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Comments on Probability that six random numbers between 0 and 1 are the lengths of a tetrahedron's edges

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Probability that six random numbers between 0 and 1 are the lengths of a tetrahedron's edges

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If six numbers are chosen at random, uniformly and independently, from the interval [0,1], what is the probability that they are the lengths of the edges of a tetrahedron?

This is Part 3 of Problem No. 81 of the Missouri State University's Advanced Problem Archive.

The website seems to have been last updated in 2015 and states that this problem is "still unsolved." Has this problem been solved since then?

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2 comment threads

Related on MathOverflow: Probability that a stick randomly broken in five places can form a tetrahedron (2 comments)
Broken link to Problem No. 81 (2 comments)
Related on MathOverflow: Probability that a stick randomly broken in five places can form a tetrahedron
JRN‭ wrote 2 months ago

Thank you for the reference. I was not aware of it. The MathOverflow problem involves breaking a stick in five randomly chosen points; the problem I mention involves having the lengths of the sticks the same as six randomly chosen points. The two seem different.