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Path: utzoo!watmath!clyde!burl!ulysses!allegra!alice!ark
From: ark@alice.UucP (Andrew Koenig)
Newsgroups: net.puzzle
Subject: Re: 5 boxes
Message-ID: <4928@alice.UUCP>
Date: Sun, 2-Feb-86 13:19:49 EST
Article-I.D.: alice.4928
Posted: Sun Feb  2 13:19:49 1986
Date-Received: Mon, 3-Feb-86 05:03:56 EST
References: <1146@ecsvax.UUCP>
Organization: Bell Labs, Murray Hill
Lines: 23

>	   _____1____________2____
>	  |           |           |
>	 3|          4|          5|
>	  |___6____7__|__8_____9__|
>	  |      |         |      |
>	10|    11|       12|    13|
>	  |______|_________|______|
>	     14       15      16

The problem as shown has no solution.  Consider: if all these cells are
to be traversed by a single line, then except for the ends of the line,
the line must leave every cell it enters.  Thus no more than two cells
may have an odd number of entrances, and if exactly two do then the
line must begin in one and end in the other.

In this diagram, FOUR cells have an odd number of entrances:

	1 3 4 6 7
	2 4 5 8 9
	7 8 12 15 11
	1 2 5 13 16 15 14 10 3  (in other words, the outside)

Hence, no legitimate solutions.