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From: ewa@sdcc3.UUCP (Eric Anderson)
Newsgroups: net.puzzle
Subject: Re: 5 boxes (SPOILER)
Message-ID: <3159@sdcc3.UUCP>
Date: Mon, 3-Feb-86 03:12:24 EST
Article-I.D.: sdcc3.3159
Posted: Mon Feb  3 03:12:24 1986
Date-Received: Wed, 5-Feb-86 01:51:14 EST
References: <1146@ecsvax.UUCP>
Reply-To: ewa@sdcc3.UUCP (Eric Anderson)
Distribution: net
Organization: U.C. San Diego, Academic Computer Center
Lines: 35

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.
>
>   _____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. 

It is impossible to draw such a line. Consider:

1. For each box, the line must 'enter' as many times as it 'leaves',
   otherwise the line must start/end in that box.

2. It is only possible for a line to enter and leave the same number of times
   if the box has an even number of 'sides' (numbered lines).

3. Three boxes have five 'sides' each.

4. The line has only two ends.

Therefore, it is impossible to draw such a line since one of the large boxes
will have a 'side' not crossed by a line.


Eric Anderson, UC San Diego         {elsewhere}!ihnp4!ucbvax!sdcsvax!sdcc3!ewa
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