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.