Circles and parts
Probability
Level
5
How many parts can 10 circles of same radii divide a plane into ?
(Please tell the maximum no of parts)
The answer is 92.
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1 solution
we can easily observe the pattern.
one circle divides a plane into 2 parts.
2 circles divide it into 4 parts.
3 circles divide it into 8 parts.
4 circles divide it into 14 parts. and so on...
so for n circles it is a recursive function:
C(n)=C(n-1) +(2n-2)