COMPUTER PROGRAM CHRISTMAS PRIZE PROBLEM 2004

To find the possible configurations, I have written and run a Pascal computer program.

For each face, I represent the points by their distances to the three sides (these distance sum up to sqrt(3)/2).

In all possible ways, n points are chosen from a regular lattice of points on the tetraeder,
with the restriction that we choose at least one vertex and use a good distribution of the points over the faces.

For larger n, I ran an alternative program, choosing many times at random n points that satisfy varying
conditions.

The distance between two points in distinct faces is determined as the minimum of four geodesic distances:
directly or via one or two other faces.

If the minimum of the n*(n-1)/2 distances is greater than the maximum up to then, the maximum is adapted, and printed
with the accessory configuration.

The runs are confirming fairly well the results that I found and calculated on paper. The best configurations in the
output are a bit worse than the best theoretical ones.