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100 Lines, all distinct

Source: 1976 AHSME Problem 28

May 19, 2014
AMC

Problem Statement

Lines L1,L2,…,L100\mathit{L}_1,\mathit{L}_2,\dots,\mathit{L}_{100} are distinct. All lines L4n\mathit{L}_{4n}, nn a positive integer, are parallel to each other. All lines L4n−3\mathit{L}_{4n-3}, nn a positive integer, pass through a given point A\mathit{A}. The maximum number of points of intersection of pairs of lines from the complete set {L1,L2,…,L100}\{\mathit{L}_1,\mathit{L}_2,\dots,\mathit{L}_{100}\} is
<spanclass=′latex−bold′>(A)</span>4350<spanclass=′latex−bold′>(B)</span>4351<spanclass=′latex−bold′>(C)</span>4900<spanclass=′latex−bold′>(D)</span>4901<spanclass=′latex−bold′>(E)</span>9851<span class='latex-bold'>(A) </span>4350\qquad<span class='latex-bold'>(B) </span>4351\qquad<span class='latex-bold'>(C) </span>4900\qquad<span class='latex-bold'>(D) </span>4901\qquad <span class='latex-bold'>(E) </span>9851
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