MathDB

Math Prize 2017 Problem 10

Source:

September 26, 2017

Math Prize for Girlsgeometry3D geometry

Problem Statement

Let

C

be a cube. Let

P

Q

, and

R

be random vertices of

C

, chosen uniformly and independently from the set of vertices of

C

. (Note that

P

Q

, and

R

might be equal.) Compute the probability that some face of

C

contains

P

Q

, and

R