In article <425973C0.2080007 / mktec.com>,
Zach Dennis  <zdennis / mktec.com> wrote:
>I have the following table of data, and I am looking to create an 
>equation to recreate the table. If anyone finds this sort of thing fun, 
>or has a online resource or a good book that helps explaining these 
>types of math concepts, please take a stab at it or post any info that 
>might aide me in my discovery! I've been trying the past several hours 
>and this sort of thing isn't my strong suit...and i'm stuck!
>
>I am first looking to understand how-to make the pattern of data into a 
>actual math equation...then from there I'd like to write ruby code for 
>the equation.
>
>Here is the sample data in a table:
>	- rows represent a different character (as labeled)
>	- columns represent the position of the character
>	  (examples represent data in decimal notation, not octal/hex)
>		example: "aaaa" would become 000 003 002 005
>		example: "zach" would become 027 003 000 012
>
>	1	2	3	4	5	6    (etc......)
>----------------------------------------------------
>a 1   |0	3	2	5	4	7
>b 2   |3	0	1	6	7	4
>c 3   |2	1	0	7	6	5
>d 4   |5	6	7	0	1	2
>e 5   |4	7	6	1	0	3
>f 6   |7	4	5	2	3	0
>g 7   |6	5	4	3	2	1
>h 8   |9	10	11	12	13	14
>i 9   |8	11	10	13	12	15
>j 10  |11	8	9	14	15	12
>k 11  |10	9	8	15	14	13
>l 12  |13	14	15	8	9	10
>m 13  |12	15	14	9	8	11
>n 14  |15	12	13	10	11	8
>o 15  |14	13	12	11	10	9
>p 16  |17	18	19	20	21	22
>q 17  |16	19	18	21	20	23
>r 18  |19	16	17	22	23	20
>s 19  |18	17	16	23	22	21
>t 20  |21	22	23	16	17	18
>u 21  |20	23	22	17	16	19
>v 22  |23	20	21	18	19	16
>w 23  |22	21	20	19	18	17
>x 24  |25	26	27	28	29	30
>y 25  |24	27	26	29	28	31
>z 26  |27	24	25	30	31	28

I think the table got a bit shifted so I shifted it back...

What's the application for this or is it just a brain teaser?

Just a few ideas:

For character 'a' it looks like the 'formula' would be something like:
  if(position.odd?)
    return position - 1
  else
    return position + 1
  end    

(BTW: it also looks like the numbers in column 1 follow this same 
pattern)

For character 'b' it's a bit stranger, recreating that row of the table:

>       1       2       3       4       5       6     (7)     (8)
>----------------------------------------------------
>b 2   |3       0       1       6       7       4      5       10
       (1+2)    (2-2)   (3-2)   (4+2)   (5+2)   (6-2)  (7-2)   (8+2)
  

I'm guessing the 7 and 8 columns will follow the same pattern.  

Also, I'd look into the idea that maybe these are modulo-n counters (?)
However, if I look at the row numbers I can see that they directly map 
onto columns as well, look at row 'c' and column 3:

       1       2       3       4       5       6    (etc......)
----------------------------------------------------
                       2
                       1
c 3   |2       1       0       7       6       5
                       7
                       6
                       5

                       


Phil