  A closed Riemannian manifold is said to have cross blocking if whenever
distinct points p and q are at distance less than the diameter, all light rays
from p can be shaded away from q with at most two point shades. Similarly, a
closed Riemannian manifold is said to have sphere blocking if for each point p,
all the light rays from p are shaded away from p by a single point shade. We
prove that Riemannian manifolds with cross and sphere blocking are isometric to
round spheres.
