From

Pizza Cut, we know the formula for maximum partitioning (pieces) of the circle, given

*n* straight lines (cuts).

______________________________________

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

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

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

(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...