 are in descending order according to (a chosen) frequency of letters.

That means there was about a 1 in 180 (or 0.55%) chance the 5 letters would have this specific property (if the group was really random).

The question of course remains: how "random" is this chosen/searched for specific property.

arnezami

PS. If you also count the sixth character (the "X" in EODMFX) then there is only a 1 in 1341 chance! So it doesn't feel random at all... (but what to do with it?) Question
PPS. I've also done some stuff regarding entropy decoding (mainly using range encoding [edit] correction: arithmetic coding) but the lack of definitive letter frequencies makes it unreliable. Using the 108 letters as base for letter frequencies doesn't seem to reveal anything (but I haven't tested this exhaustively mainly because it was getting rather "overcomplicated")

PostPosted: Tue Jun 13, 2006 9:58 am
Last edited by arnezami on Thu Jun 15, 2006 9:09 am; edited 4 times in total
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BBuck
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Joined: 13 Dec 2005
Posts: 184

 		Re: A few observations
arnezami wrote:
There are 26^5 = 1.188 million possible 5 letter groups.

Of those only 65780 are in descending order according to (a chosen) frequency of letters.

That means there was about a 1 in 180 (or 0.055%) chance the 5 letters would have this specific property (if the group was really random).


Slight typo on your maths I think, but it makes your point even more strongly. 26^5 is 11.88 million. This makes the probability even smaller that the 5 letters would have the specific property (ie 1 in 1800).

PostPosted: Tue Jun 13, 2006 10:30 am
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arnezami
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Joined: 14 Apr 2006
Posts: 136

 		Re: A few observations
BBuck wrote:
Slight typo on your maths I think, but it makes your point even more strongly. 26^5 is 11.88 million. This makes the probability even smaller that the 5 letters would have the specific property (ie 1 in 1800).
Thanks. Thats indeed a typo.

But it doesn't change the 1 in 180 chance (I used 11.88 million in my calculator). So those numbers stay the same. Wink

PostPosted: Tue Jun 13, 2006 10:48 am
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Sh1ft
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Joined: 12 Nov 2003
Posts: 110
Location: Salt Lake City, Utah
BBuck wrote:
I agree with X/X about tone (but wish people would sign in properly). Still, let's play nice and talk substance.

On this, I think Kian's ideas are all new. I read the comment about EODMF not that the letters are the five most frequent, but that they are in correct order: ie that E is more frequent than O, which is more frequent than D, which is more frequent than M, which is more frequent than F.

The Wiki on ETAOIN SHRDLU bears this out with the usual order defined as:

ETAOIN SHRDLU CMFWYP VBGKQJ XZ


My post was not meant to be condescending or patronizing, apologies if it came across that way. Once I re-read Kian's post, it became clear what he is talking about, good catch.

No more late night posting after beers for me.

PostPosted: Tue Jun 13, 2006 11:47 am
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BBuck
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Joined: 13 Dec 2005
Posts: 184

 		Re: A few observations
arnezami wrote:
But it doesn't change the 1 in 180 chance (I used 11.88 million in my calculator). So those numbers stay the same. Wink


Embarassed Mental arithmetic, eh?

PostPosted: Tue Jun 13, 2006 11:54 am
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mfm2189
Greenhorn

Joined: 18 May 2006
Posts: 6

 		In the same vein as Kian and Arnezemi's posts...has anyone noticed that none of the groups of 5 occur in alaphabetical order? Is that statistically probable with 26 groups?

PostPosted: Tue Jun 13, 2006 1:27 pm
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arnezami
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Joined: 14 Apr 2006
Posts: 136
mfm2189 wrote:
In the same vein as Kian and Arnezemi's posts...has anyone noticed that none of the groups of 5 occur in alaphabetical order? Is that statistically probable with 26 groups?
The chance of 1 random group of 5 not being in alphabetic order is 179/180 = 99.44%. The chance of all 26 groups not being in alphabetical order is 0.9944^26 = 86.5%. So its quite likely none of the groups of 5 is in alphabetical order.

This btw sort of underscores the (possible) importance of kian's find. Especially if you include the sixth character "X". But if we don't know what to do with it it won't help us...

kian wrote:
I get the following in decreasing entropy order:
EODMF 1.1, SMMOS 1.04, BIOGI 1.02, NQHRS 1.01, ETKWY 0.99, XRUTH 0.96, ITHPJ 0.95, RAGXH 0.91, LJOTY 0.91, MVBAA 0.88, FJTAM 0.87, FHURG 0.87, HGFIB 0.84, IFULP 0.83, WEZFL 0.82, LFHWY 0.79, XIHGU 0.78, FUVMR 0.7, WXOVM 0.62, YNGYJ 0.61, XAWJU 0.59, WBBMC 0.53, LUL 0.52, YKZPL 0.47, LXCQY 0.47, KPGVV 0.41


@kian: How did you calculate these numbers? Did you use a specific set of letter frequencies to calculate them?

PS. It is possible kian's first find ("SHUFFLED X FOURTH PRIME" etc) was correct and put in there as a hint and 6 letters of that hint were ordered in a way to be recognized by us as according to the letter frequencies in English. What I'm trying to say is: one does not exclude the other. There could be more than one hint in the 20 letters.

PostPosted: Tue Jun 13, 2006 2:19 pm
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brokasaphasia
Boot

Joined: 31 May 2006
Posts: 26
arnezami wrote:
I've also tried doing less than 7 shuffles. So in total (128+64+32+16+8+4+2+1=) 255 combinatons. No luck.

...Please check a few to see if I have made a mistake.

FYI, I coded this up for myself last night and checked it as well.

I even added an outer loop of checking up to 7 permutations of perfect shuffles on the 108 char string (split evenly)... So I checked 255^2 decrypts without obtaining any usable plaintext.

PostPosted: Tue Jun 13, 2006 7:56 pm
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Guin
Unfettered


Joined: 11 Jan 2006
Posts: 400
Location: Antartica
mfm2189 wrote:
In the same vein as Kian and Arnezemi's posts...has anyone noticed that none of the groups of 5 occur in alaphabetical order? Is that statistically probable with 26 groups?


do you mean the groups of letters of the letters in the groups?

The trouble with a solitaire (and i do beleive we have a solitaire) is that you cant look for "patterns" as such - letters can not appear and theres no real order as it is wholly dependant on the deck order to begin.

For example EXKYI ZSGEH UNTIQ VVSYK AZXZI DPWSM WSVGN ZHVIF STBYQ UHIFP IBBDF STHIM KKWSL DAEZQ SQJTU GPXAG JOSVJ WIKTQ ONKEP AMQFO FMXCF BDL

can be generated from a key stream of AAAAA AAAAA etc using a non suffled deck theres no real order in the groups or by the groups.

this is alas why it is such a bloody good method of hiding something
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PostPosted: Wed Jun 14, 2006 7:57 pm
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