## While everybody's sleeping...

Posted By: Luigi <lorsina@mac.com>
Date: 20 June 2001, 03:24

... I'll take advantage of having slept while you were solving it...

OK, the puzzle has been solved (thanks to Grasshopper and to his little mistake in ROT-ing numbers... more below), the reward is now in our hands, and we all have the sensation that something is now behind our shoulders: tons of efforts, in all directions, to solve the riddle.

I'd like to point out some beautiful things that happened while trying to solve the final part of the puzzle.

1) The solution was easy, and symmetric, and the anti-cyclone clue pointed in the right direction: as I read the post with ARCHIVE (which then turned out to be ARCGIVE), I almost instantly tried the solution to get to the password, but without reversing the alphabet :(

2) Human minds (and psychology) are by far better then computers: I've done *tons* of programs to convert numbers into letters, ROT-ating letters, and so on; I'm almost sure that I would have dropped the ARCGIVE solution should I have found it (after all there have been many, many coincidences). But GH (look, another coincidence!) did not, probably because he started off with other letters, or found ARC, got excited, desired to have an H just after the three letters, and so on! Thus: do not be too confident in your computer programs...

3) I've spent a lot of time looking for mathematical connections among numbers, and I can conclude as follows: given a set of 8 numbers, you can extract from them any meaning you want, if you try hard enough... (I will not tell you what I've tried by interpolating the numbers, then decomposing the corresponding polynomial in Z_p, with p prime...)

4) The only beautiful numerical pattern I found was in G4: you can split the numbers in two sets (taking them in a symmetric way in the glyph) [50 26 113 8] and [13 22 37 7]; if you take the difference of any two numbers in the first set, you get a multiple of 3, and the same holds for the second set; if you sum any number in the first with any number in the second, you still get a multiple of 3. Neat, huh? Well: G4 was WRONG!!! There was a number coding for G which should have been a number coding for H! If the numbers were correct, the beautiful pattern would have not existed! This reminds me of Murphy's law...

5) BTW, I have discovered that given a set of 8 numbers whatsoever, than you have an high probability that you can obtain a multiple of anyone of them by summing some of the others: a rather counter-intuitive property indeed, and I've asked some probabilist here at the faculty to look for a solution of this problem...

6) Last, but not least, I really enjoyed the puzzle, and the cooperative efforts of us all! When will be the next?

Have fun,

Luigi

(OK, let's add the full address here, just to explain some of the oddities)

Luigi Orsina
Full professor of Mathematical Analysis
University of Rome, Italy

Marathoneer from the first demo on the Internet