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How Many Triangles... (Posted on 2004-08-15) Difficulty: 3 of 5
... (maximum) can be formed with n straight lines?

  Submitted by SilverKnight    
Rating: 2.2857 (7 votes)
Solution: (Hide)
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
___________________________

From: The Colossol Book of Mathematics.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPuzzle Thoughts K Sengupta2023-03-16 02:20:15
Some ThoughtsI believe the official solution is incorrect...Dej Mar2008-03-14 15:22:18
re: Maximum What?Larry2004-08-16 08:13:50
re: Vehe!Larry2004-08-16 08:11:56
Some ThoughtsVehe!Vee-Liem Veefessional2004-08-16 04:57:12
Vehe!Vee-Liem Veefessional2004-08-16 04:57:06
SolutionAssuming thatDan Blume2004-08-16 02:02:19
QuestionMaximum What?Bractals2004-08-15 21:58:45
SolutionsolutionDavid Shin2004-08-15 14:20:21
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