Paint the points on a plane with three colors, so that the points on each line are a maximum of 2 colors, and all three colors are used. (Math Festival 1990)
You can do this by painting as follows:
Paint the origin blue, the rest of the x-axis red, and everything else green.
Any horizontal line will be either all green, or red and blue. Any nonhorizontal line will be all green except where it intersects the x-axis, so it will only have two colors: green and something else.
(You could actually paint the x-axis in any combination of red and blue you wanted, as long as it used both of them.)