[ba-poker] Stupid chip tricks, part deux

[JonesLeeH(deleted the rest)]

About 6-8 years ago (IIRC) I posted to r.g.p. a stupid chip fiddling question:

"If I slide one poker chip over the top of another, at what percentage of the 
way across the first chip will the top chip cover exactly half the area of the 
bottom chip?"

This provoked a serious math.debate on the best way to solve such a problem.  
Heh.

Try this one:

You have two stacks of N chips each, each stack is all the same color chip, but 
the two stacks have different color chips [1].  For the moment, let's assume 
that your chips are purple and yellow [2].

First mingle the two stacks into a single stack with alternating colors 
(yellow,purple,yellow,purple...). 

The game is to re-arrange the single stack such that all the purple chips are 
continguous and the all the yellow chips are contiguous, as if you had simply 
set the stack of purple on top of the stack of yellow.

But wait!  There is only one operation you may use to do it: remove a single 
contiguous K-chip slug from *any* place within the stack, and move it to 
*either* end of the stack.  You may do this operation as many times as you wish.

I know that for N=7 and K=3, the problem is not only solvable, but can be done 
very quickly.  The funny part is that I did it once in just a handful of moves 
(4-5?) and was never able to repeat it.  It always took me quite a few more 
after that.

So,

1. Are there a non-degenerate and reasonable values for N and K such that the 
problem is not solvable?

2. What is the optimal way for solving this?

3. Given the optimal way of solving it, that should lead to a general form of a 
solution.

Yours for more enjoyable ways to waste your time,
Lee  

[1] This game is more fun when played with $500 and $1K chips from the Bellagio.

[2] See [1].