i am looking for a formula to find the maximum number that 6 circles of the same size can intersect. they cannot be overlapping

Question

anonymous · Answer

if you have two circles the can only have one intersect.

anonymous · Answer

If you have 3 circles they can 3.

anonymous · Answer

they can have at least 2 intersection

anonymous · Answer

a fourth circle only adds an additional 2 points

anonymous · Answer

I think it may follow that pattern and if so then contact points (x) could be determined 

x = 1 + 2 x (n-2); for n > 2.

Test: 
Num of Circles(n)    Contact Points
2                                1
3                                3
4                                5
5                                7

I think this works and if it does, that means 6 circles would touch in 9 places.

What do you think?

anonymous · Answer

I was thinking it might not work if you could fit one ball in the center with all the other circles circling it in a chain. The balls going around the center circle, would touch each other 5 times plus the center circle once each for 5 times. Ack! that's 10, which would make the formula fail!

anonymous · Answer

Therefore, I don't know. Sorry. But if you wanted to think about it in ways like this, I'd be happy to try and help you. Otherwise, sorry for the long winded thinking out loud on your question.