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Inductive proof problem

Name: Anonymous 2006-10-29 12:09

Good Anonymouses, this anonymous is having a little trouble with starting this induction proof:

Two non-overlaping circles of radius 1 intersect in exactly two points. Prove by induction that given n >= 2 non-overlapping circles in the plane that the total number of intersections is never more than n(n-1).

I know this is true and I can see why, but I don't know what to do after I've done the base case and the inductive hypothesis.

Name: Anonymous 2006-10-29 12:49

That part is a little ambigous but it says that when there are 2 or more circles, then the total number of intersections is never MORE then n(n-1), so it can be less. In the example you've given it is less.

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