Problem: Lines L1,L2…,L100 are distinct. All lines L4n,n a positive integer, are parallel to each other. All lines L4n−3,n a positive integer, pass through a given point A. The maximum number of points of intersection of pairs of lines from the complete set {L1,L2,…,L100} is
Answer Choices:
A. 4350
B. 4351
C. 4900
D. 4901
E. 9851
Solution:
One hundred lines intersect at most at C2100=2100(99)=4950 points. But lines L4,L8,…,L100 are parallel; hence C225=300 intersections are lost. Also, lines L1,L5,…,L97 intersect only at point A, so that C225−1=299 more intersections are lost. The maximum number of points of intersection is 4950−300−299=4351.