164 lines
7.2 KiB
Markdown
164 lines
7.2 KiB
Markdown
# The Patience puzzle
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The Patience puzzle, probably of Chinese origin, consists of
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an iron U-shaped piece and several rings that link around
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it. The physical shape of the puzzle is very difficult to
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describe verbally, but here is an attempt.
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This description of the puzzle is presented as a set of
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instructions for constructing the puzzle. Start with a flat
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piece of iron about 15 centimeters long by about two
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centimeters wide. Drill six holes in the piece of iron.
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Through each hole, place a rod. The rod should have a
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diameter slightly less than that of the hole so that it can
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move freely. One end of the rod is like the head of a nail
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and is larger than the hole to prevent it from coming free.
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The other end is looped around a metal ring with a diameter
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of about five centimeters. This completely prevents the
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iron rod from separating from the base. Each rod, in
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addition to going through the iron base, goes through the
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ring at the end of the rod to its right. The only rod free
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of this restriction is the rightmost rod. What has been
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described so far is one of the two components of the puzzle.
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The other component is another iron rod shaped like a `U`.
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The `U` is as long from the tips to the base as the original
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piece of iron with the holes in it. The ends of the `U` are
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looped around another ring of about five centimeters in
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diameter. In the puzzle's initial configuration, the `U` is
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placed through the rings so that it is held in place by the
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iron rods. Imagine starting with the `U` piece before the
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iron loop is placed at the end. Slide the legs of the `U`
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through the loops so that the iron rods securing the loops
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to the metal strip go up the center of the `U`. Placing the
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final ring at the ends of the `U` prevents it from coming out.
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The object of the puzzle is to free the `U`-shaped piece from
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the other piece.
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The following illustration (sideways) shows a three-ring
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case of this puzzle. If you look carefully, you can see
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that the first ring could be lifted over the edge of the `U`
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and slid down through the center of the `U`, thereby freeing
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the `U` from the first iron rod. The second ring can also be
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freed in the initial configuration since it is already over
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the rod for the first ring. The third ring cannot be moved,
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however, since it is blocked by the iron rod to which the
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first ring is attached. If the first first is removed, then
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the third ring is no longer blocked by the first ring's iron
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rod and can be removed freely. The second ring, however
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cannot be moved if the first ring is gone because it will
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then be blocked by the first ring in its new position
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outside of the `U`.
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Here is an illustration of the three-ring case. The bottom
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of the puzzle is on the left-hand side of the page.
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```
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//==\\
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*****||** ||
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*** || ***||
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** || *||
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|\ ** || ||**
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| \ *** || || ***
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| \ *** | || ===
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| \ *** || // * \\
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| \ *** || || ** ||
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| | | ********** ||
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| | *****||** || \\ ||
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| | |\ | *** || ***|| ||
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|==| |=========-**-===-||-============//
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|==| |=========-**-===-||-===========//
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| | \| | *** || || ***
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| | *** || || ===
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| | ***| || // * \\
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| | *** || || ** ||
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| | ||********** ||
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| | *****||** || \\ ||
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| | |\ | *** || ***|| ||
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|==| |=========-**-===-||-============//
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|==| |=========-**-===-||-===========//
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| | \| | *** || || ***
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| | *** || || ===
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| | ***| || // * \\
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| | *** || || ** ||
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| | ||********** ||
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| | | || || \\ ||
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|==| |================-||-============//
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|==| |================-||-===========//
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\ | \\||
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\| \||
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```
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This puzzle takes other forms as well. One such puzzle is
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called "Spin-Out". This puzzle consists of one plastic
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piece that encases another piece that can slide in and out
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of it. The movement of the smaller piece is restricted by
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discs that, when turned to one angle, lock the smaller piece
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inside the larger one and, when turned the other way, allow
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it to move. This puzzle is as difficult to describe as the
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first and, since I don't have one in front of me, I will not
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attempt to describe it. The object of this puzzle is to
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free the smaller piece from the larger one. The other
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puzzle that is like this one consists of a cylinder with
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rods protruding from the top. The rods can be slid from the
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center to the edge of the cylinder constrained by a series
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of discs in the center. The discs have cuts in them that
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allow some rods to move and force others in one place based
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on the relative rotations of the discs. The object here is
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to move all the rods from the inside to the outside.
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What makes these puzzles similar is that the physical shapes
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of the puzzles put the same restrictions on the movement of
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the pieces. Specifically, there is always one piece that is
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free to move. The only other piece that is free to move is
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the second one that is still attached to the base it is
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trying to be freed from. In the case of the original
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puzzle, consider the rings numbered from 1 to 6 with ring 1
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being the one at the closed end of the `U`. Ring 1 can
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always be removed from or added to the `U`. In the initial
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state, when all rings are around the `U`, ring 2 is the other
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one that can be moved because it is second. If ring 1 is
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removed, then only two operations are possible: the
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restoration of ring 1 and the removal of ring 3. This is
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because ring 1 is always movable, and ring 3 is currently
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the second ring still attached to the `U`. This constraint
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leads to a recursive solution to the puzzle. Like the
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[Towers of Hanoi](hanoi.html), the number of steps to solve this puzzle is
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exponential in the number of rings.
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<hr style="width:10%;text-align:left;margin-left:0">
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Jump to: [top](#)
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