• #### Sliding puzzles - Algorithm?

From Busha Dinsa@21:1/5 to Willem-Jan Monsuwe on Wed Mar 17 08:15:20 2021
On Monday, May 8, 2000 at 10:00:00 AM UTC+3, Willem-Jan Monsuwe wrote:
)Thanks for the suggestion. But there is a little problem in trying to reduce )the size in this way. It may happen the the reduced puzzle has a wrong )parity and hence may be unsovable without disturbing the already solved row )or column. This happens to me by trying to reduce 4x4 puzle to 3x3. Although )I think that among several ways to arrange the first column or row in the )correct sequence there is always one for which the reduced puzzle has the )correct parity it is not always clear how to find it in a systematic way. HUH?
Is there something I'm missing ? You can only change the parity of the remaining bit by changing the parity of the already solved bit. Which you
can only do by exchanging two tiles in the solved bit. Which kind of makes 'solved' a misnomer.
In other words: if subpuzzle-plus-solved-bit has even parity, then the subpuzzle will have even parity, because the solved bit has parity zero.
The only situation I can imagine where this happens is if there is more than one solution, I.E. tiles are interchangeable.
SaSW,
--
Willem (at stack dot nl)
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT