You are given a plane n-gon having no intersecting sides. That is, each segment of the perimeter has interior points on one side and exterior points on the other. We wish to illuminate the interior of the n-gon in its entirety by placing lamps at various points in its interior. Clearly, if the n-gon is convex, one lamp will suffice. Concave points, however, may cast shadows in some interior regions. Since life here in the Den is never simple, we ask about the general case:

To illuminate the interior of a simple n-gon, what is the smallest number of lamps that will always suffice? Does the answer change if we require the lamps to be placed at vertices?

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## bonanova

You are given a plane

-gon having no intersecting sides. That is, each segment of the perimeter has interior points on one side and exterior points on the other. We wish to illuminate the interior of the n-gon in its entirety by placing lamps at various points in its interior. Clearly, if then-gon is convex, one lamp will suffice. Concave points, however, may cast shadows in some interior regions. Since life here in the Den is never simple, we ask about the general case:nTo illuminate the interior of a simple

-gon, what is the smallest number of lamps that will always suffice? Does the answer change if we require the lamps to be placed at vertices?n## Link to comment

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