Ten years ago (before PTC) I posted the problem below in the old MathCad forum.
Today I see that it is still posted, however, the then attached MathCad sheet with the answer is no longer posted.
So, I again post the problem.
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PROBLEM
Given 4 humingbirds each located at the vertice of a unit tetrahedron.
The birds begin to fly such that all birds fly at the same velocity and:
(1) bird #1 always flys directly towards bird #2
(2) bird #2 always flys directly towards bird #3
(3) bird #3 always flys directly towards bird #4
(4) bird #4 always flys directly towards bird #1
As can be visualized, the flying birds ultimately meet and crash together. (Assume birds are very small.)
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Find: Length of the flight path for each bird
