All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution An idea -- solution? (don't know if maximum is achieved) | Comment 9 of 34 |

Using the diagram where the left side wraps to touch the right side and the bottom to the top:

 ___________           ____________          _____________  
           |          |           |                      
           |  4    |     1     |     5   
           |          |           |______________________
|    5     |          |___________|                      |
|          |__________|           |                      |
|_____________________|           |                      |
                      |     2     |         6
                      |           |
                      |___________|
         6            |           |
                      |           |
                      |     3     |__________
            __________|           |          |
           |          |           |     5    |
___________|     4    |___________|          |___________

The lines around the edges are missing if the wrap-around is to a different portion of the same region. The line is shown on both sides if the region is different on the other side of the wrap-around.

Note that 1 touches 2, 4, 5 and 6 in the obvious fashion and 3 via the wrap-around. Region 2 touches all the other regions in the obvious fashion. Region 3 touches 4, 5 and 6 in the obvious fashion, as do regions 5 and 6 with each other.


  Posted by Charlie on 2005-04-23 20:22:59
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information