N points on the edge.
Geometry
Level
pending
6 points are located on a circle and lines are drawn connecting these points, each pair of points connected by a single line. What can be the maximum number of regions into which the circle is divided?
30
32
33
36
24
31
28
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1 solution
In general the maximum number of regions you can get from n points is given by
{n choose 4} + {n choose 2} + 1
This can be proved using induction (other combinatorial proofs exist too). For more information (including at least two proofs), see this: Dividing a circle into areas. This is an oft cited puzzle to show the perils of generalizing based on first few values. We get powers of 2 till n=5, after which we get 31.