If two rigid bodies contact with a plane surface in balance, is the normal force uniformly distributed on the contacted surface?

Question

The normal force may be unevenly distributed on the surface of contact between two bodies. I had a discussion with my friend but was unable to prove whether this assertion is true or false under two RIGID bodies. I know it is a unreal question. Therefore, I am seeking a mathematical solution to this question. (If this question is independent from classical mechanics, how to prove?)