2,1,4,3,2,3,4,?

3,2,1,2,3,4,3,?

0,3,2,3,2,3,4,?

First Series: consider the second 2; there is a plausible mirror around it that would extend the series (by reflection) as 3,4,1,2
Second Series: consider the 4 as the mirror.  The series then goes,   2,1,3.
Third Series: On prior assumptions, 4 again needs to be the 'point of reflection', and so we have, 3, 2,3,2,3,0.

However, I also seem to see mod 5 possibility, only because the digits range from 0 to 4.  Of course, that does not mean that the sequences may not embrace larger digits.

Now ... I do notice, considering the 3 sequences as being part of an "n *  3" array, there is an inversion (swapping) of digit places in cols 6 and 7; the same is apparent in cols 4 and 5. 

Working on a mirror principle I cannot relate those thoughts to the first 3 cols.

For the sake of some frivolity, I could simply mirror the first 6 cols against the 7th ..  [by those rules it just has to work]

But then, I am now tempted to take the first 6 'cells' of row 1 and swap them with their counterparts in row 3 and invert (as by a mirror around col7) cols 1 to 6:

2,1,4,3,2,3,4,3,2,3,2,3,0
3,2,1,2,3,4,3,4,3,2,1,2,3
0,3,2,3,2,3,4,3,2,3,4,1,2      

You could consider this as "flip the rows and mirror those columns".

Hey! Fun to play with, but, other than dismissing mod 5, I'm sure Tristan has something else in mind.

Posted by brianjn on 2005-08-20 04:07:41