Question

Ten circles are all the same size. Each pair of these circles overlap but no circle is exactly on top of another circle. What is the greatest possible total number of intersection points of these ten circles

Answer 1

Starting with one circle there are no intersections
Two circles have 2 intersections
Three circles have 4 extra intersections so the total is 6
The nth circle will cross all the previous circles twice = 2(n-1) extra intersections
The greatest number of unique intersections = 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90

Answer 2

2

Explanation: