Geometry meets Combinatorics! (A cube problem)

Discrete Mathematics Level 4

A cube has each of its faces colored with a distinct color. How many distinct sets of colors can you "see" on the cube at a given time, given that you only have one eye?


Consider your eye to be a fixed point in space outside the cube. We say that you can "see" a color if there exists a line which connects your eye to the center of the face which has that color which does not intersect with any other face of the cube.

The order in which the colors are seen is not important. {Red, Green, White} is the same as {Green, White, Red}

Hint/Extra Challenge: Prove, geometrically, that you can not "see" more than 3 colors at the same time.


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