Sender: Rick Slen
Subject: 4 Color map Theorem

I am challenging my students to find a map that can not be coloured using only 4 colours. I know that it is not possible, but one boy drew a map with a "country" totally surrounding all the others so of course it touched all other colours. How do I explain that this type of map is not permissable?

I think that you are in error. Any map that can be drawn in the plane can be 4-coloured. As for you student's example, the ocean surrounding a continent could be thought of as a country. Nothing wrong with that. I believe that his interior countries can be re-coloured to end up with only 4 colours being required.