The purpose of the game, as with the Lucky 7 puzzle, is to return the counters into their Home position , position they were in before reshuffling. The puzzle consists of several counters placed on two intersecting circles. Clicking on the upper counters induces clockwise rotations. Clicking on the lower counters results in counterclockwise rotations. Left counters rotate the left circle.
Right counters rotate the right circle.
The middle ones handle the whole set. The permutation is presented as a product of cycles . In the general framework of Graph Theory , R.Wilson gave a complete treatment of puzzles on graphs of which the Lucky 7 is a particular case. His results do not directly apply to the Happy 8 puzzles. If n is odd then every even permutation can be obtained using r and l cycles.