MathDB

Let

V

be a set of eight points in

3\text{D}

space that are the vertices of a cube with side length

1

. Compute the number of ways we can color the vertices in

V

yellow or blue such that
[*] each vertex receives exactly one color, and [/*] [*] there exists a point in

3\text{D}

space whose distance to each yellow vertex is less than

1

and whose distance to each blue vertex is greater than

1

. [/*]

3