bonanova Posted September 10, 2014 Report Share Posted September 10, 2014 With a nod to the maximally meticulous we ask: What is the greatest number of equilateral triangles that can be defined by choosing groups of three points from a set of 16 distinct fixed points in the plane? Quote Link to comment Share on other sites More sharing options...
0 k-man Posted September 19, 2014 Report Share Posted September 19, 2014 45 triangles using this configuration * * * * * * * * * * * * * * * * Quote Link to comment Share on other sites More sharing options...
0 dgreening Posted September 10, 2014 Report Share Posted September 10, 2014 Clarifying question: Do we get to choose the positions of the fixed points?? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted September 10, 2014 Author Report Share Posted September 10, 2014 Yes. Quote Link to comment Share on other sites More sharing options...
0 phil1882 Posted September 10, 2014 Report Share Posted September 10, 2014 * * * * * * * * * * * * * * * * 26? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted September 10, 2014 Author Report Share Posted September 10, 2014 * * * * * * * * * * * * * * * * 26? More. Look for a variety of lengths. In your configuration there are at least five. Quote Link to comment Share on other sites More sharing options...
0 k-man Posted September 19, 2014 Report Share Posted September 19, 2014 44 triangles using this arrangement. * * * * * * * * * * * * * * * * Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted September 19, 2014 Author Report Share Posted September 19, 2014 Very close. Extremely close. Which is to say with a slight tweak one more is possible, which I think is the max. Quote Link to comment Share on other sites More sharing options...
0 sahil12 Posted September 22, 2014 Report Share Posted September 22, 2014 I think it will be arrange 45 Quote Link to comment Share on other sites More sharing options...
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bonanova
With a nod to the maximally meticulous we ask:
What is the greatest number of equilateral triangles that can be defined by
choosing groups of three points from a set of 16 distinct fixed points in the plane?
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