Idea shamelessly stolen from this question.
I have a 4x4x4 Rubik's Cube, but all I want is a 2x2x2 Rubik's Cube.
Luckily, I also have an unlimited supply of small pieces of tape. Each piece of tape can cover the face of two neighbouring squares on my Rubik's Cube. When two pieces are taped together, they cannot be moved away from each other.
What is the minimum number of pieces of tape I must use to ensure that my 4x4x4 will always behave like a 2x2x2?