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What is the largest number of regions formed by 6 planes in space?

This was part b of the problem, I already solved part a and I am confused on why it isn't the same answer as part a. 

 

Part a's question:

By drawing 6 lines in the plane, what is the largest number of regions we can create?

 

I got an answer of 22 using a recursive formula: f(n) = f(n-1) + n. 

 

Can anyone give me any hints on how to do part b?

 

all help is appreciated - Zekken4717

 

p.s this problem isn't due at any time so I have time to do it but quicker is better :)

p.s 22 is the right answer for part a.

 Aug 8, 2021
edited by Zekken  Aug 8, 2021
edited by Zekken  Aug 8, 2021
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When a plane intersects a different plane, we get two more regions, so

f(n) = f(n - 1) + 2(n - 1).

 

Then

f(1) = 2

f(2) = 4

f(3) = 8

f(4) = 14

f(5) = 22

f(6) = 32

 Aug 8, 2021

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