Problem 42765. Maximize Non-Co-Planar Points in an N-Cube

Created by Richard Zapor

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This Challenge is to find a set with the maximum number of integer points that create planar surfaces with a maximum of three points from the set. No four points may be co-planar.
Given the size N and the number of expected points Q find a set of Q points. Only N=2/Q=5 and N=3/Q=8 will be tested. N=4/Q=10 or N=5/Q=13 are too large to process.<pre class="language-matlab">N=2 contains 8 points [0,0,0;0,1,0;1,0,0;1,1,0;0,0,1;0,1,1;1,0,1;1,1,1]
N=3 contains 27 points [0,0,0;0,0,1;0,0,2;...2,2,2]
</pre>Output is a Qx3 matrix of the non-co-planar points.Reference: The <a href = "http://68.173.157.131/Contest/Tetrahedra">March 2016 Al Zimmermann Non-Coplanar contest</a> is N=primes less than 100. Maximize the number of points in an NxNxN cube with no 4 points in a common plane.Theory: The N=2 and N=3 cases can be processed by brute force if care is taken. Assumption of [0,0,0] greatly reduces number of cases. Solving <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42762-is-3d-point-set-co-planar">Cody Co-Planar Check</a> may improve speed.

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Problem 42765. Maximize Non-Co-Planar Points in an N-Cube

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Problem 42765. Maximize Non-Co-Planar Points in an N-Cube

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