Maths - The Best Hacking Tool

Algebra Level 5

Once Nihar, the hacker claimed that he can know the number of views of each and every problem on Brilliant. But then Azhaghu was confused and thought how can Nihar do this? Then Nihar said that he has a special "hacking tool" for getting the number of views. Azhaghu was too much eager to know that tool, hence Adarsh told Azhaghu that the hacking tool was nothing but maths! Indeed Adarsh had figured out the trick. Adarsh observed that a person who solves a problem gets to know about the number of solvers and the percentage of people who were able/not able to solve that problem.

So, if a certain problem shows that x x people have solved and y % y\% of people were not able to solve the problem , So can you determine the number of views of the problem?

Details And Assumptions:

  • Assume that there is not such problem having y = 0 o r 100 y=0 \ or \ 100 and x = 0 x=0 or x = 1 x= 1 .

  • Note that the solver's number includes the problem poster himself and you must not include him in the number of solvers.

  • " [ ] \left[ \ \right] " denotes the nearest integer function. (Or you would get solvers in fractions!)

  • As a continued exercise, you can verify the formula for this problem after solving it.

Based on true events.
[ 100 x 100 − y ] \left[\dfrac{100x}{100-y}\right] [ y 100 x ] \left[\dfrac{y}{100x}\right] [ 100 ( x − 1 ) 100 − y ] \left[\dfrac{100(x-1)}{100-y}\right] [ 100 ( x − 1 ) y ] \left[\dfrac{100(x-1)}{y}\right] [ 100 x y ] \left[\dfrac{100x}{y}\right] [ 100 − y 100 x ] \left[\dfrac{100-y}{100x}\right]

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Nihar Mahajan by Nihar Mahajan , 20, India

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1 solution

Nihar Mahajan
Jun 5, 2015

Let the number of views be V V . Note that since we are not including the problem solver in solver's number , we will have the number of solvers as ( x − 1 ) (x-1) From the given data , we can form an equation :

y 100 × V = V − ( x − 1 ) ⇒ x − 1 = V − y V 100 ⇒ x − 1 = V ( 1 − y 100 ) ⇒ x − 1 = V ( 100 − y 100 ) ⇒ V = 100 ( x − 1 ) 100 − y \dfrac{y}{100}\times V= V-(x-1) \\ \Rightarrow x-1 = V-\dfrac{yV}{100} \\ \Rightarrow x-1=V\left(1-\dfrac{y}{100}\right) \\ \Rightarrow x-1=V\left(\dfrac{100-y}{100}\right) \\ \Rightarrow V=\dfrac{100(x-1)}{100-y}

Since we want the nearest integer , we have :

V = [ 100 ( x − 1 ) 100 − y ] V=\left[\dfrac{100(x-1)}{100-y}\right]

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Maybe the creator is not displayed as a solver nihar. I hope I am wrong. Actually i always use the app to access brilliant which nowdays does not show number of solvers

Satvik Choudhary - 6 years ago

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See, even though only you have solved , you can see 2 solvers there.

Nihar Mahajan - 6 years ago

But, [ 100 x 100 − y ] \left[\dfrac{100x}{100-y}\right] was very close, so I clicked it for the answer. . .

This shows the unlucky nature of Sravanth. . . .

Sravanth C. - 6 years ago

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It means you did not read the 2nd point of details and assumptions.

Nihar Mahajan - 6 years ago

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Yeah. That's what I said. It shows the unlucky nature of Sravanth. . .

Sravanth C. - 6 years ago

same here dude

Ritwik Jain - 6 years ago

Really, Nice true incident indeed :3 :3 :3

Mehul Arora - 6 years ago

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Cheers!xD :3 :3 :3

Nihar Mahajan - 6 years ago

I took problem solver in consideration

vishwash kumar - 4 years, 8 months ago

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