Ekene Franklin's messageboard.

Feel free to discuss anything here with me friends! We're here to help each other!

Note by Ekene Franklin
4 months ago

No vote yet
1 vote

  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} \( \boxed{123} \)

Comments

Sort by:

Top Newest

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 months, 4 weeks ago

Log in to reply

Ok. Thanks and also are you writing that exam.

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

@Ekene Franklin Oh !!!

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

@Ram Mohith Are you also writing the olympiads soon?

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

@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 months, 4 weeks ago

Log in to reply

@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 months, 4 weeks ago

Log in to reply

@Ekene Franklin Yes. I may.

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

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 - 3 months, 2 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

@Ram Mohith Delhi ;-) and u??

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

@Manuj Rajpal Visakhapatnam, Andra Pradesh.

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

@Ram Mohith Is this screenshot from app?

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

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 - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

I personally think Brilliant should include a biology and biochemistry section. What do you think?

Ekene Franklin - 1 month, 4 weeks ago

Log in to reply

Yes.

B D - 1 month, 4 weeks ago

Log in to reply

Before brilliant used to have biology. But recently when the staff updated brilliant they removed biology topic due to lack of problems in that category.

Ram Mohith - 1 month, 4 weeks ago

Log in to reply

Actually I asked them to remove it, because the biology problems could not be seen in the community page. You can see Calvin Lin's messageboard.

X X - 1 month, 4 weeks ago

Log in to reply

@X X Calvin Lin's message board is currently unavailable. I searched for the website for a long time but in vain. Maybe he have locked it.

Ram Mohith - 1 month, 4 weeks ago

Log in to reply

@Ram Mohith Really? Here is the link. It's still available.

X X - 1 month, 4 weeks ago

Log in to reply

@X X But last time when I went it was locked

Ram Mohith - 1 month, 4 weeks ago

Log in to reply

yes

Brock Burggraff - 1 month, 3 weeks ago

Log in to reply

Here is a link of a biology problem.

B D - 1 month, 3 weeks ago

Log in to reply

Yes, but they cannot be found in the community page.

X X - 1 month, 3 weeks ago

Log in to reply

@X X I know. And there is no biology when you're making a problem.

B D - 1 month, 3 weeks ago

Log in to reply

@B D Previously there was, but they removed it.

X X - 1 month, 3 weeks ago

Log in to reply

@X X OK

B D - 1 month, 3 weeks ago

Log in to reply

Log in to reply

Hello Everyone !!! As this note has got some immense response from young students I would like to continue this further. But the problem is that this note is getting more and more comments day by day due to which the process of loading and opening any notifications is taking more time. So, on the request of @EKENE FRANKLIN any further discussion can be continued in the new note Brilliant young students messageboard

Ram Mohith - 1 month, 3 weeks ago

Log in to reply

\(\text{Doubt : 1}\)

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 - 4 months ago

Log in to reply

\(\text{Doubt : 2}\)

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 - 4 months ago

Log in to reply

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 - 4 months ago

Log in to reply

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

Ram Mohith - 4 months ago

Log in to reply

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

Ram Mohith - 4 months ago

Log in to reply

Yeah, I solved it. My answer is 7.

Ekene Franklin - 4 months ago

Log in to reply

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

Ram Mohith - 4 months ago

Log in to reply

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

Ekene Franklin - 4 months ago

Log in to reply

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

Ram Mohith - 4 months ago

Log in to reply

\(\text{Doubt : 3}\)

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

Ram Mohith - 4 months ago

Log in to reply

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 - 4 months ago

Log in to reply

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

Ram Mohith - 4 months ago

Log in to reply

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

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

\(\text{Doubt : 4}\)

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

Ram Mohith - 4 months ago

Log in to reply

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 - 4 months ago

Log in to reply

What is the answer bro?:)

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

It is 4.

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

@Ekene Franklin It's OK.

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

@Ram Mohith You are a great guy, Ram.

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

@Ekene Franklin That's my quality quantitatively speaking.

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

@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 months, 4 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 4 weeks ago

Log in to reply

@Ram Mohith Thanks. Ask if you want more!

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

Thanks guys. Keep sending problems and lets discuss!

Ekene Franklin - 4 months ago

Log in to reply

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 months ago

Log in to reply

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 months ago

Log in to reply

Perfect bro!

Ekene Franklin - 4 months ago

Log in to reply

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

Ram Mohith - 4 months ago

Log in to reply

@Ram Mohith I am a young boy:)

Ekene Franklin - 4 months ago

Log in to reply

@Ekene Franklin Ok

Ram Mohith - 4 months ago

Log in to reply

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

Ekene Franklin - 4 months ago

Log in to reply

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

Ekene Franklin - 4 months ago

Log in to reply

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 months ago

Log in to reply

Thanks a lot, bro!

Ekene Franklin - 4 months ago

Log in to reply

@Ekene Franklin You are welcome!

B D - 4 months ago

Log in to reply

@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 months, 4 weeks ago

Log in to reply

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

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

Ok. No problem !!!

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

How do I post numerical answer problems on Brilliant?

Ekene Franklin - 3 months, 4 weeks ago

Log in to reply

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 months, 4 weeks ago

Log in to reply

Gearing up for today's 1st round olympiads!

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

Good luck!

B D - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

@Ekene Franklin Maybe you can post them like problems.

B D - 3 months, 3 weeks ago

Log in to reply

@B D Ok.

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

How did you get all possibilities?

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

X X - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@Ekene Franklin Yes I too got like that.

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@Ekene Franklin What is that?

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

Looks similar to:

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

Maybe a harder version perhaps! :D

Syed Hamza Khalid - 3 months, 2 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

I think it is \(211\)

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@Ekene Franklin Thumbs Up!

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

\(0\)

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

Of course that is the answer, but prove it.

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@Mohmmad Farhan Excellent

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@Ekene Franklin Me too

Syed Hamza Khalid - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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

X X - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

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

X X - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

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

X X - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

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

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

@Mohmmad Farhan Should see about it.

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@Ram Mohith Is it released yet?

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@Ram Mohith OH!

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@Ram Mohith Cool video!

X X - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

Oh !!! Congrats.

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

@Calvin Lin

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@Ram Mohith Which list?

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@Ram Mohith Of course I want! Thanks!

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@Calvin Lin

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

@Calvin Lin.

B D - 1 month, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

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

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

10 years old. I told you

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@Ram Mohith I am! REALLY

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

I am going to be 5th grade

Mohmmad Farhan - 3 months ago

Log in to reply

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

Ram Mohith - 3 months ago

Log in to reply

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

Mohmmad Farhan - 3 months ago

Log in to reply

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 - 3 months ago

Log in to reply

BrilliantForLife

Dare you to toggle \(\LaTeX\)

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

X X - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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 - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

Is it 5^6?

X X - 3 months, 3 weeks ago

Log in to reply

Correct. Nice stuff. What did you do?

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@X X Bro, u are amazing

Syed Hamza Khalid - 3 months, 3 weeks ago

Log in to reply

DO YOU SERIOUSLY HAVE TO GIVE ME 46 NOTIFICATIONS OVERNIGHT!

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

I HAVE EXAMS

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@Ekene Franklin English EXAMS

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@Ram Mohith Andhra Pradesh, From Khammam

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

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

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

@Mohmmad Farhan Yes. I am born in Visakhapatnam.

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

Don't call me Mohmmad

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

@Mohmmad Farhan Sorry, but why?

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

@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 months, 3 weeks ago

Log in to reply

@Mohmmad Farhan Mohammad Farhat

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

@Ram Mohith YES! FINALLY!

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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

X X - 3 months, 3 weeks ago

Log in to reply

@X X I don't bother

Mohmmad Farhan - 3 months, 3 weeks ago

Log in to reply

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 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 3 weeks ago

Log in to reply

Congratulations!

X X - 3 months, 3 weeks ago

Log in to reply

Do you know the minimum people to reach?

B D - 3 months, 2 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

@Ram Mohith Yes he is.

X X - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

@Ram Mohith OK. Thanks!

B D - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

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

X X - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

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

X X - 3 months, 2 weeks ago

Log in to reply

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

X X - 3 months, 2 weeks ago

Log in to reply

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

Manuj Rajpal - 3 months, 2 weeks ago

Log in to reply

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 - 3 months, 3 weeks ago

Log in to reply

First option.

Ekene Franklin - 3 months, 3 weeks ago

Log in to reply

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

Ram Mohith - 3 months, 2 weeks ago

Log in to reply

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

Ekene Franklin - 3 months, 2 weeks ago

Log in to reply

@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 - 3 months, 2 weeks ago

Log in to reply

@Ram Mohith I thought as much.

Ekene Franklin - 3 months, 2 weeks ago

Log in to reply

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 - 3 months ago

Log in to reply

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

Mohmmad Farhan - 3 months ago

Log in to reply

@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 - 3 months ago

Log in to reply

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

X X - 3 months ago

Log in to reply

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 - 3 months ago

Log in to reply

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

Ram Mohith - 3 months ago

Log in to reply

@Ram Mohith OH!

Mohmmad Farhan - 3 months ago

Log in to reply

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

Mohmmad Farhan - 3 months ago

Log in to reply

@Mohmmad Farhan Good one.

Ram Mohith - 3 months ago

Log in to reply

Hello guys! Which of my recent problems did you like the most?

Ekene Franklin - 3 months ago

Log in to reply

To be honest, this note has been quiet for a while

Mohmmad Farhan - 2 months, 2 weeks ago

Log in to reply

Yup

B D - 2 months, 2 weeks ago

Log in to reply

Hi guys. Why can't we together contribute to some wiki's. At present I am working on Heat Transfer, Types of Matrices, JEE Complex Numbers, Midpoint of a Line Segment and Section Formula. I need some help to build them so why can't you join me ad show brilliant the power of young students. If you have any such wiki's to build please share them to and I will try my best to contribute them. Thank You !!!

Ram Mohith - 2 months, 1 week ago

Log in to reply

You keep on changing the topic of your problems and they keep on resurging and I have to say: It is quite annoying

Mohmmad Farhan - 2 months, 1 week ago

Log in to reply

I didn't get your point. Are you asking anything about my set.

Ram Mohith - 2 months, 1 week ago

Log in to reply

@Ram Mohith No. It is about the 'new' community problems

Mohmmad Farhan - 2 months, 1 week ago

Log in to reply

OH. You are saying about me reposting the problems again and again. What to do ? It's my natural habit that I want all of them to see and solve my problems. Man is made up of desires and everybody have their own desires. You cannot stop them and they go on flowing continuously.

Ram Mohith - 2 months, 1 week ago

Log in to reply

@Ram Mohith What will you then say of those who have solved it before?

Ekene Franklin - 2 months, 1 week ago

Log in to reply

@Ekene Franklin What they can do ? They will just leave it off. If all are having problem of me reposting problems then I will stop it. Don't make this as a big issue.

Ram Mohith - 2 months, 1 week ago

Log in to reply

@Ram Mohith Blan Morrison agrees with me and Ekene Franklin

Mohmmad Farhan - 2 months, 1 week ago

Log in to reply

@Mohmmad Farhan He says that this not a big issue.

Ram Mohith - 2 months, 1 week ago

Log in to reply

I will do what I can.

Ekene Franklin - 2 months, 1 week ago

Log in to reply

Thank you.

Ram Mohith - 2 months, 1 week ago

Log in to reply

Hello guys. I just completed the second stage of my country's olympiads. Much more difficult.

Ekene Franklin - 2 months, 1 week ago

Log in to reply

Good for you.

B D - 2 months, 1 week ago

Log in to reply

Um, Ram, I think I need some clarification on your problem 'Competition in Leaf'. Transpiration occurs on the upper part, right? So cobalt (II) chloride should come in contact with more water.

Ekene Franklin - 2 months, 1 week ago

Log in to reply

No. Stomata is present on the lower surface of leaf and hence more transpiration will occur from lower surface. Search in internet if you want.

Ram Mohith - 2 months, 1 week ago

Log in to reply

But this is the case in dicots only. In monocots, it is on both surfaces

Manuj Rajpal - 2 months, 1 week ago

Log in to reply

@Manuj Rajpal Exactly, Manuj.

Ekene Franklin - 2 months, 1 week ago

Log in to reply

@Manuj Rajpal Ok. I will edit the question accordingly. Thank you.

Ram Mohith - 2 months, 1 week ago

Log in to reply

@Ram Mohith You are welcome.

Ekene Franklin - 2 months, 1 week ago

Log in to reply

Hello, I have been off from Brilliant for a month as my sports championships were coming close.

And I have term tests starting in a fortnight so I have to pack my self up. Similarly, my IGCSE ICT exam is coming closer.

However, I have a doubt in one of the questions of IGCSE Further Pure Mathematics... Can you help?

Q) a) Show that \[ \displaystyle a^3 - (a - 1)^3 \equiv 3a^2 - 3a + 1 \\ \implies \color{blue} \text{ I know how to do this. But the next one uses this, so I have given here. }\]

b) Hence show that

\[ \displaystyle \sum_{r=1}^{n} { r^3 - (r - 1)^3 } = 3 \sum_{r=1}^{n} r^2 - \dfrac{1}{2} (3n^2 + n) \]

c) Show that

\[ \displaystyle \sum_{r=1}^{n} { r^3 - (r - 1)^3 } = n^3 \]

d) Hence deduce that

\[ \displaystyle \sum_{r=1}^{n} r^2 = \dfrac{1}{6} n(n+1) (2n+1) \]

Please help me from (b) onwards.

Syed Hamza Khalid - 2 months ago

Log in to reply

Isn't last one n(n+1)(2n+1)/6

Manuj Rajpal - 2 months ago

Log in to reply

Yeah he probably forgot...

James Bacon - 2 months ago

Log in to reply

@James Bacon Yes; my bad

Syed Hamza Khalid - 1 month, 4 weeks ago

Log in to reply

(b)

\(r^3-(r-1)^3=3r^2-3r+1\)

\(\displaystyle\sum_{r=1}^n (r^3-(r-1)^3)=\sum_{r=1}^n(3r^2-3r+1)\)

\(\displaystyle\sum_{r=1}^n (r^3-(r-1)^3)=\sum_{r=1}^n 3r^2-3\sum_{r=1}^n r+\sum_{r=1}^n 1\)

\(\displaystyle\sum_{r=1}^n (r^3-(r-1)^3)=\sum_{r=1}^n 3r^2-3\times\frac{n^2+n}2+n\)

\(\displaystyle\sum_{r=1}^n (r^3-(r-1)^3)=3\sum_{r=1}^n r^2-\frac{3n^2+n}2\)

(c)

\(\displaystyle\sum_{r=1}^n (r^3-(r-1)^3)\)

\(=\displaystyle\sum_{r=1}^n r^3-\sum_{r=1}^{r=n} (r-1)^3\)

\(=\displaystyle\sum_{r=1}^n r^3-\sum_{r-1=0}^{r-1=n-1} (r-1)^3\)

\(=\displaystyle\sum_{r=1}^n r^3-\sum_{r=0}^{n-1} r^3\) (Change \(r-1\) to \(r\))

\(=\displaystyle(\sum_{r=1}^{n-1} r^3+n^3)-(0^3+\sum_{r=1}^{n-1} r^3)\)

\(=n^3\)

(d)

According to (b) and (c),

\(\displaystyle\sum_{r=1}^n (r^3-(r-1)^3)=3\sum_{r=1}^n r^2-\frac{3n^2+n}2\)

\(n^3=3\displaystyle\sum_{r=1}^n r^2 -\frac{3n^2+n}2\)

\(\displaystyle n^3+\frac{3n^2+n}2=3\sum_{r=1}^n r^2\)

\(\displaystyle\frac{2n^3+3n^2+n}2=3\sum_{r=1}^n r^2\)

\(\displaystyle\frac{2n^3+3n^2+n}6=\sum_{r=1}^n r^2=\frac{n(n+1)(2n+1)}6\)

X X - 2 months ago

Log in to reply

In this how does this happen, isn't it supposed to be 1?

Syed Hamza Khalid - 1 month, 4 weeks ago

Log in to reply

@Syed Hamza Khalid It means that you are adding 1 n times so it will be like, (1 + 1 + 1 + .... n~times \ \implies n (1) = n]

Ram Mohith - 1 month, 4 weeks ago

Log in to reply

@Ram Mohith Oh okay thx a lot

Syed Hamza Khalid - 1 month, 4 weeks ago

Log in to reply

Similarly, I don't understand the blue, red, green and yellow highlighted stuff

Syed Hamza Khalid - 1 month, 4 weeks ago

Log in to reply

@Syed Hamza Khalid The first red box is just like we write r=1 down, we write r= n up (blue) Second red box, down as r =1,r-1=0 and up(blue) , r=n therefore r-1=n-1 Yellow box, वे take the upper limit as n-1 and add n^3 in first and add 0^3 to make the lower limit as 1 in second Green : still thinking

Manuj Rajpal - 1 month, 4 weeks ago

Log in to reply

@Syed Hamza Khalid You can do it as : r^3 - (r-1)^3 = (r-r+1)(r^2+(r-1)^2+r(r-1)). (using a^3-b^3 identity)

So it will become §(3r^2 - 3r - 1) = 3§r^2 - 3§r - § 1

= 3n(n+1)(2n+1)/6- 3n(n+1)/2 - n

=n^3

Sorry i didn't have submission sign so I used §