The week before Christmas break my teacher told me about this theorem. Since then I've been wondering: How many colors would be required for a map in 3 space?

Here are a few stupid solutions to the problem:

n space requires 2n colors

1 space requires 2 colors

2 space requires 4 colors

3 space requires 6 colors

n space requires 2^n colors

1 space requires 2^1 colors

2 space requires 2^2 colors

3 space requires 2^3 colors

3 space requires infinitely many colors.

Does anyone have a good idea for the answer to this question?