looks kosher
looks kosher
shut up
shut up
shut up
shut up
shut up
If you place the letters around the grid starting top left and going clockwise (instead of counter-clockwise as before), you get the following result:
53142
29718
18697
29718
53142
As d0a0b pointed out the palindromes (in columns now) start with numbers 1-5. If we rearrange so the numbers are in order you get
12345
78912
67891
78912
12345
The middle three rows are successive numbers! That's the second confirmer.
That means the only number that is in no particular order now is the diagonal: 18815. This happens to be the zip code for Camptown, PA. The reverse (51881) is not a valid zip code. If I had found "PA" somewhere in the book, I would be booking a flight! Let me know what you think.
Originally Posted by reckhardt
...yes, you are absolutely correct. It is 13, not 12. But 13 is a good number to get too as we all are aware of.
Interesting indeed! Right now I am wondering how hard/easy it is to create this type of "magic" square. The reason I am asking is to see what MS had to go thru in creating it. If it is really hard (which I think it is) I would rule out the possibility of coincidence completely. For those of you who are sceptical still, try to build this type of square on your own using random numbers... Good find guys!Originally Posted by reckhardt
pooklover, I am not really good at math puzzles...for starters, ok?
I read all the following posts after yours, and all the 5-digit palindrome biz makes sense - I get that. Kinda sorta. Frankly, I prefer Pi.
But help me out here. I got stuck where you said, "I just started adding up the boxes." Then you showed the first set of numbers, 20+2+20+20=68 and how you placed 68 in the interior of your grid. Ok. Got that. Now, if you would be so kind as to show a series of a couple more sets of numbers, #2, and #3 for example,,,,to help me understand the pattern of what you did NEXT, and then NEXT....I might get it better. OK?
Thanks a bunch.
Hunnytree
"When you created the book, you also created us."
Let me see if I can explain Pooklovers magic trick. Once you have the border with the 20 numbers, 5 on each side. You create the inner 5x5 box. Each element is the sum of its four "anchors" in the border (left, right, top, bottom). As you see above you get high numbers for all 25 elements. You then reduce them by adding the individual digits until you get a number between 0 and 9, e.g.Originally Posted by Hunnytree
68->6+8=14->1+4=5
27->2+7=9
73->7+3=10->1+0=1
I hope this helps.
Thanks milou,,,,
I had to study on it, I did, I did, but I got it....all of it....including reckhardt 's fascinating set putting the numbers 1-5 in order and stringing the numbers into colums.
I even tried my own set of numbers and was NOT able to duplicate a numeric palindrome.
The only thing I was disappointed in was,,,no one noticed my own little joke....when I said,,,
Frankly, I prefer Pi.
"When you created the book, you also created us."
Now that we have discovered 18815, does that mean a token is hidden in Camptown, PA? I'm not so sure.
I've noticed a couple of things about the numbers that could have been encoded using this method:
1. The 1st digit must be a one because of the 12345 rearrangement scheme.
2. Because of the palindromes and successive numbers, the 4th digit must be equal to the 2nd digit+2. The fifth digit must be equal to the 1st digit+4. When doing this addition, don't count 0 after you pass 9. Count 7-8-9-1-2.
3. Zeros are not allowed. After the addition step, it is not possible to end with a zero in any square.
Using these rules narrows the field of 5 digit numbers that could be encoded with this method down to only 90. If the numbers need to be converted to letters and anagrammed, then the order doesn't matter and there are more than 90 letter combinations. If 18815 is just a zip code, then I understand what MS meant by saying he had a hard time finding places to hide the tokens.
im no math guy but without using zero, (1-9) i think you could come up with about 729 of em, those magic squares that is, of course you don't need to use that particular addition rule to make em. for instance:
53435
31213
18981
42324
29192
Edited: changed the last number 29792 to correctly read 29192
thanks reckhardt
d0a0b,
If I reorder the rows your magic square so the first column reads 12345 I get:
18981
29792
31213
42324
53435
The middle column (97234) is not successive numbers. I think you meant that column to be 91234. The number that you encoded was 19225. It follows my previous addition rules. The 4th number(2) is the 2nd number(9)+2. The fifth number (5) is the 1st number(1)+4.
My point was this: since the 1st number must be 1 and the 4th and 5th numbers are decided by the 1st and 2nd numbers, then only the 2nd and 3rd numbers (2 of the 5 digits) are able to be chosen by MS to create the code. He was very limited in the selection of the solution to the code.
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