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Text Box: Sequential Move Puzzles are Highly Organized
Sequential move puzzles have a wonderful mathematical quality about them.  For instance solving them can be a very straightforward and interesting diversion, teaching us about the powerful organizing principles going on in these puzzles.  
As a typical illustration, you can not easily write down ageneral method of attack for take apart, put together type puzzles.  These kinds of puzzles can have hidden latches, magnetic catches, and many other intricacies.  Thus no general method that guarantees a solution is possible.  Described here is a very general, very simple method that works for most of the common sequential move type puzzles.

Text Box: Solving Sequential Move Puzzles(some general observations)
By repeating a simple set of moves over and over you can always be sure that the pieces of most any sequential move puzzle will return to their starting positions, or the positions they occupied when you started the series of repeated moves.  In general, pieces that can occupy the same positions, by sequential moves, follow each other around in a cycle with a given, or set number, of the repeated moves.  This is sometimes called an orbit.  So if there are three kinds of pieces they will each have their own orbit lengths say a, b and c.  Knowing this you can be assured that the three sets of pieces will all come back home in a times b times c of the repeated moves.  Thus by doing just a times b moves you will bring a and b back home and can observe where the c pieces are.  This is a very simple way to just change the positions of only the c pieces.
Text Box: Similarly you do a times c moves and observe where the b pieces end up, or do b times a moves and observe where the c pieces end up.  In this way you can quickly develop some formulas for just making certain pieces exchange positions, while leaving other pieces unchanged in their positions.  Of course this simple method may require long series of moves, but it has the advantage of easy to remember, or repeated kinds of moves.  If you are not trying to win a speed contest it is a good way to study and begin to learn the intricacies of the these kinds of puzzles.
A Simple Strategy
For instance, a very effective cycle with two-circle type puzzles (this will work for cube or three dimension type puzzles, too) is an alternating, or zig zag, repeated set of moves.  Turn the right circle clockwise x degrees, the left circle counterclockwise x degrees, then reverse these two moves.  Repeat these four moves as often as necessary and count how many moves needed to bring all the pieces back home.  Now you can try to determine the orbit lengths of each type of piece.  Then  record where the pieces of one orbit cycle end up when all the other orbits are complete.  After developing one set of orbits you can develop a few others by choosing a different set of repeated moves.  Within probably less then an hour you should have developed formulas for completely solving the puzzle.  Have fun!