Rauch conjectured in 1959 that in a compact 1-connected Riemannian manifold M there is a point whose first conjugate locus and cut locus intersect. This is true if M is homeomorphic to the 2-sphere or isometric to a Riemannian symmetric space. Weinstein proved in 1967 that any compact smooth manifold not homeomorphic to the 2-sphere can be equipped with a metric such that there is a point whose first conjugate locus and cut locus are disjoint.