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?

Please kindly open the two sets where it is mentioned the drawing is on process.  This is due to I have completed the two for the proves that numerous cuttings with numerous touchings are possible.

Please do not see the solutions as easy.  This is due to it is hard to imaging how I solve this puzzle.  It is by luck that I could solve it and not that it is easy.

Thanks.

Posted by Jonathan Chang on 2005-04-26 15:38:37