strategy. not all patterns are obvious, and not all of them will continue.
if i put two dots on the circle and connect them, the line divides the circle into two pieces.
if i put three dots on the circle and connect each pair of dots, the lines divides the circle into four pieces.
suppose you put one hundred dots on a circle and connect each pair of dots, meaning every dot is connected to 99 other dots. how many pieces will you get? lines may cross each other, but assume the points are chosen so that three or more lines never meet at a single point.
after you have worked on the problem 