A very hard problem in a very hard competition

Geometry Level 2

If you chose 4 random points on the boundaries of a sphere, what is the probability that the spheres center is inside the tetrahedron make by the 4 points you chose?

Sources: 3 Brown 1 Blue, Annual William Lowell Putnam Math Competition.

Try not to look at the competition!

1 5 \frac {1}{5} 1 8 \frac {1}{8} 1 4 \frac {1}{4} 1 7 \frac {1}{7} 1 1 3 \frac {1}{3} 1 2 \frac {1}{2} 0

A Former Brilliant Member by A Former Brilliant Member

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1 solution

I really don't understand the solution, so here's the link:

https://www.youtube.com/watch?v=OkmNXy7er84

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Grant explains it sooo well! Here is the hyperlink

Mahdi Raza - 10 months, 2 weeks ago

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