I want to divide the surface of a donut into as many different regions as possible. The regions can be any shape, as long as they are each in one piece. Each region must touch each of the other regions (touching on a corner doesn't count). How many regions can I make?
It is clear that at least four. If the center of the donut has (x,y,z)=(0,0,0) the first section is by plain z=0. This give two half donut surfaces, superior and inferior. Now, we can section superior by plain x=0 and inferior by plain y=0. We have four portions each one connected to all the others.
Posted by armando
on 2005-04-23 13:44:11