[EPQ Vol 1A] Question 29

The pattern below helps to investigate the number of intersection points given the number of intersecting lines. Every line must intersect with every other line and no 3 lines intersect at a common point.

1. Complete the following table.
   
   
   
2. Write down, in terms of \(n\), the number of intersections between \(n\) lines.
3. Find the number of lines which will give \(66\) intersection points.