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From: bhuber@sjuvax.UUCP (B. Huber)
Newsgroups: net.puzzle
Subject: Re: 5 boxes
Message-ID: <2741@sjuvax.UUCP>
Date: Tue, 4-Feb-86 10:26:31 EST
Article-I.D.: sjuvax.2741
Posted: Tue Feb  4 10:26:31 1986
Date-Received: Thu, 6-Feb-86 21:25:51 EST
References: <1146@ecsvax.UUCP>
Reply-To: bhuber@sjuvax.UUCP (B. Huber)
Distribution: net
Organization: St. Joseph's University, Phila. PA.
Lines: 34
Summary: 

In article <1146@ecsvax.UUCP> hal@ecsvax.UUCP writes:
>
>Here's an old one that I have yet to figure out myself.  It may not be
>possible, but if you know the solution, let's see it.
>
>Here is a diagram consisting of five squares, two on top and three on
>bottom.  It has been divided into 16 lines, which I have numbered as 
>shown:
>
>
>   _____1____________2____
>  |           |           |
> 3|          4|          5|
>  |___6____7__|__8_____9__|
>  |      |         |      |
>10|    11|       12|    13|
>  |______|_________|______|
>     14       15      16
>
>
>The object is to draw a single line that crosses all of the 16 lines
>in the figure once and only once.  The line may start inside or outside
>the figure, and it may not cross itself. 

Each time your single line enters a 'room' (or the exterior), it crosses a
line.  Thus it has either to begin or end in any room whose boundary consists
of an odd number of lines.  It's easy to find three such 'odd' rooms; the 
nonsquare ones all have exactly five lines bounding them (the exterior cons-
titutes a fourth, actually, having nine lines).  Since a continuous curve can
have at most two ends, the problem has no solution.

Euler solved this one about two hundred years ago.

			Bill Huber