How many intersects are there for 4 lines?

Answer 1

Maximum 12 intersections are there! You can simply use the formula:

No. of intersections = n(n-1)/2 [where 'n' is the number of lines]

This is derived as each new line can intersect (at most) all the previously drawn lines. There if there is:

1 line => 0 intersections

2 lines => 1 intersection

3 lines => 3 intersections [1 that was there + 2 by the new line can intersect both the previous lines.]

4 lines => 6 intersections [3 that were already there + 3 because the new line can intersect all the 3 lines that were present previously.]