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Partitioning Space (Posted on 2004-09-13) Difficulty: 5 of 5
From Pizza Cut, we know the formula for maximum partitioning (pieces) of the circle, given n straight lines (cuts).

  1. Determine the maximum number of regions of the plane produced by n intersecting circles.

  2. Determine the maximum number of regions of the plane produced by n intersecting ellipses.

  3. Determine the maximum number of regions of space produced by n intersecting spheres.

No Solution Yet Submitted by SilverKnight    
Rating: 4.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Reason, don't guess | Comment 11 of 13 |
(In reply to re: Reason, don't guess by nikki)

Sorry, I did not mean to sound harsh in my tone in my previous comment.  I apologize if it sounded so.  I do think that hiding the formula from people who want to discover it themselves is a good idea. 

I was more concerned that some people may think that putting a single formula that others cannot find a counter-example for suffices to solve a problem like this.  It did seem that your first post entitled "Parts 1 and 2" claimed to solve the problem (i.e., "then the answer is...").  In that sense, perhaps a title like, "Possible formula" with Comment Type "Some Thoughts" would be more appropriate. 

As far as "improper approach", I actually think that your approach is correct - one should draw small examples and conjecture a formula to fit the initial data.  But that is only (the easier) half of the problem.  The other half of this problem seems exceedingly difficult to me...

  Posted by David Shin on 2004-09-14 17:24:40
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