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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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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).

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