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Randomly select 4 points on the surface of a unit sphere and then construct an inscribed tetrahedron (triangular pyramid) containing the random points as vertices. What is the probability that the center of the sphere is contained within the tetrahedron? This problem was on my undergraduate Applied Mathematics exam in 1964 and has tormented me for years. Any ideas for a solution is appreciated.

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  • $\begingroup$ What an interesting question. It's really got my mind going, Don't think I can get an answer to you but now its on my mind as well :). $\endgroup$ – Morgan Aug 27 '17 at 16:53
  • $\begingroup$ This post appears to answer your question: math.stackexchange.com/questions/1400/… $\endgroup$ – awkward Aug 27 '17 at 20:41
  • $\begingroup$ 3Blue1Brown recently posted a great video on the subject which includes the intuition behind the solution, see youtube.com/watch?v=OkmNXy7er84 $\endgroup$ – deque Jan 19 '18 at 2:30
  • $\begingroup$ This problem appeared as A6 on the 1992 Putnam exam; the published solutions are available online at math.hawaii.edu/~dale/putnam. Some discussion of this problem and its generalizations can also be found here: lsusmath.rickmabry.org/psisson/putnam/putnam-web.htm. $\endgroup$ – Semiclassical Jan 23 '18 at 15:10

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