A plane intersects a regular tetrahedron in such a way that the intersection forms an equilateral triangle. How many such planes can do this?

A regular tetrahedron has 4 faces, each of which is an equilateral triangle. Any plane parallel to one of these 4 faces intersecting the tetrahedron will form an equilateral triangle cross-section. Therefore, there are exactly 4 distinct orientations/planes that can form an equilateral triangle intersection.