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MathNet 2016-part-05 — 184 problems (EN–VI) Question 77

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 77

Draw 4 distinct lines in the plane and let $n$ denote the number of intersections (if more than one line passes through the same point it still only counts as one intersection). Which of the following is the set of all possible values of $n$?
(A) $\{0, 2, 3, 4, 5, 6\}$
(B) $\{0, 1, 3, 4, 5, 6\}$
(C) $\{0, 1, 3, 4, 6\}$
(D) $\{1, 3, 4, 5, 6\}$
(E) $\{0, 1, 2, 3, 4, 6\}$