  We explore an Art Gallery variant where each point of a polygon must be seen
by k guards, and guards cannot see through other guards. Surprisingly, even
covering convex polygons under this variant is not straightforward. For
example, covering every point in a triangle k=4 times (a 4-cover) requires 5
guards, and achieving a 10-cover requires 12 guards. Our main result is tight
bounds on k-covering a convex polygon of n vertices, for all k and n. The
proofs of both upper and lower bounds are nontrivial. We also obtain bounds for
simple polygons, leaving tight bounds an open problem.
