Given $n$ points on the plane, no three of which are collinear, what is the maximum number of acute triangles formed by them?

[Source: Based on Hungarian competition problem]

  • $\begingroup$ I'd guess the optimal placement would be to have the points evenly distributed on a circle, but I'm not certain. That would at least give you a pretty good lower bound. $\endgroup$
    – Arthur
    Commented Oct 26, 2014 at 20:36
  • $\begingroup$ @Arthur, for $n=12$ a better solution is to place one point in the center of a circle and other points distributed on the circle. Then you have $52$ acute triangles instead of $20$ in your solution. Am i correct? $\endgroup$
    – mijjim
    Commented Oct 27, 2014 at 7:12
  • 1
    $\begingroup$ An upper bound $\endgroup$ Commented Dec 13, 2014 at 9:31


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