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Draw a picture of a simple polygon and a set of guards, such that the guards can see every point on every edge of the polygon, but the guards cannot see every point in the interior of the polygon.

I encountered this while randomly searching for polygon triangulation problems. I feel that no such polygon + guard combination exists. but I do not know how to go about proving or disproving that. Some help would be appreciated.

Source: Page 17, Problem 1(a) on this document

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Welcome to math.SE: since you are fairly new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are so far; this will prevent people from telling you things you already know, and help them write their answers at an appropriate level. If this is homework, please add the [homework] tag; people will still help, so don't worry. –  user21436 Apr 24 '12 at 14:51
    
A slight explanation of how to form such a polygon would be enough. I cannot find a way to do so. This isn't homework. –  vh4x0r Apr 24 '12 at 14:53
    
Ok, I have added some context now. –  vh4x0r Apr 24 '12 at 14:55
    
Have you seen this book? –  J. M. Apr 24 '12 at 15:02
1  
I changed "this criteria" to "this criterion". Write "This criterion is..." or "These criteria are....", but using "criteria" as a singular noun will be grating to many people. –  Michael Hardy Apr 24 '12 at 15:36

1 Answer 1

up vote 2 down vote accepted

This should do it. Yellow stars are the guards. They cannot see the red object.

enter image description here

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