There are 3 straight lines and two circles on a plane. They divide the plane into regions. Find the greatest possible number of regions.
This is the best that I could come up with an I don't really know how to get even more regions. Using some mental calculations, I figured that I could edit the picture and make it into 20 regions. However, the answer key gave me 21 as the answer. Is there a way to find out the number of regions on a plane without using a calculator? Is there a formula for it? Please help.