What is the greatest number of intersection points possible with just 5 lines?

Answer 1

10.

Each additional line can only intersect each of the previous lines once, so for two lines, there can be only 1 intersection, for three there can be up to 3 intersections (1+2), for four there can be up to 6 intersections (3+3), and for five there can be up to 10 (6+4).

This trend continues as you increase the number of lines:

6 lines: 15 possible intersections (10+5)

7 lines: 21 possible intersections (15+6)

8 lines: 28 possible intersections (21+7)

and so on...