[gDesklets] 15 pieces puzzle: finding solvable puzzles

[Bjoern Koch <H Humpel gmx de>]

Hi everybody,

just bringing the general discussion about this problem from launchpad
(bug #515236) to the mailing list.

Not sure, but it seems not to be that simple :/.

OK, first let's take a look at the solved puzzle.
Obviously the number of inversions is zero (even).

Taking a look at the puzzle in figure 1 in the paper (see the pdf on
lauchpad by dszimmermann:
http://launchpadlibrarian.net/38683358/15%20Piece%20Analysis.pdf) it is
one: 15,14 (odd).

So far, so good.

But if we take a look at the (mirrored) puzzle in figure 3 in the paper
the inversions are:

4,3   4,2   4,1   3,2   3,1   2,1
8,7   8,6   8,5   7,6   7,5   6,5
12,11 12,10 12,9  11,10 11,9  10,9
15,14 15,13 14,13

OR (if we have to bring in the 16th piece)

16,15 16,14 16,13 15,14 15,13 14,13

So, either we won't have to consider the 16th piece (as it doesn't
matter as it can be moved horizontally without changing the inversions)
and everything is (or at least seems so far) alright

OR

it is not working. Either because the algorithm is not suitable or the
inversed (mirrored) puzzle can actually be solved ?!

Just a few first thoughts about it.

Greetings, Bjoern