force use of pandoc version >= 3.1.12.2
The `bin/pandoc-wrapper.sh` tool will verify that the ssytem has a recent enough version of `pandoc(1)`. We explain why we insist on `pandoc(1)`. version >= 3.1.12.2 in comments where the $PANDOC_MIN_VERSION is set. Added `--wrap=preserve` as a default argument to `pandoc(1)`. While this change will impact every HTML file generated, we believe this will improve the ability of someone to look at the generated HTML and correlate with the original markdown. Changed `bin/pandoc-wrapper.sh` VERSION from "1.4.2 2024-03-17" to "1.4.3 2024-03-18". Performed `make www` to achieve all of the above and to generate HTML using the new `--wrap=preserve` `pandoc(1)` mode.
This commit is contained in:
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+9
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@@ -121,14 +121,15 @@
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<!-- START: this line starts content for HTML phase 21 by: bin/pandoc-wrapper.sh via bin/md2html.sh -->
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|
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<h1 id="the-towers-of-hanoi-puzzle">The Towers of Hanoi puzzle</h1>
|
||||
<p>The Towers of Hanoi is a puzzle consisting of three posts and several
|
||||
rings of various sizes. The initial configuration of the game is that
|
||||
all the rings are stacked in decreasing order of size on one post. The
|
||||
object of the game is to move all the rings from one post to another
|
||||
subject to two rules: only one ring can be moved at a time, and at no
|
||||
time can one ring be placed on top of a smaller ring. The number of
|
||||
steps necessary to solve this puzzle is exponential in the number
|
||||
rings.</p>
|
||||
<p>The Towers of Hanoi is a puzzle consisting of three posts
|
||||
and several rings of various sizes. The initial
|
||||
configuration of the game is that all the rings are stacked
|
||||
in decreasing order of size on one post. The object of the
|
||||
game is to move all the rings from one post to another
|
||||
subject to two rules: only one ring can be moved at a time,
|
||||
and at no time can one ring be placed on top of a smaller
|
||||
ring. The number of steps necessary to solve this puzzle is
|
||||
exponential in the number rings.</p>
|
||||
|
||||
<!-- END: this line ends content for HTML phase 21 by: bin/pandoc-wrapper.sh via bin/md2html.sh -->
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<!-- START: this line starts content from: inc/after-content.default.html -->
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+56
-88
@@ -129,9 +129,9 @@
|
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|
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<h2 id="author"><a name="author"></a>Author:</h2>
|
||||
<ul>
|
||||
<li>Name: <a href="../../authors.html#E_Jay_Berkenbilt">E. Jay
|
||||
Berkenbilt</a><br> Location: <a href="../../location.html#ZZ">ZZ</a> -
|
||||
<em>Unknown location</em> <br><br></li>
|
||||
<li>Name: <a href="../../authors.html#E_Jay_Berkenbilt">E. Jay Berkenbilt</a><br>
|
||||
Location: <a href="../../location.html#ZZ">ZZ</a> - <em>Unknown location</em>
|
||||
<br><br></li>
|
||||
</ul>
|
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|
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<!-- END: next line ends content generated by: bin/output-index-author.sh -->
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@@ -148,116 +148,84 @@ Berkenbilt</a><br> Location: <a href="../../location.html#ZZ">ZZ</a> -
|
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<h2 id="try">Try:</h2>
|
||||
<div class="sourceCode" id="cb4"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./try.sh</span></span></code></pre></div>
|
||||
<h2 id="judges-remarks">Judges’ remarks:</h2>
|
||||
<p>A negative argument plays the patience puzzle. An argument greater
|
||||
than 0 plays the Tower of Hanoi puzzle. In either case the absolute
|
||||
value of the argument specifies the size of the respective puzzle. Refer
|
||||
to the web pages <a href="hanoi.html">hanoi.html</a> and <a
|
||||
href="patience.html">patience.html</a> for more information on these
|
||||
puzzles.</p>
|
||||
<p>Of course, you need a different kind of “patience” if you give the
|
||||
argument 127 to this program and want to see it finish!</p>
|
||||
<p>A negative argument plays the patience puzzle. An argument
|
||||
greater than 0 plays the Tower of Hanoi puzzle. In either case
|
||||
the absolute value of the argument specifies the size of the
|
||||
respective puzzle. Refer to the web pages <a href="hanoi.html">hanoi.html</a> and
|
||||
<a href="patience.html">patience.html</a> for more information on these puzzles.</p>
|
||||
<p>Of course, you need a different kind of “patience” if you give
|
||||
the argument 127 to this program and want to see it finish!</p>
|
||||
<p>We note that this also works under macOS just fine.</p>
|
||||
<h2 id="authors-remarks">Author’s remarks:</h2>
|
||||
<h3 id="what-this-program-does">What this program does</h3>
|
||||
<h4 id="output-solution-to-towers-of-hanoi-for-five-rings">Output
|
||||
solution to Towers of Hanoi for five rings:</h4>
|
||||
<h4 id="output-solution-to-towers-of-hanoi-for-five-rings">Output solution to Towers of Hanoi for five rings:</h4>
|
||||
<div class="sourceCode" id="cb5"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./ejb</span> 5</span></code></pre></div>
|
||||
<p>The format of the output for the Towers of Hanoi case is simply a
|
||||
text description of how to solve the puzzle.</p>
|
||||
<h4 id="output-solution-to-the-patience-puzzle-for-six-rings">Output
|
||||
solution to the Patience puzzle for six rings:</h4>
|
||||
<h4 id="output-solution-to-the-patience-puzzle-for-six-rings">Output solution to the Patience puzzle for six rings:</h4>
|
||||
<div class="sourceCode" id="cb6"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./ejb</span> <span class="at">-6</span></span></code></pre></div>
|
||||
<p>For the patience puzzle, the output is a sequence binary codes
|
||||
representing successive states of the puzzle. The rightmost digit
|
||||
represents the first ring. A <code>1</code> means the ring is on the
|
||||
<code>U</code>; a <code>0</code> means it is off the <code>U</code>. The
|
||||
program prints the word <code>"Invalid"</code> in response to illegal
|
||||
command line parameters.</p>
|
||||
<p>For the patience puzzle, the output is a sequence binary codes representing
|
||||
successive states of the puzzle. The rightmost digit represents the first ring.
|
||||
A <code>1</code> means the ring is on the <code>U</code>; a <code>0</code> means it is off the <code>U</code>. The program
|
||||
prints the word <code>"Invalid"</code> in response to illegal command line parameters.</p>
|
||||
<h3 id="motivation">Motivation</h3>
|
||||
<p>Most people who have written software for other people have been
|
||||
asked to count lines of code. Naturally, this brings up the
|
||||
controversial question of exactly what defines a line of code. This
|
||||
program serves to show that counting semicolons will not always provide
|
||||
a meaningful measure of code size. This is especially true in this
|
||||
program where the number of semicolons itself is ambiguous. Does it have
|
||||
two or three? In addition, the only C keyword this program uses besides
|
||||
type names and qualifiers is <code>return</code>, and the only function
|
||||
defined in the code is <code>main()</code>. The level of complexity of
|
||||
the program without multiple semicolons, statements, and functions is
|
||||
achieved by abusing C operators, especially the comma operator.
|
||||
Considerable use of <code>||</code>, <code>&&</code>, and
|
||||
<code>?:</code> helps too. In addition, <code>main()</code> is called
|
||||
recursively. The NULL pointer that terminates <code>argv</code> is used
|
||||
to pass additional information into <code>main()</code>. Even though the
|
||||
algorithms used by this code are simple, this program is still hard to
|
||||
follow even when indented properly. (It is pretty hard to indent this
|
||||
code reasonably, however.)</p>
|
||||
<p>Although this program has only been tested on UNIX systems it will
|
||||
probably run on just about any machine with an ANSI C compiler. It does
|
||||
not use the C preprocessor at all. The only functions it uses are
|
||||
<code>atoi()</code>, <code>malloc()</code>, <code>memset()</code>,
|
||||
<code>printf()</code>, and <code>puts()</code>. It does, however,
|
||||
require that the architecture it runs on have bytes that are at least
|
||||
eight bits long and pointers that are at least four bytes long. In
|
||||
addition, it requires an ANSI compiler since it uses
|
||||
<code>signed char</code> and ANSI-style function declarations.</p>
|
||||
<h2 id="copyright-and-cc-by-sa-4.0-license">Copyright and CC BY-SA 4.0
|
||||
License:</h2>
|
||||
<p>This file is Copyright (c) 2023 by Landon Curt Noll. All Rights
|
||||
Reserved. You are free to share and adapt this file under the terms of
|
||||
this license:</p>
|
||||
controversial question of exactly what defines a line of code.
|
||||
This program serves to show that counting semicolons will not
|
||||
always provide a meaningful measure of code size. This is
|
||||
especially true in this program where the number of semicolons
|
||||
itself is ambiguous. Does it have two or three? In addition, the
|
||||
only C keyword this program uses besides type names and
|
||||
qualifiers is <code>return</code>, and the only function defined in the code
|
||||
is <code>main()</code>. The level of complexity of the program without multiple
|
||||
semicolons, statements, and functions is achieved by abusing C
|
||||
operators, especially the comma operator. Considerable use of <code>||</code>,
|
||||
<code>&&</code>, and <code>?:</code> helps too. In addition, <code>main()</code> is called recursively.
|
||||
The NULL pointer that terminates <code>argv</code> is used to pass additional
|
||||
information into <code>main()</code>. Even though the algorithms used by this
|
||||
code are simple, this program is still hard to follow even when
|
||||
indented properly. (It is pretty hard to indent this code
|
||||
reasonably, however.)</p>
|
||||
<p>Although this program has only been tested on UNIX systems it will probably run
|
||||
on just about any machine with an ANSI C compiler. It does not use the C
|
||||
preprocessor at all. The only functions it uses are <code>atoi()</code>, <code>malloc()</code>,
|
||||
<code>memset()</code>, <code>printf()</code>, and <code>puts()</code>. It does, however, require that the
|
||||
architecture it runs on have bytes that are at least eight bits long and
|
||||
pointers that are at least four bytes long. In addition, it requires an ANSI
|
||||
compiler since it uses <code>signed char</code> and ANSI-style function declarations.</p>
|
||||
<h2 id="copyright-and-cc-by-sa-4.0-license">Copyright and CC BY-SA 4.0 License:</h2>
|
||||
<p>This file is Copyright (c) 2023 by Landon Curt Noll. All Rights Reserved.
|
||||
You are free to share and adapt this file under the terms of this license:</p>
|
||||
<pre><code>Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)</code></pre>
|
||||
<p>For more information, see:
|
||||
https://creativecommons.org/licenses/by-sa/4.0/</p>
|
||||
<p>For more information, see: https://creativecommons.org/licenses/by-sa/4.0/</p>
|
||||
|
||||
<!-- END: this line ends content for HTML phase 21 by: bin/pandoc-wrapper.sh via bin/md2html.sh -->
|
||||
<!-- START: this line starts content for HTML phase 22 by: bin/output-index-inventory.sh via bin/md2html.sh -->
|
||||
|
||||
<!-- START: this line starts content generated by: bin/output-index-inventory.sh -->
|
||||
|
||||
<h1 id="inventory-for-1993ejb"><a name="inventory"></a>Inventory for
|
||||
1993/ejb</h1>
|
||||
<h1 id="inventory-for-1993ejb"><a name="inventory"></a>Inventory for 1993/ejb</h1>
|
||||
<p><a href="#top">Jump to top</a></p>
|
||||
<h2 id="primary-files">Primary files</h2>
|
||||
<ul>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/ejb.c">ejb.c</a>
|
||||
- entry source</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/Makefile">Makefile</a>
|
||||
- entry Makefile</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/ejb.orig.c">ejb.orig.c</a>
|
||||
- original source</li>
|
||||
<li><a href="hanoi.html">hanoi.html</a> - about the Towers of Hanoi
|
||||
puzzle</li>
|
||||
<li><a href="patience.html">patience.html</a> - about the Patience
|
||||
puzzle</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/try.sh">try.sh</a>
|
||||
- how to run</li>
|
||||
<li><a href="1993_ejb.tar.bz2">1993_ejb.tar.bz2</a> - download entry
|
||||
source</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/ejb.c">ejb.c</a> - entry source</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/Makefile">Makefile</a> - entry Makefile</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/ejb.orig.c">ejb.orig.c</a> - original source</li>
|
||||
<li><a href="hanoi.html">hanoi.html</a> - about the Towers of Hanoi puzzle</li>
|
||||
<li><a href="patience.html">patience.html</a> - about the Patience puzzle</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/try.sh">try.sh</a> - how to run</li>
|
||||
<li><a href="1993_ejb.tar.bz2">1993_ejb.tar.bz2</a> - download entry source</li>
|
||||
</ul>
|
||||
<h2 id="secondary-files">Secondary files</h2>
|
||||
<ul>
|
||||
<li><a href="index.html">index.html</a> - entry home page</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/.entry.json">.entry.json</a>
|
||||
- description of entry in JSON</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/.gitignore">.gitignore</a>
|
||||
- list of files that should not be committed under git</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/.entry.json">.entry.json</a> - description of entry in JSON</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/.gitignore">.gitignore</a> - list of files that should not be committed under git</li>
|
||||
<li><a href=".path">.path</a> - directory path from top directory</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/README.md">README.md</a>
|
||||
- markdown source for index.html</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/hanoi.md">hanoi.md</a>
|
||||
- markdown source for hanoi.html</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/patience.md">patience.md</a>
|
||||
- markdown source for patience.html</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/README.md">README.md</a> - markdown source for index.html</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/hanoi.md">hanoi.md</a> - markdown source for hanoi.html</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/1993/ejb/patience.md">patience.md</a> - markdown source for patience.html</li>
|
||||
</ul>
|
||||
|
||||
<!-- END: next line ends content generated by: bin/output-index-inventory.sh -->
|
||||
|
||||
+80
-71
@@ -121,49 +121,54 @@
|
||||
<!-- START: this line starts content for HTML phase 21 by: bin/pandoc-wrapper.sh via bin/md2html.sh -->
|
||||
|
||||
<h1 id="the-patience-puzzle">The Patience puzzle</h1>
|
||||
<p>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.</p>
|
||||
<p>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.</p>
|
||||
<p>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.</p>
|
||||
<p>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.</p>
|
||||
<p>The other component is another iron rod shaped like a <code>U</code>.
|
||||
The <code>U</code> is as long from the tips to the base as the original
|
||||
piece of iron with the holes in it. The ends of the <code>U</code> are
|
||||
looped around another ring of about five centimeters in diameter. In the
|
||||
puzzle’s initial configuration, the <code>U</code> is placed through the
|
||||
rings so that it is held in place by the iron rods. Imagine starting
|
||||
with the <code>U</code> piece before the iron loop is placed at the end.
|
||||
Slide the legs of the <code>U</code> through the loops so that the iron
|
||||
rods securing the loops to the metal strip go up the center of the
|
||||
<code>U</code>. Placing the final ring at the ends of the <code>U</code>
|
||||
prevents it from coming out. The object of the puzzle is to free the
|
||||
<code>U</code>-shaped piece from the other piece.</p>
|
||||
<p>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 <code>U</code> and slid down through the
|
||||
center of the <code>U</code>, thereby freeing the <code>U</code> 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
|
||||
to 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 <code>U</code>.</p>
|
||||
<p>Here is an illustration of the three-ring case. The bottom of the
|
||||
puzzle is on the left-hand side of the page.</p>
|
||||
looped around another ring of about five centimeters in
|
||||
diameter. In the puzzle’s initial configuration, the <code>U</code> is
|
||||
placed through the rings so that it is held in place by the
|
||||
iron rods. Imagine starting with the <code>U</code> piece before the
|
||||
iron loop is placed at the end. Slide the legs of the <code>U</code>
|
||||
through the loops so that the iron rods securing the loops
|
||||
to the metal strip go up the center of the <code>U</code>. Placing the
|
||||
final ring at the ends of the <code>U</code> prevents it from coming out.
|
||||
The object of the puzzle is to free the <code>U</code>-shaped piece from
|
||||
the other piece.</p>
|
||||
<p>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 <code>U</code>
|
||||
and slid down through the center of the <code>U</code>, thereby freeing
|
||||
the <code>U</code> 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 to 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 <code>U</code>.</p>
|
||||
<p>Here is an illustration of the three-ring case. The bottom
|
||||
of the puzzle is on the left-hand side of the page.</p>
|
||||
<pre><code>
|
||||
|
||||
|
||||
@@ -216,37 +221,41 @@ puzzle is on the left-hand side of the page.</p>
|
||||
\ | \\ ||
|
||||
\ | \\||
|
||||
\| \||</code></pre>
|
||||
<p>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.</p>
|
||||
<p>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 end of the <code>U</code>. Ring 1 can always
|
||||
be removed from or added to the <code>U</code>. In the initial state,
|
||||
when all rings are around the <code>U</code>, 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 <code>U</code>. This
|
||||
constraint leads to a recursive solution to the puzzle. Like the <a
|
||||
href="hanoi.md">Towers of Hanoi</a>, the number of steps to solve this
|
||||
puzzle is exponential in the number of rings.</p>
|
||||
<p>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.</p>
|
||||
<p>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 end of the <code>U</code>. Ring 1 can
|
||||
always be removed from or added to the <code>U</code>. In the initial
|
||||
state, when all rings are around the <code>U</code>, 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 <code>U</code>. This constraint
|
||||
leads to a recursive solution to the puzzle. Like the
|
||||
<a href="hanoi.md">Towers of Hanoi</a>, the number of steps to solve this puzzle is
|
||||
exponential in the number of rings.</p>
|
||||
|
||||
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|
||||
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|
||||
|
||||
Reference in new issue
Block a user