Format/typo check 1993/ejb
This includes updates to the patience.md file. The hanoi.md did not require any changes.
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@@ -21,38 +21,39 @@ 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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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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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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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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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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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 two which the
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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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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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@@ -105,7 +106,8 @@ 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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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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@@ -131,14 +133,14 @@ 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 send 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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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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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.md), the number of steps to solve this puzzle is
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exponential in the number of rings.
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