50% of people got this right

Algebra Level 5

After submitting a correct answer to a problem on Brilliant, you witness the percentage of people getting the question right update from 50% to 51%. You were the 101 9 th 1019^\text{th} solver.

How many Brilliant users, including yourself, attempted the problem?


Details and Assumptions:

  • The percentage success of Brilliant users is rounded to the nearest integer.
  • 3 attempts from one Brilliant user only accounts for 1 attempt from that particular user.

Click here for a second Brilliant themed algebra problem.


The answer is 2017.

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1 solution

Dan Ley
Jan 8, 2017

Let's call the original number of attempts x x .

In order for the percentage of successful attempts to increase from 50 % 50\% to 51 % 51\% , we have that 1018 x × 100 \frac{1018}{x}\times 100 rounds to 50 50 , and 1019 x + 1 × 100 \frac{1019}{x+1}\times 100 rounds to 51 51 .

This firstly lets us know that 1018 x × 100 < 50.5 2015.84 < x \frac{1018}{x}\times 100<50.5\implies 2015.84<x ,

whilst also telling us that 1019 x + 1 × 100 > 50.5 x < 2016.82 \frac{1019}{x+1}\times 100>50.5\implies x<2016.82 .

The only integer solution that fits these boundaries is x = 2016 x=2016 , and so 2017 2017 people, including yourself, attempted the problem.

Another New Year number giveaway! :D

Michael Huang - 4 years, 5 months ago

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I'll be honest, I was like "hmm, seems like it's a bit over 2000..." Let's try 2017!

Alex Li - 4 years, 5 months ago

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I'll have to wait a few years before this question becomes harder then haha

Dan Ley - 4 years, 4 months ago

But Brilliant problems gives 3 attempts to one person . So why didn't you consider that while solving ?

It is an important feature of the Brilliant Problems!

Nashita Rahman - 4 years, 5 months ago

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I asked about it in the comments below. Also, the question asks how many Brilliant users attempted the question, not how many attempts there were- I hope it doesn't change the final answer!

Dan Ley - 4 years, 5 months ago

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Oh I see. Okay , I got it!

Nashita Rahman - 4 years, 5 months ago

Only 40% got this question right :(

Razzi Masroor - 4 years, 4 months ago

@Calvin Lin if someone achieves 2 wrong answers and 1 correct answer to a problem does that count as 3 attempts, or does it count as 1?

Dan Ley - 4 years, 5 months ago

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It counts as 1.

Consider including "Assume that the percentage is rounded to the nearest integer" in the problem statement.

Calvin Lin Staff - 4 years, 5 months ago

There are actually 1998 people who attempted the problem. If you have the figure 2017, and from now being shown the answer, take this to be the total number of users who have attempted the problem so far, then 51% of 2017 should give 1019, whereas it actually gives 1028.67, so let us assume that you are then the 1029th solver. Now we say that 51% of users who attempted the problem, solve the problem, including yourself. If the total number of users equals 1998, then you being the 1019th person would make the claim true, that 51% of people solved the problem correctly. So actually, not meaning to be rude, but I don't quite understand your explanation.

Surayyah Aziz - 2 years, 10 months ago

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Note that the question states "The percentage success of Brilliant users is rounded to the nearest integer.". So, in your scenario, when there are 1997 people who attempted it and 1018 got it correct, then it will round the percentage of 50.97% to 51%.

Calvin Lin Staff - 2 years, 10 months ago

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