> 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...

I tried quite a number of counting methods. Encouraged that using the last method I used, I got all numbers <=26, I ROTted them. When I encountered ARCGIVE, I became pretty sure that had to be the answer, and that the faulty G had to be either due to an error in encryption, or an error in decryption, both of which happen all the time. Read the Beale ciphers for a good example of this... what made me so convinced that ARCGIVE was correct is that there is a archives.bungie.org server, which CLAUDE manages! He he he ... And Luigi, you might try your hand at both the Beale and the Voynich, both "real" puzzles which have eluded cryptologists for quite some time now.... sounds like you've got what it takes to "crunch" them...

> 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...

Wait, didn't you also come up with the *41 theory? That one was really gorgeous (even though I could barely understand it :))

> 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...

Hmmm, that's cool, starting to get way over my head there though... :)

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

I know! I still can't belive the lack of flame wars. Really amazing.

> 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

Have you ever been to to the Marathon Story page? There's lots of fun numbers to play with there... it's a little overwhelming at first, but you'll get the hang of it soon enough. marathon.bungie.org/story

Cheers,