Puzzles from the xkcd book (big puzzle SOLVED!)

A forum for good logic/math puzzles.

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Re: Puzzles from the xkcd book

Postby operator[] » Sat Feb 20, 2010 2:27 pm UTC

I have, in collaboration with medgno, written a brute-force for the last part of the key. On a one-core ~2 GHz machine, the program takes roughly one hour to test every combination of bytes. I have yet not found the message though, which may be due to a number of causes:
  • The message is not encrypted with ecb (the simplest cipher mode, not needing an iv - see wiki), but instead something like cbc, cfb or ofb, all of which need an initialization vector. For cbc, its length is 16-bytes (32 hexadecimal digits), for the others I'm not sure, but I'd guess it's the same. I have tested cbc with the two first suggestions by danm, any ideas about what other iv's I can test?
  • There are typos in the already decrypted parts of the code. Can someone double check their correctness?
  • There are a lot of successful decryptions that turn out to be nonsense, so I use the simple heuristic of discarding messages containing character codes higher than 127. It may be possible that Randall put some "invalid" characters in the message just to mess with this approach.
Any suggestions on how we can continue from here?

--
As this is the pagetopper, I will include the unsolved puzzle for easy reference:
Spoiler:
101110-big.png
101110-big.png (224 Bytes) Viewed 57637 times

10111110101111110111111
11111111101011110100001
10111111111111111010100
11011001001001001010111
01100101011110100000001
01101110101100111111111
10111101011011110111110
01111111111010100100001
10111111111111001101111
(edited for error pointed out by TrueJournals; thanks!)
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bruteforce.tgz
(10.02 KiB) Downloaded 1753 times
Last edited by operator[] on Tue Feb 23, 2010 7:56 pm UTC, edited 1 time in total.
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Re: Puzzles from the xkcd book

Postby Sentynel » Sat Feb 20, 2010 9:21 pm UTC

My copy of the book finally showed up today. Some stuff:

First, what if the significance of the prime factors comic to the pixel block is that it's 3x3x23, i.e., the data should be considered as 23 items of 3x3 data. My first thought was 9-bit RGB, but although that gives a bunch of colours, I don't think it does anything useful. It then occurred to me that Marain, the language from Iain Banks' Culture novels, is written in a 3x3 grid (essay on Marain by Banks). Unfortunately, while some of the symbols you get by plotting the contents of the block as 3x3 sections do occur in the Marain alphabet he provides, far from all do. I was able to get "??rv?rpyptch?tch??y??eh?????" or "?y?ee?th???h?z?ll?f?kt?h??p" depending on the order I plotted things in, neither of which are very helpful. I have no idea if this is likely to lead anywhere.
Edit: Also tried eight-bit bytes plus a parity bit, and nine-bit bytes including Hamming coded parity bits, but it doesn't seem to work.

skeptical scientist wrote:page 10112
Spoiler:
0011001001011100000101100000110111100100001010100110011000010010110011 is 70 binary digits. Breaking this into 14 sequences of 5 digits, and converting binary to decimal, we have 6 9 14 1 12 3 15 4 5 9 19 1 5 19. Making the substitution 1=a, 2=b, etc., we get finalcodeisaes, i.e. "final code is aes". This seems rather redundant (we already knew that from page 11), but it seems to be the solution.

Could this be referring to something other than the 10020 code? I don't like the redundancy at all, but I can't see what else it could apply to.


The brute force program in the post above provides nothing useful for me either. I'm checking others' work on the known keyparts. There have been a couple of different values for page 11002 posted, but it definitely gives me 735646B0.
Edit: Okay, all known keyparts checked. No discrepancies noted. For reference, my values are:
Spoiler:
1:EE985118
2:73CD4542
3:DA101CBC
4:735646B0
5:9BE32BE0
6:
7:CB4D62AE
8:8662384F

Brute force code still doesn't get any hits. Are we positive the code works? I assume this has been done, but can someone with more knowledge of OpenSSL than me double check by encoding a message with the known keyparts and some made up 6th part, then run the forcer on it and check we get the plaintext back?
Are we sure part 3 (from page 1111, the crypto conference) is correct, and it is just the numbers on the screen? That and assumed part 4 bother me, since neither are directly labelled like the other parts.
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Re: Puzzles from the xkcd book

Postby Xutar » Mon Feb 22, 2010 2:09 pm UTC

Sentynel wrote:Are we sure part 3 (from page 1111, the crypto conference) is correct, and it is just the numbers on the screen? That and assumed part 4 bother me, since neither are directly labelled like the other parts.

regarding part 3:
Spoiler:
Yes, the comic was also altered regarding the hair of the audience, which spells out "3 OF 8" IIRC
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Re: Puzzles from the xkcd book

Postby Sentynel » Mon Feb 22, 2010 2:26 pm UTC

Xutar wrote:
Sentynel wrote:Are we sure part 3 (from page 1111, the crypto conference) is correct, and it is just the numbers on the screen? That and assumed part 4 bother me, since neither are directly labelled like the other parts.

regarding part 3:
Spoiler:
Yes, the comic was also altered regarding the hair of the audience, which spells out "3 OF 8" IIRC

Yes, but all the other key parts we've found have had contiguous messages like "key x of 8: yyyyyyyy". I'm pretty confident about the decryption of part four, and I went through the book yesterday looking for any signs of other comics that have changed or could have data encoded in them somehow with no luck. Given the brute force isn't working, the most likely candidate for a misdecryption becomes 3, because while labelled, the label and the key weren't in the same string of data, and there are operations listed that could be performed on the values on the screen to then get the key data.
It's a long shot, but the other option is that it's a more complicated version of AES and we'll have to start guessing IVs, which would probably require breaking the pixel block code; trying IVs while brute forcing the final section of the code rapidly becomes computationally unfeasible.
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Re: Puzzles from the xkcd book

Postby yehudasa » Tue Feb 23, 2010 2:20 am UTC

Sentynel wrote:Given the brute force isn't working, the most likely candidate for a misdecryption becomes 3, because while labelled, the label and the key weren't in the same string of data, and there are operations listed that could be performed on the values on the screen to then get the key data.
It's a long shot, but the other option is that it's a more complicated version of AES and we'll have to start guessing IVs, which would probably require breaking the pixel block code; trying IVs while brute forcing the final section of the code rapidly becomes computationally unfeasible.


Yeah, #3 is one that I also suspect at being wrong. My take on it would be something like this:
Spoiler:
One option would be to use the numbers as the plaintext and apply the operations as in Feistel cipher:

plaintext = 0xDA101CBC

--> L[0] = 0xDA10
R[0] = 0x1CBC

L[i+1] = R[i]
R[i+1] = L[i] ^ F[i](R[i])

F[0](x) = shr(x, 1)
F[1](x) = ~(x)
F[2](x) = reverse(x)

And thus:

L[1] = 0x1CBC
R[1] = 0xDA10 ^ shr(0x1CBC, 1)
= 0xDA10 ^ 0x0E5E = 0xD44E

L[2] = 0xD44E
R[2] = 0x1CBC ^ ~(0xD44E)
= 0x1CBC ^ 0x2BB1 = 0x370D

L[3] = 0x370D
R[3] = 0xD44E ^ reverse(0x370D)
= 0xD44E ^ B0EC = 64A2

And this gives us: 0x370D64A2


Another option would be to use the binary number encoded by the crowd as the plaintext, the numbers on the board as the K for every Feistel stage. Not completely sure which functions to use then because we have 4 keys and only 3 functions.
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Re: Puzzles from the xkcd book

Postby skeptical scientist » Tue Feb 23, 2010 6:33 am UTC

Xutar wrote:
Sentynel wrote:Are we sure part 3 (from page 1111, the crypto conference) is correct, and it is just the numbers on the screen? That and assumed part 4 bother me, since neither are directly labelled like the other parts.

regarding part 3:
Spoiler:
Yes, the comic was also altered regarding the hair of the audience, which spells out "3 OF 8" IIRC

Good eye.
Spoiler:
But you are right, interpreting bald head as 0 and hairy head as 1, we get "01001011011001010111100100110011011011110110011000111000" which, when converted to ascii, gives "Key3of8". But again this is redundant, since the page already says "3 of 8" in red plaintext at the bottom. So I'm not sure what the point of this was.

Personally I'm more uncomfortable with
Spoiler:
page 11002's "UATAQANUUNG..." which doesn't seem to bear any label, which is odd given how carefully labeled the other key parts are. Does anyone have comfirmation that this is part of the key?
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Re: Puzzles from the xkcd book

Postby Sentynel » Tue Feb 23, 2010 1:38 pm UTC

skeptical scientist wrote:Personally I'm more uncomfortable with
Spoiler:
page 11002's "UATAQANUUNG..." which doesn't seem to bear any label, which is odd given how carefully labeled the other key parts are. Does anyone have comfirmation that this is part of the key?

We do now.
Spoiler:
Look at the "a softer world" parody comic, first and second panels, on the computer screen. Naturally, I only notice this after a couple of failed attempts at getting a label out of the bits that give the key.
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Re: Puzzles from the xkcd book

Postby TrueJournals » Tue Feb 23, 2010 7:33 pm UTC

I just noticed there's a mistake in the transcription of the image at the top of this page. On the right side, the fifth block down should be red, not white:
101110-big.png
101110-big.png (224 Bytes) Viewed 57642 times

10111110101111110111111
11111111101011110100001
10111111111111111010100
11011001001001001010111
01100101011110100000001
01101110101100111111111
10111101011011110111110
01111111111010100100001
10111111111111001101111
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Re: Puzzles from the xkcd book

Postby childofsai » Tue Feb 23, 2010 10:11 pm UTC

There's two thoughts I've had about the red pixel image.

- Would it be possible to split the binary grid into numbers from the page?

- 207 = 23 x 3 x 3 -- could this be an indication to go to 3 dimensions in some way?

Some random ideas, really...
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Re: Puzzles from the xkcd book

Postby kaimason1 » Wed Feb 24, 2010 12:07 am UTC

I don't know much about cryptography, and I don't even own the xkcd book, but that pattern of ones in TrueJournal's post looks a bit like a pattern visually.
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Re: Puzzles from the xkcd book

Postby cjr22 » Wed Feb 24, 2010 3:08 pm UTC

I'm not sure the brute forcer is working correctly. Or if it is, I'm not using it correctly. I did this:
Code: Select all
openssl aes-256-ecb -K EE98511873CD4542DA101CBC735646B09BE32BE000000000CB4D62AE8662384F -in NOTES -iv 00000000 > encoded.txt

Which, I believe, encodes the text in the NOTES file using the known puzzle answers and 00000000 as the missing key. I believe the brute forcer should try this key first.
I then ran
Code: Select all
./a.out encoded.txt

Which should crack the encoded text with the first key it tries.

It didn't, it got as far as 63/256 before I remembered to kill it without producing any other output.

Any flaws in my methodology? If not, I can have a look through the brute force code to see if I can see the bug in it.
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Re: Puzzles from the xkcd book

Postby operator[] » Wed Feb 24, 2010 5:35 pm UTC

I think the reason is that the code defaults to cbc mode instead of ecb; I forgot to change this before publishing it. :oops:

Anyway, I updated the code to handle parameters more flexibly (like -parameter [value] instead of hard-coded formats), it is attached.

And for the interested, I took some (blurry) pictures of the puzzles from the book, available here.
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Re: Puzzles from the xkcd book

Postby Sentynel » Thu Feb 25, 2010 11:28 am UTC

On different AES modes - at least with the options my version of OpenSSL is offering me, the only 256 bit modes are ecb and cbc. With a 0 IV, they operate identically (at least over the sort of data length we're talking about here), but they differ with nonzero IVs. I've tried the brute force with several different values of key 3 (straight off the screen and with a couple of different operations on it) with no luck.
I suspect we've pretty much run out of options that don't include "solve the pixel block puzzle", which I'm still not getting anywhere with. If we get that solved, we can run a modified brute force on each key part to check them, and if that still doesn't work, start guessing IVs. I don't like the IV thing, though. There's absolutely no mention of one, whereas everything else has been given pretty explicitly.
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Re: Puzzles from the xkcd book

Postby Carlington » Thu Feb 25, 2010 11:48 am UTC

As a floating-point double number, the binary of that puzzle comes out to e0d0ebff efd7e74b

Could be useful. Never know.
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Re: Puzzles from the xkcd book

Postby aspragg » Tue Mar 09, 2010 12:36 am UTC

I believe I have solved Key 6... has anyone else?

I'm new here. What should I do now?

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Re: Puzzles from the xkcd book

Postby aspragg » Tue Mar 09, 2010 12:50 am UTC

Wow.

Using all the keys given above, and the solution to part 6, I was able to successfully decrypt the encrypted message.

WOO HOO!
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Re: Puzzles from the xkcd book

Postby aspragg » Tue Mar 09, 2010 12:59 am UTC

The pixel block picture thing is solved thusly...

Spoiler:
The image block is 23 x 9. The comic talks about prime factorization, so I made this 23x3x3.

I had the suspicion that this was an actual graphical image. So I took the original image, and made it 23x3 across, and 3 pixels high.

10111110101111110111111
11111111101011110100001
10111111111111111010100
11011001001001001010111
01100101011110100000001
01101110101100111111111
10111101011011110111110
01111111111010100100001
10111111111111001101111

turns into:

101 111 101 011 111 101 111 111 111 111 110 101 111 010 000 110 111 111 111 111 111 010 100
110 110 010 010 010 010 101 110 110 010 101 111 010 000 000 101 101 110 101 100 111 111 111
101 111 010 110 111 101 111 100 111 111 111 101 010 010 000 110 111 111 111 111 001 101 111

I replaced 1's with X's and 0's with spaces in a proportional font and was able to read:
KEY SIX OF EIGHT: D0E0C9A6
Last edited by aspragg on Tue Mar 09, 2010 1:05 am UTC, edited 1 time in total.
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Re: Puzzles from the xkcd book

Postby aspragg » Tue Mar 09, 2010 1:02 am UTC

THE FINAL ANSWER...

Maybe this is old news, but I haven't seen it yet.

THIS IS THE FINAL ANSWER TO THE ENTIRE PUZZLE. DON'T READ IF YOU WANT TO WORK IT OUT YOURSELF!

Spoiler:
Key: EE98511873CD4542DA101CBC735646B09BE32BE0D0E0C9A6CB4D62AE8662384F
Ciphertext: 772A3A35DEF88CA70BDFD18620B05684934721F8F64762FD03F8D76B3FA0CB8C2756B2D0A9F00A1BCFF1603EDB05426C
IV: 00000000000000000000000000000000

I get the following:

<3<3<3 2010-06-26 14:28:57 37.769573 -122.483123

Do I win?
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Re: Puzzles from the xkcd book

Postby alxndr » Tue Mar 09, 2010 1:10 am UTC

aspragg wrote:THIS IS THE FINAL ANSWER TO THE ENTIRE PUZZLE. DON'T READ IF YOU WANT TO WORK IT OUT YOURSELF!

Spoiler:
Key: EE98511873CD4542DA101CBC735646B09BE32BE0D0E0C9A6CB4D62AE8662384F
Ciphertext: 772A3A35DEF88CA70BDFD18620B05684934721F8F64762FD03F8D76B3FA0CB8C2756B2D0A9F00A1BCFF1603EDB05426C
IV: 00000000000000000000000000000000

I get the following:

<3<3<3 2010-06-26 14:28:57 37.769573 -122.483123

Do I win?


So ...
Spoiler:
that's the middle of Golden Gate Park in San Francisco, June 26th at 2:30pm-ish.
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Re: Puzzles from the xkcd book

Postby Qaanol » Tue Mar 09, 2010 1:51 am UTC

The thing that is on, it is game.
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Re: Puzzles from the xkcd book

Postby skeptical scientist » Tue Mar 09, 2010 2:26 am UTC

Congrats!
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby kaimason1 » Tue Mar 09, 2010 3:10 am UTC

I bet Randall will be there under the tree with a bunch of other xkcders at that date and time.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby e^iπ+1=0 » Tue Mar 09, 2010 3:12 am UTC

I'm hoping it'll be like the last one was. And thought it's about a 7 hour drive from here, I can probably make it. Especially because it's also a short, cheap plane ride.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby aspragg » Tue Mar 09, 2010 7:46 pm UTC

So... uh... now what? :)

I, for one, would love to see a full start-to-finish write-up of the process, including each puzzle and the full solutions. It's also fun to see failed solutions, and a little more of the thought process behind each one. Does anyone have the time to get something like that started?

As far as the final solution... On one hand, it feels a little counter-intuitive to share the answer with everyone. On the other hand, it's not going to be a very fun party if no one knows it exists. :)
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby whackedspinach » Wed Mar 10, 2010 1:24 am UTC

2,100 miles for me. Ah, well. Maybe someday I'll be out there when a new book is released.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby quintopia » Wed Mar 10, 2010 10:21 am UTC

congrats on solving it! (inb4 thread explodes?)
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby Ended » Wed Mar 10, 2010 10:32 am UTC

Congrats! Also, you made it on Slashdot. That would explain the 512 guests I think.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby Atamido » Wed Mar 10, 2010 1:52 pm UTC

Is the time in local time, or is it in UTC?
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby cdehaan » Wed Mar 10, 2010 3:02 pm UTC

aspragg wrote:So... uh... now what? :)

I, for one, would love to see a full start-to-finish write-up of the process, including each puzzle and the full solutions. It's also fun to see failed solutions, and a little more of the thought process behind each one. Does anyone have the time to get something like that started?

As far as the final solution... On one hand, it feels a little counter-intuitive to share the answer with everyone. On the other hand, it's not going to be a very fun party if no one knows it exists. :)


I'd really enjoy that. The puzzles had me going for a while, but I'd never have gotten them on my own. Example: The enigma?? I really enjoyed reading everyone figure it out, and would like to share that with everyone else. I'll start it tonight, and maybe post something tomorrow night.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby halightw » Wed Mar 10, 2010 5:07 pm UTC

Is that the location of where....
Spoiler:
the Klingon ship landed in Star Trek IV?
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby hoffmanbike » Wed Mar 10, 2010 6:01 pm UTC

awwww, i won't be able to get out there this year. damn.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby FoolishOwl » Wed Mar 10, 2010 6:04 pm UTC

Hey, it's walking distance from where I live. So I'm planning to be there.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby aspragg » Wed Mar 10, 2010 8:41 pm UTC

cdehaan wrote:I'd really enjoy that. The puzzles had me going for a while, but I'd never have gotten them on my own. Example: The enigma?? I really enjoyed reading everyone figure it out, and would like to share that with everyone else. I'll start it tonight, and maybe post something tomorrow night.


That would be awesome. Stuff like this should be officially documented for posterity. I'd love to help out.
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby tagno25 » Thu Mar 11, 2010 5:45 am UTC

halightw wrote:Is that the location of where....
Spoiler:
the Klingon ship landed in Star Trek IV?

Possibly near it, but this spot is a tree.
http://www.google.com/maps?q=37.769573,-122.483123
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby gjbloom » Thu Mar 11, 2010 5:20 pm UTC

Spoiler:
I believe this is the tree:
xkcd tree.jpg
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby aspragg » Thu Mar 11, 2010 11:27 pm UTC

Here's my first draft of a solution document. I lifted some pictures and text from this forum without permission. Hope that's ok.

I'm hoping someone can clean this up a bit, add some credits and publish it somewhere official.

Adam
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby skeptical scientist » Fri Mar 12, 2010 3:53 am UTC

aspragg wrote:Here's my first draft of a solution document. I lifted some pictures and text from this forum without permission. Hope that's ok.

It's fine as far as anything I wrote, but you should really give credit to the people whose solutions you are quoting. I can't speak for anyone else, but I can't imagine why anyone would have a problem as long as you give credit where credit is due. As far as the images of the puzzles in the book, that's all copyrighted by Randall Munroe, and licensed under a creative commons 3.0 attribution/non-commercial license. You should credit him as the author (which right now you are not) but other than that you should be fine there (which is probably the important part, since the author of a published book is going to have much stronger legal standing than a random forum contributor).

somewhere official.

What does that even mean?
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby Qaanol » Fri Mar 12, 2010 11:12 am UTC

@SkepSci: It means under that tree in Golden Gate Park, using a movable-type press, of course!

I made an animation showing how key six is decoded:

Spoiler:
Image
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby aspragg » Fri Mar 12, 2010 3:16 pm UTC

skeptical scientist wrote:It's fine as far as anything I wrote, but you should really give credit to the people whose solutions you are quoting.


Yes, please. My post was only intended as a springboard. If the document is lacking, I invite anyone to update it as they see fit.

somewhere official.

What does that even mean?


I have absolutely no idea. I was kind of hoping someone else would. :)
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Re: Puzzles from the xkcd book (big puzzle SOLVED!)

Postby aspragg » Fri Mar 12, 2010 3:17 pm UTC

Qaanol wrote:@SkepSci: It means under that tree in Golden Gate Park, using a movable-type press, of course!

I made an animation showing how key six is decoded:

Spoiler:
Image


I know I just woke up, but that's the coolest thing I've seen all day. Nice work.
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