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<html>
<head>
<title>maze</title>
<script type='text/javascript' src='jquery-1.3.2.min.js'></script>
<script type='text/javascript' src='maze.js'></script>
<style type='text/css'>
#maze > canvas { float:left }
#maze + * { clear:left }
</style>
</head>
<body>
<div id='maze'><canvas style='float:left'></canvas>Moves:<div id='moves'></div><div id='description'>
<hr/>
<p>
The objective is to get from the top of the circle to the bottom.
This maze is recursive, but the circle only exists on the top level of the maze.
</p>
</div></div>
<p>
This maze was invented by the (clearly) brilliant Mark J. P. Wolf, and I found it
<a href='http://www.maa.org/editorial/mathgames/mathgames_11_24_03.html'>here</a>,
and a couple of solutions <a href='http://www.mathpuzzle.com/18Nov2003.html'>here</a>.
Like <a href='../snakes/'>snakes</a>, <a href='maze.js'>code</a>
and <a href='doc/'>documentation</a> is available.
</p>
These first two solutions come from the internet: a
<span class='solution'
name='long'
path='nnwswsnnswsnnswwnwseeneswwnwwwneswwnwses'>
From <a href='http://www.mathpuzzle.com/18Nov2003.html'>here</a>. <br/>
I like this solution because it uses all 3 immediate submazes
in their canonical order (they used to be labeled A,B,C clockwise from top left).
Here's <a href='?path=nnwswsnnswwnwwseeneswwnwwsswwnwses'>another</a> one
with a simpler traversal through the first Red submaze.
</span>
and a <span type='button' class='solution'
name='short'
path='nnnwwnnsesnnswwnwses'>
From <a href='http://www.mathpuzzle.com/18Nov2003.html'>here</a>. <br/>
This is an easy solution to memorize: right through red, over to blue,
in red twice, unwind around, up and left, back into red, in-and-out to the bottom,
and out.
</span> one.
Armed with this toy and a couple solutions, I set out to find my
<span class='solution'
name='first'
path='neewwnnsesnnnwnnwnnes'>
A good way of solving these is to pick a top-level path and just go for it.
Identify sub-goals as you recurse in and the challenge becomes keeping track of
which subgoal you're solving as you unwind. With a little persistence, I believe most
if not all paths are actually connected. This solution is noteworthy because of the complexity
of the red submaze's path compared that of the blue submaze.
</span>
solution,
and a chai later I found my
<span class='solution'
name='second'
path='nesssnnseennseseswwnwses'>
I like this one because of the fairly even balance of complexity between the red and
blue submaze traversals.
</span> and
<span class='solution'
name='third'
path='nnnwwnwseswwnwseees'>
This path targeted the little roundabout on the east side of the blue submaze, which
had been unused (at any depth) in all my previously known solutions. When I replayed this
maze, I noticed that the path only crosses itself once, a trait also shared with the
'short' solution from the internet.
I hypothesized the existence of a non-crossing solution,
and I managed to find <a href='?path=nnnwwnwsswsnnnwnwswsnnswwnwwses'>one</a>.
</span>.
Then I
<span class='solution'
name='played'
path='nnnwwnwwneswwnwswwswwnwwwnnwnnewnnes'>
Long paths are long and fun.
</span>
<span class='solution'
name='around'
path='nnnwwnwsswwnwswwswwnwwwnnwnnewnnes'>
Long paths are long and fun.
</span>
for a
<span class='solution'
name='while'
path='nnwswsnnswwnwseeneeswwnwseennseseswwnwses'>
Another solution developed by picking a target and following it, in this case the
green-line red-to-blue submaze connection.
</span>.
<span class='solution'
name='Worst Path Ever'
path='neewwnwseswwnwseeewwwswsnnswsnnnswwnwsesnnswsnnsweneswwnwwseeswwnwwwwnnwnwswsnnswsnnswwnwses'>
Worst PATH EVER. (PAX East 2010)
</span>
</body>
</html>