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$N$ points are to be put on sides of a square. What's the maximum number of triangles which are formed by joining those points?

Hints would be appreciated.

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    By "joining those points", do you mean joining each pair of points by a line segment?2011-03-02
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    Can you give an equation for "the number of triangles" given the relative data, e.g. the number of points on each side? Or is it more complicated than that?2011-03-02
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    @joriki Joining points in sets of three (because a triangle has three points =).)2011-03-02
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    @Filmus The problem doesn't limit how you arrange these N points on four sides. And I guess this is why it asks for the maximum number.2011-03-02
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    @Covi: Your answer seems to imply that only triangles having the given points as vertices are counted. I had understood the question to refer to any triangles formed, including triangles that are formed within the square by vertices formed by crossing lines.2011-03-02
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    @joriki Indeed, only triangles having the given points as vertices are counted.2011-03-02
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    This is a problem on a mathcamp admissions exam. Applicants are not supposed to look for help online.2011-03-02
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    @april Sorry. Though I was not asking for SOLUTIONS, just hints. I think the rule says if cited properly outside help could be used. I will close the discussion anyway.2011-03-02
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    @Covi: THere are no discussions here. I have rolled back to the original version.2011-03-02
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    @Covi, we do not delete posts which have already gotten answers—even less when the answers have been upvoted.2011-11-23

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