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Answer: We can


As a bit of an update. Having seen a recent post on this question I asked Ernie if he knew the optimal solutions for six or more holes. Ernie muttered a bit about optimality but then drew the following diagram for me. He spent some time pointing out the regular tetrahedrons and the four axes of symmetry in the 9 hole solution and said that he thought that &...


I guess you were And your grandfather was Note:


This is a system of 4 equations with 4 variables: From 2nd and 4th equation: For easier writing let's put $1/c=x$ and insert $a$ and $d$ into 1st and 3rd equation: From here it is easy:

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