Colored Squares and Cubes
Extra Credit: How do the answers change if we allow wrapping - that is, if
we assume left touches right, top touches bottom, (and front touches back,
for the second part)?
Color each square in a grid, such that no two neighboring squares have the
same color, and each square neighbors any other color only once. (Neighboring
squares share sides - don't consider corner-touching squares to be neighbors.)
What is the minimum number of colors needed for:
- a 3x3 grid?
- a 4x4 grid?
- the plane?
Color each cube in a 3-D lattice such that no two neighboring cubes have
the same color, and each cube neighbors any other color only once.
(Neighboring cubes share faces - don't consider corner- or edge-touching
cubes to be neighbors.) What is the minimum number of colors needed for:
- a 2x2x2 cube?
- a 3x3x3 cube?
- a 4x4x4 cube?
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