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

 Dividing a donut (Posted on 2005-04-23)
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.)
 re: An idea -- solution? (don't know if maximum is achieved) | Comment 18 of 34 |
(In reply to An idea -- solution? (don't know if maximum is achieved) by Charlie)

I see that in my original diagram 6 touches 5 along two boundaries, as do 6 and 2, and 6 and 3, so introducing a new area that cut off one of each of these accesses is ok.  The following diagram introduces a seventh mutually touching region:

` ___________           ____________          _____________             |          |           |                                  |  4       |     1     |     5               |          |           |______________________ |    5     |          |________   |_____                 ||          |__________|        |__|     |                ||_____________________|           |     |                |                      |     2     |     |   6                      |           |     |                      |___________|     |________         6            |           |              |                      |           |     7        |                      |     3     |__________    | ___________ __________|           |          |   |_______     7     |          |           |     5    |___________|     4    |___________|          |___________`

 Posted by Charlie on 2005-04-24 15:22:29

 Search: Search body:
Forums (0)