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As long as no two lines are drawn parallel, and no more than two intersect at any given point, then every set of three lines must form one triangle.
Every set of three lines forms at most one triangle, so the number formed in this way is the maximum.
Thus, this is equivalent to the question: In how many different ways can n lines be taken three at a time?
This is, of course, n(n-1)(n-2)/6
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From: The Colossol Book of Mathematics. |
