Solution to: Fourteen Fifteen
It is impossible to solve this puzzle. All possible positions of the 15 tiles and the empty space can be divided into two distinct groups. Each position in one of these groups is reachable from any other position in the same group, but not from any position in the other group. The required solution (all tiles in the correct order with the empty space again in the lower right corner) and the given begin position are not in the same group.
It is, however, possible to get all tiles in the correct order with the empty space in the upper left corner (see the second question at the puzzle)!