Posted by Leasha on .
Consider the following diagram and fill in the table: It's a diagram of circles with points around the circumference based off of the table. The table reads
# of Points: 2, 3, 4, 5, 6
# of Regions: 2, 4, 8, ?, ?
For the 5 points I got 16 regions
when i use inductive reasoning there should be 32 regions for 6 points but if you draw it out there are only 30 regions. Why is this so?

Geometry 
Reiny,
Even though you posted this question 4 times now, you are probably not getting any replies because, speaking for myself, I don't know what you mean by "region".
Secondly, are we dealing with one circle? You mentioned circles, so how many.
Or, ... is there a single circle with, let's say, 4 points on it, another with 5 etc?
Looking at the # of regions the answers appear to be powers of 2
So I would guess that
Number(n) = 2^(n1) , where n is the number of points on the circle.
so 5 points > 16 regions
6 points > 32 regions
7 points > 64 regions, etc
This seems to be a question dealing with number of subsets.
e.g. given points A,B,C,D
I can form 2^4 or 16 subsets
{}  1
A,B,C,D  4
AB,AC,AD,BC,BD,CD 6
ABC,ABD,ACD, BCD  4
ABCD  1 for a total of 16
Can you related this to the number of regions?