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# Challenge Yourselves, 'Masters' XD

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Hello, Challengers!

I come to you today with a sobering fact... Math has become too easy! It has stopped challenging us to use our brains in new ways and had dulled itself to the point where it is simply repetition! Thus, I start a new tradition: let us challenge ourselves to truly think and to push ourselves!

I ask that you would respect the honor of the challenge. Please refrain from using other sites for answers and post only the method you used to calculate the answer. If you cannot figure out the answer, PM me and I will reply with a link to the YouTuber 3Blue1Brown's video on how he found the solution. It is truly enlightening and shows how much more we could learn if we changed how we thought.

Anyways, that's enough rambling. Note that this question isn't for the occasional dabbler. It will confused and befuddle all but the greatest minds. You have been warned. XD

Four points are chosen uniformly at random on the surface of a sphere. What is the probability that the center of the sphere lies inside the tetrahedron whose vertices are at the four points?

Simple enough, eh? Well, I wish you luck!

Feb 8, 2019

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Think of splitting up the area!

Feb 8, 2019
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That's one way of doing it. I highly recommend against calculating each possible configuration. My friend tried and gave up after 2 1/2 days without rest.