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Thread: A different way to fill the box?

  1. #21
    d0a0b's Avatar
    d0a0b is offline Getting the hang of it. Copper d0a0b is an unknown quantity at this point
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    yeah, you caught my typo. I checked back and had it written on paper as a 1 not a 7.

    But that is interesteing, I must've misunderstood your addition rules. Thanks for pointing that out to me. I think I understand them now.

    When I created that last one, I had changed my own creation rules around a bit, thinking that would change the way things worked out.

    In that particular example, the first set of palindromes had the numbers 1-5 but you could make them start with 1-9 and even 0-9 if you wanted. My calculations on the amount you could come up with was based using the 1-9 as a possible starting number for each palindrome. using 1-5 as a possible starting number you could still make about 405 of them.

  2. #22
    Milou's Avatar
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    For those of you who are still interested in this thread (I am...) I thought I could share some results I got regarding the magical 5x5 box of palindromes.

    According to my calculations, the chance of the 20-letters conforming to the pattern described in this thread is about 7,000 to 1. That would we very strange if it was just a coincidence, right? I am convinced we are onto something big here.

    Here is an outline of the process I went thru to come up with this estimate of the chance.

    My task was to find how big chance it is to fill out the border with 20 random letters that result in a 5x5 box with all rows being palindromes as described above. I told my self that this would give me an idea of how relavant this thread is. If you have tried to fill out the 20-letter border by hand you have probably realized that it is not that easy to make sure the inner 5x5 box turns out to be "magical". How how hard is it then? Well, I wrote a small piece of code that generate random borders and analyzes the result. It seems that the chance of doing it "correct" is about 1.25% or about 80 to 1. After two 100,000 random tests my computer came up with 1242 (1.24%) and 1282 (1.28%) correct "solutions". I then had it run 500,000 tests and it came back with 6236 correct solutions (1.25%). We have to remember that there are 25^20 possible combinations in total (approx. 10^28!). That is a HUGE number so I have no intent of trying them all... That is why we have to rely to statistics here (this is the famous Monte Carlo Method).

    If we now include the fact that Reckhardt pointed out, that if the rows are sorted starting with the smallest, the columns all turn out to be nice sequences. If sort the original 5x5 square mentioned above we get:

    17671
    28782
    39893
    41914
    52125

    As you see, the columns are all nice sequences!. Note that no zeros are possible so 78912 is a "good" sequence too (1 comes after 9 in this type of system).

    I went back and modified my computer program. To be a "corect" solution, the 5 rows, when sorted, now also have to provide columns with numbers in order as the example above. For sure this is going to reduce the number of solutions dramatically. But how hard is it now to find a solution then? I had my program perform two 100,000 random tests again. This time only 14 and 16 correct solutions were found! That gives us the chance to find a solution to be around 0.015% which is about 7,000 to 1. Now that is quite something!!! To check the numbers I ran the program (on my slow computer...) 1 million times and 126 solutions came out of it (0.0126%).

    Finally, let me share some of the correct solutions that I have found. The original 20-letter "solution" used by MS in the book, as first pointed out by Pooklover (see first post in this thread), is

    ZFDBWBASAOTYTTTPRHIT

    And here are 8 other "correct" solutions my program found:

    WYXFFNKLPPYNUNWGXGBR
    OOAGGYUPOXRKGVIKWYZJ
    IJJMJLJSKCXEYWNEYUZE
    YNKGNILHWOPBZOSNZFSB
    IVOIUGBAPSSHAKNRXNTU
    VKXKNFVKFTVDSFSOOJZT
    GXGJOXGZVHEDUGEVWSBX
    BGUZUFBGIVSVYGRHVDKO

    Again, the solutions mentioned above all yield palindrom numbers in the inner 5x5 box and when sorted, the colums have numbers that are in order. To give you an example. If we use the last solution above, i.e.

    BGUZUFBGIVSVYGRHVDKO

    the inner 5x5 box is given as:

    56465
    89798
    45354
    67576
    78687.

    If we sort the 5 rows we get:

    45354
    56465
    67576
    78687
    89798

    And as you can see, all the columns are in nice sequences. All that remains now is to understand how to use this information...

    Grab your pen and write down the border as given by Pooklover and try to match up things you see in the text. Perhaps something pops up?

    Have fun!

  3. #23
    Milou's Avatar
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    I have yet to come up with the ground braking clue that is hidden behind all this. However, this is what I think at the moment:

    1. The 20-letter sequence is not random. MS had a good reason for starting the chapters with these letters.

    2. The 20-letter sequence does not contain a message in it self, i.e. it should not used in an anagram.

    This leaves me with one option. We are dealing with key(s) here.

    But I do not think the individual letters are keys. I think that the inner box contains the keys. I say keys, because I doubt that the box contains explicit information such as zip codes. I like to think MS picked his locations, then created the codes to find them. Not the other way. What do you thinK?

  4. #24
    pooklover is offline Needs to say Hello! pooklover is an unknown quantity at this point
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    Wow! I never thought as far as all the rearranging of numbers that everyone has done on this "magic box"!! Personally, I do not think the 20 letter sequence is random, nor the box of numbers created from it. I think that the box itself is somehow the key to decoding the text, and that will spell out an EXACT location for a token. Not just a zip code, but true directions to a specific spot. Remember, that in the foreward, it says that we can find the treasure just the way one of the characters in the story did. In his dream, Zac found the treasures by filling a box that was as long as it was wide, with smaller boxes arranged in rows, 5 to a side. (the 25 square box). After that, he knew exactly where the jewels were. So I feel we have to do the same. I also think we have to remember the rest of the poem, and somehow apply it. We can't forget the faeries and their importance to the clues. At one point I felt really strongly that the moon like, moon like song was to be used in combination with this box, I haven't figured out a way to make it fit however. Anyway, maybe this will spark an idea with someone else...

  5. #25
    mackadoo is offline Junior Twelever +1 Silver mackadoo is an unknown quantity at this point
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    OK, now I am excited!

    What a fantastic line of thought. I want to thank pooklover for sharing it with the rest of us.

    I definitely agree that when we come up with a location it isn't going to something vague like a zip code. It is going to have to give us a pretty clear indication of where the tokens are. Now, it seems this would have to apply to all the tokens. Will it reveal the "name where the treasures abide" (planter, under a bench, in a knothole, etc) or will it be used differently for each treasure to give us the exact, precise location? I don' know, but man, I can't wait to find out!!
    Calgon, take me away! To the jewels preferably!

  6. #26
    mackadoo is offline Junior Twelever +1 Silver mackadoo is an unknown quantity at this point
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    One more question... for the seasoned veterans of treaure hunting out there - Is it possible that we might combine Doc's theories with this numbered grid? In other words, take the directions he's gotten from the pictures and move through the grid to get a "code of numbers" that will then be converted back to letters? Or is that too contrived?
    And other than just subbing the letter for the number it is in the alphabet (1=A, 2=B, etc) what are the other ways to convert the numbers to letters? I don't think just subbing the numbers for letters would work though because then we only have the first nine letters of the alphabet to work with.
    I guess I just don't know how we go from what we have from pooklover to having a word, a place, and name, a location that makes perfect sense.
    Well now, that's silly... if I knew that, I suppose I'd have a token, right?
    Calgon, take me away! To the jewels preferably!

  7. #27
    weepixel is offline Junior Twelever +1 TwelevePlus
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    I am thinking the same thing you are. Let's say we've used the string of letters to create a 5x5 grid which is verified in the text/images. However, we're supposed to be looking for a "code of numbers" so we convert the letters in the grid to numbers, then find a key to convert them back to letters forming a name/location? Is this normal? I'm new to treasure hunting and ciphering. Does this sound right?

    At one point, I wanted to find the treasures myself, but now I just want them found so they can tell me how they solved it!!

    -pix

  8. #28
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    Milou- great find!!!! very few solutions... I think I understand what you've done, but can you find any solutions that have a palindrome for the diagonals? If so, I believe that is the one we should work on.
    Or am I just paranoid...

    *Of course*

  9. #29
    Milou's Avatar
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    Quote Originally Posted by _~BlAnK
    Milou- great find!!!! very few solutions... I think I understand what you've done, but can you find any solutions that have a palindrome for the diagonals? If so, I believe that is the one we should work on.
    Blank,
    I could search for anything since it is easy to change my program to look for other patterns. I thought it was a cool idea to test what you suggested. But in doing this we are kinda in MS shoes prior to writing ATT. We are now stuck with his 20-letter combination, the one he slected for his chapters. But if he is to write a sequel, he could start the chapters with this 20-letter sequence:

    EVSWSAEKUZFHYITKEAUI

    It yields the inner 5x5 magic box as:

    86168
    53735
    97279
    53735
    86168

    As you see, all numbers are nice palindromes!!

    If anybody has ideas and need a brute force search for patterns, let me know since I can put together programs fairly easily. Right now I am just short of ideas myself...

  10. #30
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    Nice... and thanks for checking that for me. you'll be the first I turn to with this sort of problem!
    Or am I just paranoid...

    *Of course*

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