Amazing approach to hardest mathematics problem.

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.

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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Mathematics problem

Find the next member in this sequence. 1 , 11, 2 1 , 121 1, 1 1 1 221, ........... Comment down your answers.

Mathematics Problem

A census-taker knocks on a door, and asks the woman inside how many children she has and how old they are. "I have three daughters, their ages are whole numbers, and the product of the ages is 36," says the mother. "That's not enough information," responds the census-taker. "I'd tell you the sum of their ages, but you'd still be stumped." "I wish you'd tell me something more." "Okay, my oldest daughter Annie likes dogs." What are the ages of the three daughters? Comment down your answer below.

Which is brightest metal?

I’ll give you the short, and mildly incorrect, answer first: Silver is the brightest metal. Silver has been revered for thousands of years for its brightness. It is used to make the finest mirrors, though it must be covered with glass because it tarnishes quickly in the presence of oxygen. For a slightly longer answer… By “brightest,” you’re likely asking which metal reflects the most visible light. This is measured scientifically through a property called Reflectance . Reflectance measures the effectiveness of a material of reflecting radiant energy. As you might know, radiant energy exists on a broad spectrum, only a tiiiiiiiiny portion of which is visible. This area, between about 390 nanometers and 700–750 nm, is known as the visible spectrum . I bring this up because the Reflectance of a material depends upon the wavelength of the energy it’s reflecting. By looking at this chart on the Reflenctance of Gold (Au), Silver (Ag) and Aluminum (Al), you...

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