Something very exciting happened recently. Our building and settling has been going well, but I just had to talk about this new event.

One of the hunters went to scout out the formation of rocks we had seen. Then he sent us a message saying that he had found a magical stone artifact. It takes the form of a series of stone rings. The outermost is fixed but the inner and middle can be rotated. Inscribed upon the rings are symbols, numbers in fact. The hunter said they had originally been symbols in a foreign alphabet but they changed into the numbers used by the [System].

Jedditor worked up a way to manipulate the rings through the [System]. (I think he was itching for something to do.) We haven't figured out what the rings mean, so we'd like you to help out. Query the [System] for more information. We suspect there is one configuration that is correct, but we need to know why.

The rings

- by The Mirror at Tue, 30 Oct 07 22:07:15 -0400

The numbers are the Fibonacci sequence, but on a base 8 numeric scale number scale
Perhaps the device will be correctly calibrated once you complete and align the Fib sequence for the smallest circle.
(1 1 2 3 5 0 5 5 2 7 1 0 )

The rings

- by Alvyurin Ekkatran at Tue, 30 Oct 07 23:47:48 -0400

Jedditor apparently doesn't believe in documentation, so I put some in. Now if you'll excuse me I'll have to read up on this Fibonacci person you mentioned.

possible solution!

- by thebruce at Wed, 31 Oct 07 02:45:30 -0400

I think I might know the solution - I have submitted it already, just in case.

The outer ring is fibonacci sequence in base 8, as The Mirror revealed above... the 2nd ring is intriguing - if you line up the zeros, you get two possible outcomes:
011235055271 (outer ring)
033617077653 (middle ring with the double 3 below the double 1)
077653033617 (middle ring with the double 7 below the double 1)

First, the obvious parallel is that the inner ring only shows us a 3 and a 7.
Second, both positions of the middle ring are, as with the outer ring, the final digit of the fibonacci sequence in base 8 multiplied by either 3 or 7.

Let me clarify... the fibonacci sequence of the outer ring is:
0,1,1,2,3,5,8,13,21,34,55,89
in octal, that's:
0,1,1,2,3,5,10,15,25,42,67,131
which gives us the final digits of the outer ring:
0,1,1,2,3,5,0,5,5,2,7,1

If we multiply the outer ring by 3 we have
0,3,3,6,9,15,24,39,63,102,165,267
Or in octal:
0,3,3,6,11,17,30,47,77,146,245,413
Giving us the final digits:
0,3,3,6,1,7,0,7,7,6,5,3 - the very sequence found on the middle ring

However, if we multiply the outer ring by 7, we get
0,7,7,14,21,35,56,91,147,238,385,623
Or in octal:
0,7,7,16,25,43,70,133,223,356,601,1157
Giving us the final digits:
0,7,7,6,5,3,0,3,3,6,1,7 - the very same sequence found on the middle ring, but starting with the other 0!

It's quite a spooky mathematical wonder!
But the final step - not only are these the results of the fibonacci multiplied by 3 and by 7, but the inner ring only matches the alignment of the fibonacci*3 sequence, which means I believe the answer was to align the rings as so:
011235055271 (outer ring)
077653033617 (middle ring with the 0's aligned with the 7's first)
-3------7--- (inner ring so the 3 and 7 match the *3 sequence below)
033617077653

I submitted the *3 sequence, with the explanation of the ring numbers and alignment. I hope that was right! That's quite an intriguing mathematical wonder with the fibonacci sequence... He certainly discovered an amazing natural occurance

TheBruce

- by The Mirror at Wed, 31 Oct 07 10:52:06 -0400

TheBruce, you're wicked smart!

Numbers

- by Alvyurin Ekkatran at Wed, 31 Oct 07 15:13:30 -0400

[Wow], that was a lot to wrap my head around...but good job!

Correct me if I'm wrong, but if you multiply each number in a Fibonacci sequence by a constant, you get another Fibonacci sequence? And also if you divide, but then division is multiplication as well. So each one of those in the rings is a Fibonacci sequence. And they loop because there are only a finite number of combinations of number pairs in base eight. Right?

This is all fascinating, but Jedditor keeps ranting that we're on the wrong track and the ultimate answer has to do with base ten. He's also upset today that someone was messing with the mail program. But if you ever want to talk about numbers like this, just let me know.