Problem #81
This month there are three related problems:

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

Given that these three numbers are the lengths of the sides of a
triangle, what is the probability that the triangle is acute?

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?
The tetrahedron problem is still unsolved