Guest Posted November 25, 2009 Report Share Posted November 25, 2009 You will select X points inside the volume occupied by a regular tetrahedron with edge length of 2 units. The condition is that there should be at least 1 unit distance between each of these points. What is the maximum possible value of X? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2009 Report Share Posted November 25, 2009 If surface of tethraedron is also "inside" - answer is 10 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 25, 2009 Report Share Posted November 25, 2009 I came up with 11: - 1 at each of the 4 corners - 1 at the center of each of the 6 edges - 1 at the exact center It took me a while because I don't remember enough trig to do it the easy way, so I had to break everything down to right angles to use basic geometry (which is tricky when you start with all 60 degree angles in 3 dimensions). Anyway, if my math is right, a point in the center would be exactly 1 unit from each of the edge points (and father from the corner points). Quote Link to comment Share on other sites More sharing options...
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You will select X points inside the volume occupied by a regular tetrahedron with edge length of 2 units. The condition is that there should be at least 1 unit distance between each of these points. What is the maximum possible value of X?
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