The Patience puzzle, probably of Chinese origin, consists of    an iron U-shaped piece and several rings that link around    it.  The physical shape of the puzzle is very difficult to    describe verbally, but here is an attempt.    This description of the puzzle is presented as a set of    instructions for constructing the puzzle.  Start with a flat    piece of iron about 15 centimeters long by about two    centimeters wide.  Drill six holes in the piece of iron.    Through each hole, place a rod.  The rod should have a    diameter slightly less than that of the hole so that it can    move freely.  One end of the rod is like the head of a nail    and is larger than the hole to prevent it from coming free.    The other end is looped around a metal ring with a diameter    of about five centimeters.  This completely prevents the    iron rod from separating from the base.  Each rod, in    addition to going through the iron base, goes through the    ring at the end of the rod to its right.  The only rod free    of this restriction is the rightmost rod.  What has been    described so far is one of the two components of the puzzle.    The other component is another iron rod shaped like a U.    the U is as long from the tips to the base as the original    piece of iron with the holes in it.  The ends of the U are    looped around another ring of about five centimeters in    diameter.  In the puzzle's initial configuration, the U is    placed through the rings so that it is held in place by the    iron rods.  Imagine starting with the U piece before the    iron loop is placed at the end.  Slide the legs of the U    through the loops so that the iron rods securing the loops    to the metal strip go up the center of the U.  Placing the    final ring at the ends of the U prevents it from coming out.    The object of the puzzle is to free the U-shaped piece from    the other piece.    The following illustration (sideways) shows a three-ring    case of this puzzle.  If you look carefully, you can see    that the first ring could be lifted over the edge of the U    and slid down through the center of the U, thereby freeing    the U from the first iron rod.  The second ring can also be    freed in the initial configuration since it is already over    the rod for the first ring.  The third ring cannot be moved,    however, since it is blocked by the iron rod two which the    first ring is attached.  If the first first is removed, then    the third ring is no longer blocked by the first ring's iron    rod and can be removed freely.  The second ring, however    cannot be moved if the first ring is gone because it will    then be blocked by the first ring in its new position    outside of the U.    Here is an illustration of the three-ring case.  The bottom    of the puzzle is on the left-hand side of the page.                               //==\\                              ||    ||                              ||    ||                         *****||**  ||                       ***    || ***||                       **     ||   *||          |\           **     ||    ||**          | \           ***   ||    ||  ***          |  \            ***  |    ||    ===          |   \             ***     ||  // * \\          |    \              ***   || || **  ||          |     |             | **********    ||          |     |             ||    || ||     ||          |     |             ||    || ||     ||          |     |        *****||**  ||  \\    ||       |  | |\  |      ***    || ***||        ||       |==| |=========-**-===-||-============//       |==| |=========-**-===-||-===========//       |  |  \| |       ***   ||    ||  ***          |     |         *** ||    ||    ===          |     |           ***|    ||  // * \\          |     |             ***   || || **  ||          |     |             ||**********    ||          |     |             ||    || ||     ||          |     |        *****||**  ||  \\    ||       |  | |\  |      ***    || ***||        ||       |==| |=========-**-===-||-============//       |==| |=========-**-===-||-===========//       |  |  \| |       ***   ||    ||  ***          |     |         *** ||    ||    ===          |     |           ***|    ||  // * \\          |     |             ***   || || **  ||          |     |             ||**********    ||          |     |             ||    || ||     ||          |     |             ||    || ||     ||       |  |     |             ||    ||  \\    ||       |  | |\  |             ||    ||        ||       |==| |================-||-============//       |==| |================-||-===========//       |  |  \| |             ||    ||          |     |             ||    ||          |     |             ||    ||          |     |             ||    ||          \     |             ||    ||           \    |              \\   ||            \   |               \\  ||             \  |                \\ ||              \ |                 \\||               \|                  \||    This puzzle takes other forms as well.  One such puzzle is    called "Spin-Out".  This puzzle consists of one plastic    piece that encases another piece that can slide in and out    of it.  The movement of the smaller piece is restricted by    discs that, when turned to one angle, lock the smaller piece    inside the larger one and, when turned the other way, allow    it to move.  This puzzle is as difficult to describe as the    first and, since I don't have one in front of me, I will not    attempt to describe it.  The object of this puzzle is to    free the smaller piece from the larger one.  The other    puzzle that is like this one consists of a cylinder with    rods protruding from the top.  The rods can be slid from the    center to the edge of the cylinder constrained by a series    of discs in the center.  The discs have cuts in them that    allow some rods to move and force others in one place based    on the relative rotations of the discs.  The object here is    to move all the rods from the inside to the outside.    What makes these puzzles similar is that the physical shapes    of the puzzles put the same restrictions on the movement of    the pieces.  Specifically, there is always one piece that is    free to move.  The only other piece that is free to move is    the second one that is still attached to the base it is    trying to be freed from.  In the case of the original    puzzle, consider the rings numbered from 1 to 6 with ring 1    being the one at the closed send of the U.  Ring 1 can    always be removed from or added to the U.  In the initial    state, when all rings are around the U, ring 2 is the other    one that can be moved because it is second.  If ring 1 is    removed, then only two operations are possible: the    restoration of ring 1 and the removal of ring 3.  This is    because ring 1 is always movable, and ring 3 is currently    the second ring still attached to the U.  This constraint    leads to a recursive solution to the puzzle.  Like the    Towers of Hanoi, the number of steps to solve this puzzle is    exponential in the number of rings.