Pickett

I may have a small error in my code, I need to double check the results above...

Umm...what? I mean, if there is a repeatable pattern that you follow in order to solve a problem, which in the case of the OP there is, then you can write a computer program to solve it (that's what programs are...repeatable steps) From my understanding of the OP (and forgive me, because I may have missed something in the intermediate posts), the way this sort works is basically you grab a DVD, you KNOW what position it should be in, and you insert it there. So for example: Define this as a single "move": Look at a DVD...does it belong at the beginning of the list of DVDs? If not, take it out...shift all of the DVDs between its old position and its new position over and insert it at its correct spot. Now the OP also says they don't care about ascending or descending order...whichever takes fewer of the above moves (but WORST case...in other words, take the WORST POSSIBLE permutation of the DVDs using the above sort, and figure out the fewest number of "moves" it would take to sort them either ascending or descending...that is the REQUIRED number of moves to ENSURE you have sorted them.)

If any of you would like to play around with the little app I created for this (hats off to Anza Power for giving me the idea to use HTML5 for visualizing this), here it is: TestCanvasDraw.html Viewing the source (if you're at all a developer) should show you how to create your own shapes and try it out.

Alright, I'm done now...this was just fun to do!

I figured this would be solved while I was away over the weekend

Unfortunately I am probably done working on this until Monday (by which time I imagine it will be solved)...This has been really fun so far, though! Good luck, all!

This is a fantastic puzzle...