Suppose one wants to color the points in the plane so any two points at distance one apart are different colors. How many colors are needed?


I heard this problem when I was a kid. Back then the most I knew was that 3 is impossible and 7 is possible (tile hexagons of diameter 1-ε). I haven't heard about this problem since then and I don't know how to search for it. Is more known? Is this problem well known in certain circles?



Coloring Points in the Plane
This is the [Hadwiger–Nelson problem](http://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem).


