Rotating the Fifteen Puzzle

Extract

The Fifteen puzzle is well known. In its original form it consists of a shallow square box that can just hold sixteen small squares. Squares, numbered 1 to 15, are placed in any order in the box, leaving the sixteenth position empty (e.g. Fig. 1). The problem is to slide the squares, without lifting them out, until the numbers are in their natural order (Fig. 2).