mathschallenge.net

Problem

A Mystic Rose consists of twenty points evenly spaced around a circle and every point is joined to every other point.

How many lines are required to construct the Mystic Rose?

Solution

Starting at the first point, it must be joined to nineteen other points. The second point only needs to be joined to eighteen points now. The third point needs to join seventeen points and so on.

Number of lines, L = 19 + 18 + 17 + ... + 1 = ½ 19 (19 + 1) = 190.

It can be seen that the 1st line is drawn between points 1 and 2. The 2nd line is drawn between points 1 and 3, and so on. Between which two points is the 50th line drawn?
What about for the n th line?