Hi Folks,
A friend recently told me the proper name of the old 'slider' game : TAQUIN.
So I was able to do research into its history, and especially the logic as described by mathematicians.
It transpires that using random tiles, only half the games can be resolved ! This would be difficult to establish by trial and error....
The solution would be to not use configurations where the number of moves to completion would be an odd number, but to establish this,one would have to know how many moves were required, and NO algorithm to do that is possible, as the problem is 'NP-Hard', (to use a maths expression).
Sorry about that, as it must be annoying not to be able to complete the game on 'odd' occasions... Aaiiee - Mea Culpa !
Steve.