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Path: utzoo!linus!decvax!harpo!eagle!mhuxl!ulysses!princeton!leei
From: leei@princeton.UUCP
Newsgroups: net.puzzle
Subject: Re: LOOKS SIMPLE -and maybe to simple.
Message-ID: <159@princeton.UUCP>
Date: Tue, 6-Dec-83 03:28:57 EST
Article-I.D.: princeto.159
Posted: Tue Dec  6 03:28:57 1983
Date-Received: Thu, 8-Dec-83 20:38:12 EST
References: <2651@gatech.UUCP>
Organization: Princeton Univ. EECS
Lines: 40

This is an interesting problem, but it has been wildly misrepresented on
the net.  In the original problem, CORNERS DO NOT ACT AS NODES.
Thus, when we define an arc as any line connecting two nodes in the diagram,
there is only one arc at each corner of the box.  By a simple reduction, we
can see that this reduces to an old, familiar graph tracing problem with
a graph that looks like:

	  /-------------------*--------------------\
	  |  /---------------/|\----------------\  |
	  |  | +---------+----|----+---------+  |  |
	  |  | |         |    |    |         |  |  |
	  |  \------*---------*---------*-------/  |
	  |    |    |    |   / \   |    |    |     |
	  |    +----|----+--/-+-\--+----|----+     |
	  |    |     \     /  |  \     /     |     |
	  \-----------*---/   |   \---*------------/
	       |       \-------------/       |
	       +--------------+--------------+


As you can see, there are six nodes (*) in the graph and four of them have
odd cardinality (? I don't think this is the right word).  Since you can't
trace (without lifting your pencil) any graph with more than two odd nodes
(remember, if you enter a node, you have to leave by a different route) then
you can't fulfill the requirements for the puzzle.  It's impossible.

Even if you count the corners as nodes, there are still four odd cardinality
nodes in the corresponding graph.  It cannot be done.

Needless to say, the `solutions' that have come over the net are not only
suspect but wrong.  It was proven some three hundred years ago that these
problems are unsolvable, and it is obvious why if you think about it for
more than three seconds.  SO STOP IT ALREADY!!!

-- 
------
Lee Iverson
Princeton University
..!princeton!leei