  Given a small polygon S, a big simple polygon B and a positive integer k, it
is shown to be NP-hard to determine whether k copies of the small polygon
(allowing translation and rotation) can be placed in the big polygon without
overlap. Previous NP-hardness results were only known in the case where the big
polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT
is presented where a small polygon is constructed to encode the entire circuit.
