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Dividing a donut (Posted on 2005-04-23) Difficulty: 3 of 5
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?

See The Solution Submitted by Tristan    
Rating: 4.0000 (5 votes)

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easy way to 7 | Comment 20 of 34 |

An easy way to divide into 7 surfaces is:

Divided it before into 4 surfaces as I say in the first comment:

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.

And now divide the superior external part of the donut (not that one towards the hollow) in three similar 120 grades pieces, with one of the sections in plain y=0.

Edited on April 25, 2005, 1:39 pm
  Posted by armando on 2005-04-25 13:25:06

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