Let N circles intersect each other as many times as possible (no circles passing through the same point). How many lower spring segments (not overlapping) are formed?
I got this far with the question: Since two circles will intersect at most two points, the number of intersection points that a circle will make with the previous n-1 circle must be 2(n-1). For example, the 2nd circle cuts the other at 2 points (there are 4 sub circle segment), while the 3rd circle cuts the other two at 4 points(there are 12 sub circle segment). How can we generalize this? Thank you.