Hey, there's no problem in this universe which had no solution. The need is to just nicely analyse the problem and approach to the solution in the right way.
Q. If you choose four random points on a sphere, and consider a tetrahedron with those points as its vertices, what is the probability that the centre of the sphere is inside the tetrahedron?
You should try this question once yourself.
And if you got stuck on it, then here's a video of it's solution in the easiest way.
THIS VIDEO IS AMAZING!!!
The "Putnam competion" is one of the toughest exam based on maths problems. It is a six hour long test and have just 12 questions each of 10 marks. It's difficulty level could be understood by seeing the median marks of student appearing in this test that is 1 or 2 out of 120. hence it is a pretty hard test. The hardness level of problem goes on incresing as you go from question 1 to 6. It means the sixth question is the hardest.
Here I am going to share a problem which came in a while back in this exam and it was the sixth problem.
Q. If you choose four random points on a sphere, and consider a tetrahedron with those points as its vertices, what is the probability that the centre of the sphere is inside the tetrahedron?
You should try this question once yourself.
And if you got stuck on it, then here's a video of it's solution in the easiest way.
THIS VIDEO IS AMAZING!!!
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