The 15-puzzleis a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. Starting from the initial position of pic.1 we apply a finite number of planar reordering in such way that the bottom right square is not filled.
Every such reordering is a permutation of {1,2,…,15} , which is an element of 
The reordering is done by the means of the altering permutations 
Which are all the possible re orderings ? The answer is that G is equal to the group of even permutations. So
zeracuse 