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Note by Ekene Franklin
1 month ago

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  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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My country's national olympiads 1st round is to be conducted tomorrow. I will most likely post all of them here for our consumption! I expect them to be pretty easy.

Ekene Franklin - 3 weeks, 6 days ago

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Ok. Thanks and also are you writing that exam.

Ram Mohith - 3 weeks, 6 days ago

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It is actually meant for students two years older than I am, but I will give it a shot.

Ekene Franklin - 3 weeks, 6 days ago

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@Ekene Franklin Oh !!!

Ram Mohith - 3 weeks, 6 days ago

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@Ram Mohith It there a minimum age requirement to be eligible to write your country's olympiads?

Ekene Franklin - 3 weeks, 6 days ago

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@Ekene Franklin Yes, I think it is 13 or 14. People from class 8 or 9 onwards can write the exam.

Ram Mohith - 3 weeks, 6 days ago

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@Ram Mohith Are you also writing the olympiads soon?

Ekene Franklin - 3 weeks, 6 days ago

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@Ekene Franklin No. At present I am not interested. The main goal of student student studying in class 11 and 12 in India is to get into IIT (Indian Institute Of Technology)

Ram Mohith - 3 weeks, 6 days ago

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@Ram Mohith Oh, so that is what JEE and IIT are all about. I hope you get into it seamlessly. But say, do you hope to write olympiads in the future?

Ekene Franklin - 3 weeks, 6 days ago

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@Ekene Franklin Yes. I may.

Ram Mohith - 3 weeks, 6 days ago

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This is a marvelous secret and I benefited a lot from this. If you want to write any question for the problems of the week the better option is to write a physics problem rather than maths. Out of 5 problems 3 are allotted for maths and 2 for science. In the maths category there will be a much competition from many users. But in the science category there are only 4 competitors namely Rohit Gupta, Pranshu Gaba, and two staff members Blake Farrow, Danielle Scarano. So, I posted some good physics problems and 3 of them are featured now. But I won't force you to post only physics problems then there will be much competition for science. If you have good problems in maths you can post them (as 3 of my maths problems are also featured although I say that I am basically a physics man).

Ram Mohith - 3 weeks, 2 days ago

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How do you send questions to them to select for weekly problem??Do they themselves select from your sets?

Manuj Rajpal - 2 weeks, 3 days ago

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No. Only staff will select the problems of the week. In general, the notification will be as if I have written the problem of the week.

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith They themselves select it by seeing your sets or you send them via some forum and then they choose one of the all sent questions??

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal The community members write problems and post them to community and the staff selects the best 15 questions among all the problems and they will feature them as problems of the week. There is no forum involved in this process.

Ram Mohith - 2 weeks, 2 days ago

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Where is the show full site option??(from ur mt. Everest Q discussion)

Manuj Rajpal - 2 weeks, 4 days ago

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Here is the screenshot of where is it present. Can you find it now ?

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith Is this screenshot from app?

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal No. It is from from the main website.

Ram Mohith - 2 weeks, 3 days ago

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It will be in the main option bar. It is the place where you can find links like "profile", "stats", "search", etc. The "view" full site option will be present there.

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith Main option bar : Those 3 lines on left corner?? Or in the stats section of taskbar?

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal Oh so this is on website. Can this be done in app?

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal Ohh !! You are doing in the app. Sorry, I don't know whether this is possible in app or not. But can't you find any option like this. in the screenshot.

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith No :-( how can I send screenshot on this chat?

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal You have to copy the link of the picture and paste it here.

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith K thnx a lot for helping, and sorry for disturbing..

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal Mauj Rajpal, from which part of India are you from.

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith Delhi ;-) and u??

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal Visakhapatnam, Andra Pradesh.

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith Oh nice. From where do you put your problems in sets(source) and how do you have sets of other people in yours??

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal Can you suggest me some of your book(especially maths)

Manuj Rajpal - 2 weeks, 3 days ago

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@Manuj Rajpal It's our college material. It is a collection of all good problems from various books.

Ram Mohith - 2 weeks, 3 days ago

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@Manuj Rajpal In every set there will be a option at the bottom called "save". If you click that, that particular set will be saved into your sets. Some of my problems are original whereas some other are completely taken from books or the problems and the remaining are the problems which I have taken from books and modified them.

Ram Mohith - 2 weeks, 3 days ago

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@Manuj Rajpal It's OK. No problem. I went to brilliant only once in the mobile app so I am not much aware of the options present in it.

Ram Mohith - 2 weeks, 3 days ago

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@Manuj Rajpal The three line aside the option "Premium"

Ram Mohith - 2 weeks, 3 days ago

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Thanks guys. Keep sending problems and lets discuss!

Ekene Franklin - 4 weeks, 1 day ago

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The multiple choice of a problem brilliant doesn't order them any more you chose on which place is the correct answer.

B D - 4 days, 8 hours ago

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We know that

Mohmmad Farhan - 4 days, 8 hours ago

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Hello to everyone! I have not been around for some time now on Brilliant. However, I met on my return a delightful change in the method of posting options for multiple choice questions on Brilliant. Kudos to Calvin Lin and the truly brilliant Brilliant team!

Ekene Franklin - 5 days, 7 hours ago

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@Calvin Lin Sir, I am very much happy. But I hope multiple correct answer format will also be soon available for the community.

Ram Mohith - 5 days ago

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Actually, I sort of did that. So, I made a correct answer then removed it (crossing it with the x) and then the two dummy answers above it, became the correct answers.

Mohmmad Farhan - 4 days, 13 hours ago

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@Mohmmad Farhan But after that it says only 1 correct answer must give.

Ram Mohith - 4 days, 13 hours ago

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@Ram Mohith OH!

Mohmmad Farhan - 4 days, 12 hours ago

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@Mohmmad Farhan See my set: \(\LaTeX\) Help

Mohmmad Farhan - 4 days, 12 hours ago

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@Mohmmad Farhan Good one.

Ram Mohith - 4 days, 11 hours ago

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I think and hope this change is a step up to the multiple correct answer releasing.

X X - 4 days, 15 hours ago

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Which questions would you handpick for people? (ie. Your favourite questions)

Mohmmad Farhan - 5 days, 6 hours ago

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DO or DIE

You are lost in a forest on a cold midnight day. The temperature is quite low and it is bitter cold. Now you have only two chances :

  • You should lie on the ground and should shrink your body like a tight pack.

  • Go and stay in the water in a pond nearby.

There not much time left. Take your decision before cold kills you. So, what wold you choose ?

Ram Mohith - 2 weeks, 6 days ago

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First option.

Ekene Franklin - 2 weeks, 6 days ago

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But the second one is the correct choice you have to make.

Ram Mohith - 2 weeks, 4 days ago

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@Ram Mohith Why? Because of anomaly in expansion and contraction of water.?

Ekene Franklin - 2 weeks, 3 days ago

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@Ekene Franklin And also due to the high specific heat capacity of water. This question is a slight modification of air currents (due to which it is cool during the day and warm during night near coastal areas) and I am going to post this very soon.

Ram Mohith - 2 weeks, 3 days ago

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@Ram Mohith I thought as much.

Ekene Franklin - 2 weeks, 3 days ago

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Finally I reached it. I have reached 1 lakh (100 k) solvers in 91 problems.

Ram Mohith - 3 weeks ago

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Do you know the minimum people to reach?

B D - 2 weeks, 1 day ago

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I didn't get your point !!! Are you asking about minimum people required to get contribution page.

Ram Mohith - 2 weeks, 1 day ago

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@Ram Mohith Yes he is.

X X - 2 weeks, 1 day ago

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@X X @X X, I want your help. I am trying to write a new problem but I got struck up at one point. Here is my doubt :

Suppose lets say a man jumps from a building with initial velocity \(u\). After \(x\) seconds another man freely falls from the same building and from the same height. Now, we can say that the displacement of both the man's are equal as they both reach the ground simultaneously after they jump from same point, so we can equate their distances. Here is what I did : \[ut + \dfrac12 gt^2 = \dfrac12 g(t - x)^2\] where \(t\) is the time taken by the first person to reach the ground. The main part of my doubt is that whether we should write the time taken by second person as \((t - x)\) or \((t + x)\).

Ram Mohith - 2 weeks, 1 day ago

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@Ram Mohith It should be t+x as he is free falling and the previous one jumped with velocity u

Manuj Rajpal - 2 weeks ago

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@Ram Mohith I'm not good at physics, though. I think the time taken by the second person should be as same as the first one, maybe?

X X - 2 weeks, 1 day ago

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@X X What I think is that as the second person jumps after \(x\) seconds his time period will be \((t - x)\) seconds. Let's ask it to staff.

Ram Mohith - 2 weeks, 1 day ago

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@Ram Mohith So, are you caculating " when the first man fell to the ground, what is the distance between the two man"?

X X - 2 weeks, 1 day ago

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@X X No. Both man reach the ground simultaneously so can we write the equation as in my before comment in which we equate displacements.

Ram Mohith - 2 weeks, 1 day ago

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@Ram Mohith Yes, I too think the time taken by the second person is \(t-x\)

X X - 2 weeks, 1 day ago

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@Ram Mohith Oh! Sorry, I misread the problem.

X X - 2 weeks, 1 day ago

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@X X I think you must minimum have 5K people reached. But the main parameter I think is that the contribution page is mostly obtained either by up votes or by solvers to the question (more than 1K). When I got my contribution page I have around 120 upvotes, around 300 solvers, around 30 views for my notes.

Ram Mohith - 2 weeks, 1 day ago

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@Ram Mohith OK. Thanks!

B D - 2 weeks ago

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Congratulations!

X X - 3 weeks ago

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Did you know that :

\[1 + \omega = \omega \ but \ \omega + 1 \neq \omega\]

Freakin' cool right?

P.S. \(\displaystyle \omega \ is \ the \ second \ lowest \ level \ of \ \infty \ after \ \aleph_0 \)

Mohmmad Farhan - 3 weeks, 2 days ago

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DO YOU SERIOUSLY HAVE TO GIVE ME 46 NOTIFICATIONS OVERNIGHT!

Mohmmad Farhan - 3 weeks, 2 days ago

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Is that bad, Mohmmad? I am usually on Brilliant throughout the night.

Ekene Franklin - 3 weeks, 2 days ago

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Don't call me Mohmmad

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan Sorry, but why?

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin See, My brother's name is Farhan but I am Farhat. And Mohmmad is his surname and Mohammad is my surname. (Stupid Passport errors)

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan Mohammad Farhat

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith YES! FINALLY!

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan You can change your name in the account settings

X X - 3 weeks, 2 days ago

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@X X I don't bother

Mohmmad Farhan - 3 weeks, 2 days ago

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I HAVE EXAMS

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan I see. But you can use Brilliant to prepare.

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin English EXAMS

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan Farhat, from which part of India are were from ?

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith Andhra Pradesh, From Khammam

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan I am also from Andhra Pradesh. From Visakhapatnam.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith I am Telugu. You are Telugu right because you are from Andhra Pradesh right?

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan Yes. I am born in Visakhapatnam.

Ram Mohith - 3 weeks, 2 days ago

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Problem 9: How many \(6\) digit numbers can be formed using only odd digits?

Ekene Franklin - 3 weeks, 2 days ago

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Is it 5^6?

X X - 3 weeks, 2 days ago

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Correct. Nice stuff. What did you do?

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin There are 1,3,5,7,9 five odd digits. There are six digits, each digit has 5 possibilities, so there are 5^6 possibilities

X X - 3 weeks, 2 days ago

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@X X Bro, u are amazing

Syed Hamza Khalid - 3 weeks, 2 days ago

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Problem 8: A unit square is completely covered by \(3\) identical circles. Find the smallest possible diameter of the circles.

Ekene Franklin - 3 weeks, 2 days ago

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Problem 7: Simplify \(S = (cot 10^\circ - 3\sqrt{3})(cosec 20^\circ + 2cot 20^\circ)\)

Ekene Franklin - 3 weeks, 2 days ago

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For trigonometric functions, logarithms, limts, etc you must keep a slash before them. Like \cot will be as \(\cot\) and \log will be as \(\log\).

Ram Mohith - 2 weeks, 6 days ago

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Why are you keeping square brackets. For square root you just need to keep flower brackets.

Ram Mohith - 3 weeks, 2 days ago

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Problem 6: Find all primes which are the sum of two primes and difference of two primes.

Ekene Franklin - 3 weeks, 2 days ago

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5=7-2=3+2,this is the only possibility.

X X - 3 weeks, 2 days ago

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Exactly. Just what I did during the exam, using the logic that if a prime satisfies those conditions, then the only even prime, 2 must be in the sum and difference.

Ekene Franklin - 3 weeks, 2 days ago

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Brilliant DATE OF BIRTH?

B D - 3 weeks, 3 days ago

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B D : Brilliant Date :p

Mohmmad Farhan - 3 weeks, 3 days ago

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2004?

B D - 3 weeks, 2 days ago

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@B D I think it will be 10 years

Ram Mohith - 3 weeks, 2 days ago

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X X said it

Mohmmad Farhan - 3 weeks, 3 days ago

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I have a proof for the existence of infinite dimensions.

On a line (1 Dimension), a number can be represented by a point. On a grid (2 Dimensions), an intersection is represented for the data in a cell. In a cube (3 Dimensions), data can still be represented on a point (where straight lines intersect). Following this pattern, there are infinite dimensions (because there are \(\aleph_0\) numbers).

Mohmmad Farhan - 3 weeks, 3 days ago

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You can play a game in brilliant called Word problem Here

B D - 3 weeks, 3 days ago

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BrilliantForLife

Dare you to toggle \(\LaTeX\)

Mohmmad Farhan - 3 weeks, 3 days ago

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What courses would you recommend for a 4th grader like me?

Mohmmad Farhan - 3 weeks, 3 days ago

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You are 4 the grade ????!!!!!

Ram Mohith - 3 weeks, 2 days ago

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My first trophy was in Grade 1(third)[english], Second in grade 2 (1st)[first scrabble competition] and third in grade 2(Best school player award)[first scrabble competiton]

Mohmmad Farhan - 4 days, 11 hours ago

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I am going to be 5th grade

Mohmmad Farhan - 4 days, 13 hours ago

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@Mohmmad Farhan Oh !!! Good. All the best

Ram Mohith - 4 days, 13 hours ago

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@Ram Mohith Actually I am 1 year away from board exam (in 2020)

Mohmmad Farhan - 4 days, 11 hours ago

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10 years old. I told you

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan But, I didn't think you are 4 th grade.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith I am! REALLY

Mohmmad Farhan - 3 weeks, 2 days ago

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@X X, @Michael Mendrin, @Chew-Seong Cheong, @Mohmmad Farhan,and the rest of all, Can you please participate in this message-board (as requested by Ekene Franklin)

Ram Mohith - 3 weeks, 3 days ago

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@Calvin Lin

Ekene Franklin - 3 weeks, 3 days ago

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@Calvin Lin

Mohmmad Farhan - 3 weeks, 3 days ago

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I think you there is some error in spelling or you have kept a gap between the symbol and name. Once check again. If it is correct then you should get it in blue color link and not just normal text.

For example you should type it as @ _ Ekene Franklin ( _ symbol means no gap) then you will get it as @EKENE FRANKLIN

Ram Mohith - 3 weeks, 3 days ago

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It is not still working. Do I need to add something like a code or anything, or should I just type it?

Ekene Franklin - 3 weeks, 3 days ago

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@Ekene Franklin You should select from the list which will appear when you type the name. Also the name should be exactly matching with that particular user even capital letters should be taken into consideration.

Ram Mohith - 3 weeks, 3 days ago

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@Ram Mohith Which list?

Ekene Franklin - 3 weeks, 3 days ago

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@Ekene Franklin Ok. If you want I will do it on behalf of you.

Ram Mohith - 3 weeks, 3 days ago

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@Ram Mohith Of course I want! Thanks!

Ekene Franklin - 3 weeks, 3 days ago

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@Ekene Franklin Tell the names of whom do you want to be called to this note.

Ram Mohith - 3 weeks, 3 days ago

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@Ram Mohith @Calvin Lin, @Harsh Shrivastava, @Chew Seong Cheong, @Michael Mendrin, @X X, @Aniket Sanghi.

Ekene Franklin - 3 weeks, 3 days ago

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Hi guys !!! I want to tell you some secret. I think next week would be a week of physics. Because this week I have found six problems which have equal chances in coming to problems of the week. There are Rohit Gupta's Trick Spring Balance and Spring Balance, Pranshu Gaba's Three blocks Sliding and Relative Stuntmen Motion, Danielle Scarano's Thermographic Dog and my Mt. Everest vs Mt. Godwin Austin. I think these question will be featured definitely this week if not possible then next week.

Ram Mohith - 3 weeks, 4 days ago

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I made the cut for the 2nd round! I scored \(76.70\) out of a maximum possible 110. Hurray!

Ekene Franklin - 3 weeks, 4 days ago

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Oh !!! Congrats.

Ram Mohith - 3 weeks, 4 days ago

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Thanks a lot. But no one apart from us is solving the problems. I want to check my solutions and my faulty areas. Please direct the problem solving masters of Brilliant here to help me out.

Ekene Franklin - 3 weeks, 4 days ago

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@Ekene Franklin If you want to direct anyone to this place just keep the symbol @ and type the name of the person. Immediately a notification will be sent to that particular user.

Ram Mohith - 3 weeks, 4 days ago

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Problem 5: Find the general term of the sequence described by \(a_n = 4a_{n - 1} - 3a_{n - 2}\) given that \(a_1 = 1\) and \(a_2 = 9\).

Ekene Franklin - 3 weeks, 4 days ago

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\(a_n=4\times3^{n-1}-3\)

X X - 3 weeks, 2 days ago

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Great. This was what I got. But do you mind showing your solution so I can clarify mine?

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin Solve the equation \(x^2=4x-3\) and get \(x=3\) or \(1\). Let \(b_n=3^n-1^n\).

The first few terms of \(b_n\) is \(2,8,26,80...\) and \(b_n\) also satisfies the recursion \(b_n=4b_{n-1}-3b_{n-2}\)

Compare the two sequences: \(a_n=\frac43b_n-\frac53=4\times3^{n-1}-3\)

X X - 3 weeks, 2 days ago

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@X X Not exactly what I did, but something similar. Thanks a lot. If I may ask, have you ever participated in an olympiad before, or do you hope to participate in one?

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin No, I haven't. I knew few things about it, so I'm not sure about participating in one.

X X - 3 weeks, 2 days ago

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@X X Ok. Thanks. By the way, I really admire your problems. They are very cool. One of my major problems here is creating problems. My original problems are too easy(you can check them out). But solving others problems(of course not those extremely hard ones) is not a big problem for me.

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin @X X I think this is your first problem of the week in easy catogery.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith You're right! (Ha, ha! I'm a little jealous of you because your problems are often the first problem in the easy category, and in your contributions page, the number of people are banging up:p)

X X - 3 weeks, 2 days ago

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@X X Don't worry mister !!! You have the skill to post and solve tough questions (level 4 and 5).

Ram Mohith - 3 weeks, 2 days ago

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@X X But some of your problems came in Intermediate and Advanced catogery.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith I know. (Fewer people solves those, that is why I was so happy to see my problem as the second of the basic category)

X X - 3 weeks, 2 days ago

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@X X OH !!! Your problem is featured as the second one in the problems of the week. But my first problem (Thundering Question) is the third one.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith How is my new problem, check it here. It is posed by B.D

Ram Mohith - 3 weeks, 1 day ago

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@Ram Mohith Cool video!

X X - 3 weeks, 1 day ago

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@X X Yes. I liked that so much that I framed the question based on that.

Ram Mohith - 3 weeks, 1 day ago

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@Ram Mohith Oh, I remember that one! (I loved that week because a lot of my solutions appeared in that week. )

X X - 3 weeks, 2 days ago

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@X X It's a Fact :

I have made a hatrick in June 9 - June 29 (3 weeks) as 3 of my problem continuously came in easy part of the POTW. Now again the chance has come for me. Last week and this week too two of my problems are featured. So, if luck favors next week to I can have a problem in POTW. I am thinking very hard on which question should I post the next.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith The sequel to the Mt Everest problem about pressure cookers?

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan Should see about it.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith Is it released yet?

Mohmmad Farhan - 3 weeks, 2 days ago

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@Mohmmad Farhan No. Still under construction. Before that one I have two more questions, Raising Balloons - 2 and Popping balloons which are yet to be released. After these two the sequel for My. Everest vs Mt K 2 will be released.

Ram Mohith - 3 weeks, 2 days ago

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@Ram Mohith OH!

Mohmmad Farhan - 3 weeks, 2 days ago

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@X X Ram Mohith and X X, both of you are excellent problem contributors, some of the best here. I hope I can reach your level!

Ekene Franklin - 3 weeks, 2 days ago

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@X X Yes, Vamprie Fan Club. It is were I had my first individual century. After that, the next week I had got 150 upvotes for my question Rising Balloons and the next week is a memorable for me, as I had my first double century for the question Counting 0's.

Ram Mohith - 3 weeks, 2 days ago

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@X X But I am not fully done. I expected that Number + Reciprocal will take me to 1 lakh (100 K) solvers. But it fell short of 7 K. But luckily this week too my question came in one of the problems of week (the first one) so it is confirmed that I will reach the milestone in one or two days.

Ram Mohith - 3 weeks, 2 days ago

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What is the remainder when \(1^{241} + 2^{241} + 3^{241} + 4^{241}\) is divided by \(5\)?

Ekene Franklin - 3 weeks, 5 days ago

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\(0\)

Mohmmad Farhan - 3 weeks, 3 days ago

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Of course that is the answer, but prove it.

Ekene Franklin - 3 weeks, 3 days ago

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@Ekene Franklin Since the divisibility rule of 5 only concerns the last digit, we have to find the last digits of the values. \(1^{124}\) is obviously 1. Since the repetition in the last digit is (for 2): 2, 4, 8, 6 then \(241 \div 4 = k (\text{Remainder}1\)) the first number is 2 (in this set). Apply this to the other powers. Summing the last digits, we get 10 and \(10 \div 5 = k (\text{Remainder}0)\)

Mohmmad Farhan - 3 weeks, 3 days ago

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@Mohmmad Farhan Excellent

Ram Mohith - 3 weeks, 3 days ago

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@Ram Mohith Great job. I did modular arithmetic during the examination.

Ekene Franklin - 3 weeks, 3 days ago

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@Ekene Franklin Me too

Syed Hamza Khalid - 3 weeks, 2 days ago

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Problem 3: \(20\) lines are drawn in a plane. What is the maximum number of parts into which the plane can be divided by the \(20\) straight lines?

Ekene Franklin - 3 weeks, 5 days ago

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There is a trick. First, take the 20th triangular number. \(\displaystyle\frac{20(20+1)}{2} = 210\) Add 1. \(210+1=211\) These numbers are known as pizza numbers and are always one more than a triangular number.

P.S. @EKENE FRANKLIN did you use this method?

Mohmmad Farhan - 3 weeks, 3 days ago

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Great! Just what I wanted, and what I used during the examination!

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin Thumbs Up!

Mohmmad Farhan - 3 weeks, 2 days ago

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I think it is \(211\)

Mohmmad Farhan - 3 weeks, 3 days ago

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Problem 2: What is the maximum possible area of a quadrilateral of sides \(1, 4, 7, 8\)?

Ekene Franklin - 3 weeks, 5 days ago

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Looks similar to:

https://brilliant.org/problems/hexagon-octagon-in-a-rectangle/?ref_id=1538063

Maybe a harder version perhaps! :D

Syed Hamza Khalid - 1 week, 6 days ago

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I think we should use the concept of maxima and minima.

Ram Mohith - 3 weeks, 5 days ago

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Perhaps you should solve it. I used the maximality condition of Bretschneider's formula. My answer was \(18\).

Ekene Franklin - 3 weeks, 5 days ago

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@Ekene Franklin What is that?

Manuj Rajpal - 1 week, 6 days ago

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@Ekene Franklin Yes I too got like that.

Ram Mohith - 3 weeks, 5 days ago

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Problem 1: A password consists of \(4\) distinct digits such that their sum is \(19\) and exactly two of its digits are prime, e.g. \(0397\). How many possible such passwords exist?

Ekene Franklin - 3 weeks, 5 days ago

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2,3: (2,3,6,8)

2,5: (2,5,4,8)

2,7: (2,7,4,6),(2,7,1,9)

3,5: x

3,7: (3,7,1,8),(3,7,0,9)

5,7: (5,7,1,6)

There are \(7\times4!=168\) possibilities

X X - 3 weeks, 2 days ago

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How did you get all possibilities?

Ekene Franklin - 3 weeks, 2 days ago

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@Ekene Franklin Find the 7 possibilities one by one, then times 24

X X - 3 weeks, 2 days ago

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Gearing up for today's 1st round olympiads!

Ekene Franklin - 3 weeks, 5 days ago

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Good luck!

B D - 3 weeks, 5 days ago

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Thanks. The results will be uploaded online in about 1.5 hours. Meanwhile I am posting them here for our consumption. Solve some, post solutions and invite others to do same!

Ekene Franklin - 3 weeks, 4 days ago

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@Ekene Franklin Maybe you can post them like problems.

B D - 3 weeks, 4 days ago

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@B D Ok.

Ekene Franklin - 3 weeks, 4 days ago

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How do I post numerical answer problems on Brilliant?

Ekene Franklin - 3 weeks, 6 days ago

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I think you have posted many problems in brilliant. However, when you are writng a question there will be two options, either Number or Multiple choice. You can select whatever you wish.

Ram Mohith - 3 weeks, 6 days ago

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@Mohmmad Farhan why can't you come here. I think this is a best place for a student like you. You can post your quires here.

Ram Mohith - 3 weeks, 6 days ago

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Sorry! I am not really active these days because of exams

Mohmmad Farhan - 3 weeks, 3 days ago

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Ok. No problem !!!

Ram Mohith - 3 weeks, 3 days ago

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Does anyone know how to post a solution of a problem that doesn't have a posted solution yet?

Ekene Franklin - 4 weeks ago

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If you got it correct you click the button "No solution" under Continue and write. And if you got it wrong you can't.

B D - 4 weeks ago

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Thanks a lot, bro!

Ekene Franklin - 4 weeks ago

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@Ekene Franklin You are welcome!

B D - 4 weeks ago

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Explain the Bohr theory of atoms, combining both mathematics and physics in your explanations.

Ekene Franklin - 4 weeks, 1 day ago

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Hi guys! For sure we all have noticed that the derivative of kinetic energy is momentum. Is there a physical explanation for this?

Ekene Franklin - 4 weeks, 1 day ago

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Quantitatively speaking, momentum is the product of mass of a body and its velocity. It is denoted by \(\overline{P}\). \[\large \overline{P} = m \overline{v}\] But the above definition is valid only when velocity of the body is constant. If the velocity of the body is variable we cannot use this formula and we should go by calculus. Physically speaking, momentum is the rate of change of kinetic energy with respect to its velocity. So, you ca say it as kinetic energy at that instance. Here is how we get \(\overline{P} = m \overline{v}\) from kinetic energy. \[K.E = \dfrac12 m (\overline{v})^2\] Now, differentiate both side with respect to velocity. We get : \[\dfrac{d}{dx} K.E = \dfrac{d}{dx} \left ( \dfrac12 m (\overline{v})^2 \right )\] As, we know \(\dfrac{d}{dx} K.E = \overline{P}\), we get : \[\overline{P} = \dfrac12 \cdot m \cdot 2 \overline{v}\] So, we get : \[\large \boxed{\color{blue} \overline{P} = m \overline{v}}\]

Ram Mohith - 4 weeks, 1 day ago

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Perfect bro!

Ekene Franklin - 4 weeks, 1 day ago

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@Ekene Franklin Thanks. But what I should say you, brother or sister

Ram Mohith - 4 weeks ago

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@Ram Mohith I am a young boy:)

Ekene Franklin - 4 weeks ago

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@Ekene Franklin Ok

Ram Mohith - 4 weeks ago

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\(I\ accidentally\ dropped\ the\ milk\ box\ (from\ paper)\ and\ it\ fell\ on\ cap\ even\ when\ I\ dropped\ with\ the\ bottom\ to\ the\ ground.\)

B D - 1 month ago

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Wow, that's funny. What did you mean?:)

Ekene Franklin - 4 weeks, 1 day ago

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Because I dropped it with the bottom to the ground I was wondering why it fell on cap.

B D - 4 weeks ago

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@B D Are you inviting physics?

Ekene Franklin - 4 weeks ago

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@Ekene Franklin Yes it is physics.

B D - 4 weeks ago

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@B D Can you give a shot at explaining it?

Ekene Franklin - 4 weeks ago

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@Ekene Franklin No. That's why I ask here.

B D - 4 weeks ago

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@B D The air in the box initiates a couple, whose direction depends on the side that has greater aerial density. Thus the block may either fall with its top or its bottom.:)

Ekene Franklin - 4 weeks ago

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\(\text{Doubt : 4}\)

In \((Si_4O_{12})^{8-}\), how many \(Si - O - Si\) linkages are there ?

Ram Mohith - 1 month ago

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What is the answer bro?:)

Ekene Franklin - 4 weeks ago

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It is 4.

Ram Mohith - 4 weeks ago

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@Ram Mohith I was actually sure of 4 linkages, but I was not sure of one more. Thanks anyways.

Ekene Franklin - 4 weeks ago

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@Ekene Franklin It's OK.

Ram Mohith - 4 weeks ago

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@Ram Mohith You are a great guy, Ram.

Ekene Franklin - 4 weeks ago

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@Ekene Franklin That's my quality quantitatively speaking.

Ram Mohith - 4 weeks ago

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@Ram Mohith My goal in many interactions is to make them frictionless. Trivially speaking, I resist every enmity and conduct friendliness. I have even successfully transmuted people from an angry ground state, to a happy excited state!

Ekene Franklin - 3 weeks, 6 days ago

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@Ekene Franklin Oh !!! That's good.

Ram Mohith - 3 weeks, 6 days ago

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@Ram Mohith Thanks. Ask if you want more!

Ekene Franklin - 3 weeks, 6 days ago

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I have an answer, but I am not totally sure it is correct. Coordination structure chemistry of silicates and silicones is my weakest point in chemistry. Perhaps I need to practise more!:)

Ekene Franklin - 1 month ago

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\(\text{Doubt : 3}\)

Uncertainty in position and momentum are equal. Then what will be the Uncertainty in velocity ?

Ram Mohith - 1 month ago

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I don't think uncertainty in position and momentum are relativistically equal. However, if a non-relativistic assumption is to be made, then from Heisenberg's, and taking p=mv, then uncertainty in velocity>=(h/2pi)X(1/(uncertainty in position X mass)). Sorry for the math ambiguity. My device doesn't type LaTeX.

Ekene Franklin - 1 month ago

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Yes you are correct. You got the correct answer. Regarding the latex you can keep it in \ (...\ ).

Ram Mohith - 1 month ago

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@Ram Mohith The LaTeX is not still working. It prevents me from posting some reeeeeeallly cool problems.;(

Ekene Franklin - 4 weeks ago

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\(\text{Doubt : 2}\)

In the following reaction : \[\large aNO_3^- + bCl^- + cH^+ \rightarrow dNO + eCl_2 + fH_2O\] find the value of \(\dfrac{a^2(b + c)}{d \times f}\)

Ram Mohith - 1 month ago

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Did you tried it. What is the answer you got.

Ram Mohith - 1 month ago

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Yeah, I solved it. My answer is 7.

Ekene Franklin - 4 weeks, 1 day ago

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@Ekene Franklin That's correct answer. Can you atleast keep the values of a,b,cd,e,f.

Ram Mohith - 4 weeks, 1 day ago

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@Ram Mohith a=2, b=6, c=8, d=2, e=3 and f=4

Ekene Franklin - 4 weeks, 1 day ago

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@Ekene Franklin Ok. Thanks i will check with mine.

Ram Mohith - 4 weeks, 1 day ago

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Simply balance the redox equation and substitute the stoichiometric coefficients of the balanced reaction into your expression.( I would have posted a solution if only my device could type LaTeX.)

Ekene Franklin - 1 month ago

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Ok. Try now after keeping it in \ (....) without spaces which will give you \(...\)

Ram Mohith - 1 month ago

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\(\text{Doubt : 1}\)

If the mole fraction of a solute is changed from \(\dfrac14\) to \(\dfrac12\) by adding some solute in the \(800~g\) of \(H_2O\) solvent, then what will be the ratio of molarity of the two solutions ?

Ram Mohith - 1 month ago

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I really like this note that is why I saved it!

B D - 1 week, 6 days ago

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Pls see my problem 'The Strange Angle' and also how to use latex

Manuj Rajpal - 2 weeks ago

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Here is a note how to use \(LaTeX\).

B D - 2 weeks ago

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Anyone knows some app for drawing geometry figures??

Manuj Rajpal - 2 weeks ago

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I want your help. I am trying to write a new problem but I got struck up at one point. Here is my doubt :

Suppose lets say a man jumps from a building with initial velocity \(u\). After \(x\) seconds another man freely falls from the same building and from the same height. Now, we can say that the displacement of both the man's are equal as they both reach the ground simultaneously after they jump from same point, so we can equate their distances. Here is what I did : \[ut + \dfrac12 gt^2 = \dfrac12 g(t - x)^2\] where \(t\) is the time taken by the first person to reach the ground. The main part of my doubt is that whether we should write the time taken by second person as \((t - x)\) or \((t + x)\).

What do you think @Blake Farrow , @Calvin Lin , @Danielle Scarano , @Brilliant Physics , @Pranshu Gaba, @Rohit Gupta and others ??

Ram Mohith - 2 weeks, 1 day ago

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It should be 't+a' as 1st man had jumped with velocity u so he will reach earlier than the freely falling man and it isn't necessary that the extra time 2nd man takes is equal to 'x'

Manuj Rajpal - 2 weeks ago

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Doesn't really matter, as long as you're clear on what the definition of "positive x" is. IE If you used \(t+x\) and then solved for \(x\) and got that it is negative, what is the interpretation?

In a similar manner, if we say that gravity acts downwards in the positive direction, then the "height at which the ball is thrown upwards" will (likely) be negative. Or vice versa.

Calvin Lin Staff - 2 weeks ago

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@Calvin Lin Yes. You are correct. I understood it now. Thanks for clarifying.

Ram Mohith - 2 weeks ago

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Hi guys !!! How is my note Square Root Of a Complex Number. It is a quite interesting and good technique to find square root of a complex number.

Ram Mohith - 2 weeks, 1 day ago

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Pls see my problem 'the blue one' and tell how I can make it look better.

Manuj Rajpal - 2 weeks, 2 days ago

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At the end of the question where you have kept Bonus there is a latex mistake I think. If you want it to be in bold letters you should keep in in between two * such that there is no space between * and the next letter or the previous one.

Ram Mohith - 2 weeks, 2 days ago

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How can I draw a figure for my question (on website in phone)?

Manuj Rajpal - 2 weeks, 2 days ago

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@Manuj Rajpal But if you want you can draw the figures in Microsoft, Paint or any other drawing apps and keep that picture.

Ram Mohith - 2 weeks, 2 days ago

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@Ram Mohith kk

Manuj Rajpal - 2 weeks, 2 days ago

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@Manuj Rajpal Any mobile app you know??

Manuj Rajpal - 2 weeks, 1 day ago

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@Manuj Rajpal We cannot draw a figure. We can only keep pictures or gif's.

Ram Mohith - 2 weeks, 2 days ago

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Do you know that brilliant staff has been removed the leader board from all the sets?

B D - 2 weeks, 4 days ago

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Really.

Ram Mohith - 2 weeks, 4 days ago

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Comment deleted 3 weeks ago

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The slashes your are using are wrong. It should be in the reverse direction like this \ (Exam) with no spaces between slash and bracket. You will get it as \(Exam\).

Ram Mohith - 3 weeks, 5 days ago

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Thanks a lot bro! You're awesome!

Ekene Franklin - 3 weeks, 5 days ago

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\(Ok\)

Ekene Franklin - 3 weeks, 5 days ago

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