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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Silver Puzzle Cards
Primer #228 ivy set
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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Relish
Boot

Joined: 12 Dec 2005
Posts: 57
Location: Sunny Sunny Wales!

 		Primer #228 ivy set
sorry, no acces to a scanner but the card has a large blackboard with the following on there:

PRIMER = 4293499561

4918667 = ?

2240348582946499351859483091577187440 = ?

164990462647551511589599262129081060112 = ?


theres a pic of a cat drawn on the board in the bottom left and a heart with BE + KS in the bottom right


under the board is some text which is very hard to see due to the colour (prob wont show on any scans) it says:

for Kim:
8577584129109097887023387461941996431858554496
8318734217971798842263771174966898974462083362
5566401900287017962041449669898506168327073084
9760478363853739695360857802221189398757162415
6135437506827327944082124147375360938816960421
315129537


So i guess 'KS' in the heart is kim but after that im stuck, something else to do with prime numbers?

Question
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there are 10 types of people in this world, those who understand binary and those who dont

PostPosted: Fri Apr 07, 2006 3:17 pm
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fretty
Decorated

Joined: 19 Nov 2004
Posts: 281
Location: South Yorkshire, England

 		I think the numbers may need factorising.

PostPosted: Fri Apr 07, 2006 6:43 pm
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sotonrich
Veteran


Joined: 08 Nov 2005
Posts: 110
Location: southampton , UK

 		I stole this from Ebay Razz , hopefully it will suffice until someone can scan it in.


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Oscar Wilde

PostPosted: Fri Apr 07, 2006 7:39 pm
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BBuck
Decorated

Joined: 13 Dec 2005
Posts: 184

 		Some thoughts on a solve, with an answer for the first equation

Spoiler (Rollover to View):
4293499561=59*67*29*43*13*67

59 is the 16th prime, P is the 16th letter
67 is the 18th prime, R is the 18th letter

So this makes 4918667=13*71*73*73 an anagram of ESTT, probably TEST.

This takes 3 as the first prime. 224...440 is even, so I guess that the number of 2's might indicate spaces.

224...440=2*2*2*2*5*13*2154181329756249376787964511131911. The last number does not have a prime factor below 101, which is the 26th prime. So I reckon that the letters will loop round, ie the 27th, 53rd, etc primes will be A.

Factorising this could be a lengthy process if the primes involved are large. It shouldn't be as long as factoring a similar length number from RSA, as there will be more than one prime involved. But it could still take a while, particularly the 89 digit "for Kim" number.

One shortcut might be to look for vowels, by testing the (1+26n)th, (5+26n)th, etc. Lists of prime numbers (first 1000, first 15 million) are available here.

EDIT: Just occurred to me that the "space" might also loop round, so it could also be (1+27n)th for A, (5+27n)th for E. Possibly unlikely, as there are already four spaces (if my guess above is right).

I can't code, so can't offer a quick way to do this. Anyone?


PostPosted: Sat Apr 08, 2006 12:53 am
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donxkey
Kl00


Joined: 09 Apr 2006
Posts: 42

 		can anyone give me a quick reminder on how factorising works? i probably should now (i did a lot of maths at school) but my mind is just completley blank.

I also have a scan of the back, not sure if it's of interest.#

box reads:
Triple Wheel Stadium
There are few subjects as
contentious as Triple Wheel in
Perplex City, and few sports as
popular. The Triple Wheel
Stadium in Quadrant Park has a
long history and has been rebuilt
several times over the years,
with the most recent renovation
taking place in 262, when the
central spire was added to
provide prtoection against the
weather by means of an
ultralightweight unfolding lattice
dome.

thanks
peg013.jpg
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peg013.jpg

PostPosted: Sun Apr 09, 2006 11:40 am
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GasparLewis
Unfettered


Joined: 19 Nov 2005
Posts: 474
Location: vicinty of NYC

 		I just want to say, BBuck, that was flippin' brilliant.
But a tick off.

Spoiler (Rollover to View):
Not to worry; rights itself if you go about it more like a modulo calculation.
Or with a dummy, anyway.

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
0 1 2 3 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 025 026

107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251
000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026

59 67 29 43 13 67
16 18 09 13 05 18
P. R. I. M. E. R.

73 13 71 73
20 05 19 20
T. E. S. T.



And lo, the system is found; now to go about cracking the buggers open.

PostPosted: Sun Apr 09, 2006 2:30 pm
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addybobble
Boot


Joined: 01 Jan 2006
Posts: 23

 		For the more patient of you, here's an applet you can use to break down the factors by hand: http://www.apfloat.org/apfloat_java/applet/calculator.html

I guess when you end up with a very small number you've got yourself an anagram of primes to multiply. Having a go now...

PostPosted: Sun Apr 09, 2006 5:18 pm
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GRTae
Greenhorn

Joined: 09 Apr 2006
Posts: 7

 		Here is a good link that uses ECM to factor numbers.

http://www.alpertron.com.ar/ECM.HTM

I'm currently factoring the large "Kim" number -- assuming it is to be taken as a single large number.

Some thoughts:

Spoiler (Rollover to View):

I have a feeling that the large prime 2154181329756249376787964511131911 number doesn't really need to be converted to a letter. beacuse the other factors give:
_ _ B E

_ = 2 or a "space"

I think "BE" is more than a coincidence (KS + BE). Maybe looking up primes corresponding to "K", and "S", and "B" and "E" and then subing them in "K*S + B*E" will give us a factor for the "Kim" block?

maybe "C*A*T" is also a factor somewhere?

Using the mod approach, the question becomes which prime do we pick for K, S, B, E, C, A, T!?

+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_

Factoring 164990462647551511589599262129081060112 gives:
3 ^ 5 x 11 x 13 ^ 2 x
19 ^ 2 x 23 ^ 2 x 29 ^ 2 x 43 ^ 2 x 47 ^ 2 x 59 x 67 ^ 3 x 71 ^ 2 x 73 ^ 3

Which would correspond to:

_ _ A A A A A D E E G G H H I I M M N N P R R R S S T T T

I'm going to work on this Anagram. I guess the best way would be to deocde these before moving to Kim because as the title states it is a "Primer Test" so we don't waste our time on the "Kim" block.


Cheers

PostPosted: Sun Apr 09, 2006 5:53 pm
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addybobble
Boot


Joined: 01 Jan 2006
Posts: 23

 		How about this. The spaces tell you how many words the anagram consists of, so you could use a site like this
http://www.wordsmith.org/anagram/advanced.html to home in on the answer quicker, probably pulling out 'sente' or the like before submitting.[/url]

PostPosted: Sun Apr 09, 2006 6:24 pm
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GRTae
Greenhorn

Joined: 09 Apr 2006
Posts: 7

 		Sounds interesting but the link you provided won't anagram beyond 24 characters. The last line on the board has 27.

The 3rd line has 4 spaces, but not enough letters for 4 words.

Can anyone in UK try and get a Von's hint for this one?

PostPosted: Sun Apr 09, 2006 6:36 pm
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addybobble
Boot


Joined: 01 Jan 2006
Posts: 23

 		I see what your saying, and that's why I said 'pulling out sente or the like' to reduce the number of words to crunch. Also please bear in mind that the number of characters available depends on server load for this site. Of course there are other ways to do this (and code up), but I thought this might be an easy thing for many people to play around with. We are collaborating after all Very Happy

PostPosted: Sun Apr 09, 2006 6:45 pm
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GRTae
Greenhorn

Joined: 09 Apr 2006
Posts: 7

 		Yeah...I pulled out a few things here is what I have:

Spoiler (Rollover to View):

I pulled out "PRIMER TEST". *Part* of the remainder could be up:
ANAGRAM, DATAGRAM, HASHING, HAS?

I'm still trying to narrow down the search for the last part. Maybe its just a coincidence that we have "A PRIMER TEST ANAGRAM...." or "A PRIMER TEST DATAGRAM..."


PostPosted: Sun Apr 09, 2006 6:50 pm
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Hunting4Treasure
Unfettered


Joined: 06 Aug 2005
Posts: 385
Location: Tampa Bay Area, FL USA

 		Addybobble and GRTae,
What spaces? I don't have this card (or any others, for that matter), and all I have to go on is what's listed in the first post. Are the strings of numbers to Kim broken up? If that's the case, the applet I've been running the past 3 hrs (not including the 1 hr I lost when my computer overheated and crashed) is worthless. I've been running it as one long 224-digit line. Shocked
_________________
E=MC˛
Energy (Power) = Mind Candy's Cube
PerplexCityTrades - Hunting4Treasure

PostPosted: Sun Apr 09, 2006 8:27 pm
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GRTae
Greenhorn

Joined: 09 Apr 2006
Posts: 7

 		Re: spaces

Spoiler (Rollover to View):


The numbers given in the top portion are all factorize to prime numbers -- except for two numbers (the last two) that also have 2 (and its powers) as their factor. This was clearly intentional and must indicate something. The theory is that it indicates spaces.

I'm trying ECM on the last number also -- after dividing it by 17 which is one of its factors. I'm quit certain that the two lines and the Cat, and BE+KS are clues as to a large factor of the "Kim" block, which will give us a much smaller number that can then be quickly factored using ECM and decrypted.


PostPosted: Sun Apr 09, 2006 8:33 pm
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EvilGenius
Decorated


Joined: 04 Mar 2006
Posts: 227
Location: Vancouver
Spoiler (Rollover to View):

Gathering the above work and adding to it.

factors:

4293499561:
Factors are 13*29*43*59*67*67
Letters are: eimprr
anagram for "primer"

4918667:
Factors are: 13*71*73*73
Letters are estt
anagram for "test"

2240348582964699351859483091577187440
Factors are:
2*2*2*2*3*3*5*13*13*13*13*13*23*29*43*43*47*47*59*67*67*67*67*71*71*73*79*89
Letters - aabeeeeehImmnnprrrrsstuw
anagram for "prime numbers are the answer"


164990462647551511589599262129081060112:
Factors are 2*2*2*2*3*3*3*3*3*11*13*13*19*19*23*23*29*29*43*43*47*47*59*67*67*67*71*71*73*73*73
Letters are (with 3 being the first prime as per primer):
aaaaadeegghhiimmnnprrrssttt (please check this as I made about a million mistakes getting here).
anagram for ?

If the two's are spaces (I doubt it but worth looking in to; otherwise they can just be discarded which really is the same this anyway if they don't add any letters to the anagram) then this should be 5 words. There are so many possibilities here that a clue would be nice (I don't have the card to examine). Probably the correct solve of 244...440 would be that clue. [note - number was wrong, post above corrected]

Haven't yet sorted out the huge number. Maybe it's a concatenations of primes. Even if we manage to factor it, surely we can't be trying to make an anagram of all those letters?! That would take forever Wink Or we would need some good idea what it's about.

We don't have a "Kim" in the game, as far as I know, so I wonder who is being referred to.

Also, the initials in the corner, I wondered if they were just a signature but there are no characters with those initials (or are there?). Maybe KS is Kente Siteway Smile Or Sente Kiteway in reverse? Could be anything still.

Here's an awesome anagram generator:
http://www.mi.uib.no/~ingeke/anagram/index_eng.html

The partial (I hope) factor of 224...440 are B and E as noted (ignoring the 2's as either spaces or dross). K and S, by the same reasoning are 11 and 19, product is 209. For whatever that is worth, I don't see it adding anything unless the number has been transcribed wrongly. KS + BE is 209 + 65 = 274 (which factors to 2*137).

BTW - C*A*T is 7*3*73, or 1533. Of course, both C*A*T and K*S+B*E could me modulo26 and so represent much larger numbers.

Can some who has this card confirm these long numbers have been
transcribed properly, particularly the one that doesn't factor well? I don't like the look of the factors for 224...440 - that long one is silly - that, mod26, would be stupidand I'm hoping for an error in the transcription. [note: that number was wrong and has been corrected as above. I continue to update this post as a single reference point for me to work from and includes the work of others - I don't claim all this work for myself]

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Yogurt, curd, cream, cheese and butter's made from liquid from my udders - I am cow!

PostPosted: Sun Apr 09, 2006 10:36 pm
Last edited by EvilGenius on Tue Apr 11, 2006 1:33 pm; edited 19 times in total
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