# Prasun Biswas' Messageboard

Well... since everybody is making their messageboards, I thought I should make one too.

P.S - I don't think that anybody's gonna comment here anyway. Haha..

Note by Prasun Biswas
6 years, 7 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

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Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
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2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
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\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

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Hi Prasun , I'm AA from slack. In case you want to know how me psoting the problem with the hyperqueens again went know that the staff or rather Calvin was smart enough to ban me as immediate as i went online on slack haha.

Of course i posted the problem pretty much with the same text as yesterday which was clear enough as you said. Nonetheless clarity or reason doesn't seem to be anything which I can attribute to Calvin so I suppose he will not agree but that wouldn't really matter since I am right about that problem anyway. Therefore there is no problem with me being banned by idiots. The fact that I am right and anybody would approve is enough to say so to me anyway.

- 4 years, 9 months ago

How's life?

Have you ever attempted RMO? Have you qualified for it?

- 6 years ago

Swapnil I think you have great interest in Physics right ?

Yes! You are right! But maths too!

- 6 years ago

So Swapnil do you have interest in black holes and quantum physics and also string theory?

Yes, in future I want to specialize in string theory and build the theory of everything.

- 6 years ago

Nope. I heard about RMO the first time just a year ago when I was already in class 12. It was until 2013 that even class 12 students were eligible to attempt for RMO but that changed in 2014 when class 12 students were no longer eligible to attempt for RMO. As a result, I never got the chance to attempt for RMO, let alone qualify for it.

In any case, I'm not good with olympiads and stuff. I'm not good with exams. Time limits scare me. :|

It's a good thing I never did attempt for RMO. I probably wouldn't have qualified for it anyway.

- 6 years ago

So you want to become a mathematician?

- 6 years ago

Sure, I'd like that to happen in the near future. But, to be honest, I wonder whether I'll get that opportunity (i.e., to go into research). It's hard to do that in India, given the current socio-economic conditions of the country. Mathematical research isn't well funded here compared to most of the other countries (in my opinion).

- 6 years ago

Please solve all my doubts on this

- 6 years, 4 months ago

Hi , I know that it's not in tomorrow's test but can you tell me how do you memorise the different values of $\sin^{-1} ( sinx)$ ?

- 6 years, 4 months ago

First of all, sorry for replying late. The thing is, my internet connection is screwed up for now and hence I'll be less active than usual for the next few days. I'm currently in a cyber cafe.

Now, coming onto your question, why would anyone memorize the values of $\arcsin(\sin x)$ ? There is a nice way to calculate the values. You simply need to understand 2 things first: (1) the function $g(x)=\arcsin(x)$ is the inverse function of $f(x)=\sin(x)$ and, (2) Since invertible functions are bijections, the domain and range are set in such a way that the domains and ranges are continuous as well as they form bijections.

$\bullet\quad\arcsin(\sin x)=x~,~\textrm{iff } x\in \left[-\frac{\pi}{2},\frac{\pi}{2}\right]\\ \bullet\quad\sin(\pi-x)=\sin x\\ \bullet\quad\sin(-x)=-\sin(x)$

There is a trick to remembering some of these identities. Just remember the following form ($x$ is acute and $n$ be a positive integer):

$\sin\left(n\cdot\frac{\pi}{2}\pm x\right)=\begin{cases}\sin x~,~\textrm{if } n\textrm{ is even and the total angle in the parameter falls on 1st or 2nd quadrants}\\ -\sin x~,~\textrm{if } n\textrm{ is even and the total angle in the parameter falls on 3rd or 4th quadrants}\\ \cos x~,~\textrm{if } n\textrm{ is odd and the total angle in the parameter falls on 1st or 2nd quadrants}\\ -\cos x~,~\textrm{if } n\textrm{ is odd and the total angle in the parameter falls on 3rd or 4th quadrants}\end{cases}$

A question naturally comes to find. Why $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ ? Why not any other interval? The answer is simple. We need a continuous domain for $f(x)=\sin x$ or (say) a continuous range for $f(x)=\arcsin(x)$ that can produce all possible values that repeat over the entire reals. Simply observing the graph of $f(x)=\sin x$ shows that the selected interval is the best. Some may say, why not $\left[\frac{\pi}{2},\frac{3\pi}{2}\right]$ ? It produces the same result too. The answer for that is also simple and straightforward. We try to find ranges for trigonometric functions within the principal range $[-\pi,\pi]$ so as to keep it simple.

If you say, I can provide some worked out examples later, but I won't be much active for the next few days till my internet connection is up and running again.

- 6 years, 4 months ago

First of all thanks for giving me these tips :)

Also I do feel bad for you since you have to go to a Cyber Cafe! Btw I'm too in the same boat as you , it's just a few hours ago that I utilised 90% speed of my Internet connection .

- 6 years, 4 months ago

Can you solve this? (This is one of my best problems)

- 6 years, 4 months ago

Is this some kind of joke ?

- 6 years, 4 months ago

Yes! I was just checking if Prasun would comment or not .

Ofc , this is not a joke . I just wanted to know if there are any other interesting ways to memorise those values (currently I use the Graph to memorise it) .

- 6 years, 4 months ago

You use graphs to memorize values of $\arcsin(\sin{x}) = x$

- 6 years, 4 months ago

I've provided you pics related to it . View them first .

- 6 years, 4 months ago

Is that a photo of some booklet of some iit coaching class ? Seems so

- 6 years, 2 months ago

yes .

- 6 years, 2 months ago

PACE?

- 6 years, 2 months ago

No , it's from the question booklet of IIT Ashram . But I'm sure even they have copied it from somewhere , one day they'll be caught for copyright infringements .

Those guys have a long history of copying things off other institutes's books .

- 6 years, 2 months ago

Does $\sin^{-1}$ mean $\arcsin{x}$

- 6 years, 4 months ago

Yes

- 6 years, 4 months ago

I can't believe I wasn't able to solve this.
A person picked up 13 cards from 52 cards. Find Probability that he has no ace , Probability that he has exactly one ace ?
Please solve this $\ddot\smile$

- 6 years, 4 months ago

Are the cards drawn with replacement, i.e., are the cards refilled after each draw?

- 6 years, 4 months ago

NO.

- 6 years, 4 months ago

https://brilliant.org/problems/inclined-string-on-an-incline-plane/?group=wKzP6vIjZN6D&ref_id=662387

Can you take a look at this problem. I resolved the force and got the answer as $98 \times \cos45 \times cos25$ but in reality it was $\frac{98 \times \cos45}{\cos25}$

I'm still not getting how is it so.

- 6 years, 4 months ago

Its very easy. I will tell you it later on. Busy right now.

- 6 years, 4 months ago

oh..k

- 6 years, 4 months ago

The solution is here.

If in future doubts comment there.

- 6 years, 4 months ago

Got it brother.

- 6 years, 4 months ago

Check this out!

Do re-share and participate.

- 6 years, 4 months ago

Please tell me are you really 16 ??

And besides, in which standard do you read brother.... ??

And yes, I'm asking this just because I'm of your age and unable to understand many of your solutions.. I've not even studied them yet. I'm just curious about your knowledge attainment. :)

- 6 years, 4 months ago

First of all, yes, I'm 16. To be precise, I'm 16 years 10 months old as of today and am studying in class 12 of the academic year 2014-15. Just for the record, my board exams are going on. That's the reason that I'm less active for the time being and am replying to your comment now. Sorry for the late reply though. :)

Second of all, are you being sarcastic? Because I don't think I have any knowledge whatsoever. I just implement methods which I learnt by scouring the Internet for resources, etc in solving problems. Almost anyone who puts even a bit of self-effort into learning stuff can do that.

And finally, which solutions of mine are you unable to understand? If you can't understand a part, I expect you to make a comment there. The members of this community (including me) are always there to help others. :)

- 6 years, 4 months ago

Oh..kk well i found the reason why I'm really unable to understand some of your solutions. Actually I'm (precisely like you :D) 16 years 7 months but still in 10th standard and I'm giving my boards too.

And apology accepted brother. In reality I was thinking that you're not gonna reply 'cause I didn't get any notification for two days.

Plus, I'm not being sarcastic man. I was really amused that if you're of my age and studying in same standard then it is an exceptional case that you can solve Level 4 and 5 questions.

I'm working to get through the problems which I'm facing. I too scour the internet and I'm trying to learn some new concepts including calculus.

Last thing, you have knowledge dude. You were the first person I followed on Brilliant.org and I've even given my fellows your example of how you despite being of our age group have a far better knowledge.

- 6 years, 4 months ago

Man, this is embarrassing. You guys flatter me way too much, much much more than what I deserve.

Anyway, you can mention the solutions you didn't understand here. I'll try my best to make it clear. Also, always keep in mind that your age and class doesn't determine how good you are at problem solving. Just practice as much as possible and enjoy math!

Interesting fact, when I was in class 11, I wasn't even half as smart as you are currently.

- 6 years, 4 months ago

Hey hey.. I'm not flattering you I'm just expressing what I think.

I get some problem in Combinatorics and Number Theory. I've leaned much in these topics after joining this site but still I want some sets of problems so that I can practice particular type of problems together and hence I'll be in a habit of solving those problems.

I write any new thing which I learn, but you know that's not enough. Without solving a good deal of questions we cannot learn something.

- 6 years, 4 months ago

I noticed that your message boards empty , don't worry dude , I'll help you fill it up like I did it with my friend Deepanshu Gupta 's message board !

- 6 years, 4 months ago

Haha, don't bother. I don't really care about my messageboard. I made it just because everybody else were making one for themselves. I spend most of my time in Facebook and so I mostly chat with my friends there. I rarely check this messageboard anyway.

- 6 years, 4 months ago

Could you help me fill up my contest with many participants.

- 6 years, 4 months ago

I just reshared it , I'll do it again tomorrow . You see finding people to participate is difficult , since I can't force them to do so . I'll keep on resharing your note , that's the only thing that I can do right now :)

- 6 years, 4 months ago

Could you reshare my note again ?

- 6 years, 4 months ago

I have done it :)

- 6 years, 4 months ago

Thanks a lot !

- 6 years, 4 months ago

:)

- 6 years, 4 months ago

Check tis out!

- 6 years, 4 months ago

@Prasun Biswas Pls help in the unawersed questions and check my solution in which i have tagged you. Go on my question board.

- 6 years, 5 months ago

I'll try to help as much as I can. But I may not be much active here for a while because my board exams are nearing.

- 6 years, 5 months ago

hey!do you like S.S.T?

- 6 years, 6 months ago

S.S.T? Do you mean "Social Studies"?

- 6 years, 6 months ago

yep!

- 6 years, 6 months ago

In that case, my answer would be: $\Large \text{HELLS NAW!}$

If you'd like that in binary, then here goes: 01001000 01000101 01001100 01001100 01010011 00100000 01001110 01000001 01010111

- 6 years, 6 months ago

I don't like it either!

- 6 years, 6 months ago

- 6 years, 6 months ago

What drives you to do Math?

- 6 years, 7 months ago

Well, I do math just because I love doing it. There's no other reason whatsoever!

- 6 years, 7 months ago

Could you please check up this problem and give me the solution. Question

- 6 years, 2 months ago

Well, first of all, that isn't your posted problem. Secondly, I can see you haven't solved it yourself. If I gave you a solution here, wouldn't that be cheating?

- 6 years, 2 months ago

When did i say i posted that question.. ? post your solution on that question itself then it wont be a cheatin ryt?

- 6 years, 2 months ago

But there's already a solution posted there.

- 6 years, 2 months ago

Is it ryt? Please check and tell na?

- 6 years, 2 months ago

Hmm, I am commenting here. :P......A few questions for you. Why do you feel that Math doesn't love you? What would you call your "claim to fame"? Why is your stance on most issues a "controversial" one? (To say, the LGBT one)What do you aspire to become in the future? and the final , 5th one:- "Do you like carrots" XD .... HAVE A GREAT TIME ANSWERING THESE.

- 6 years, 7 months ago

Answering that second question of yours took a lot of time. The rest took only a few minutes. xD

- 6 years, 7 months ago

1) Because it doesn't.

2) Achieving a Fields medal someday. $[$Probability of this event $=P=\displaystyle \lim_{x\to \infty} \dfrac{1}{x}]$

3) Because I love pissing people off. In fact, that's what I do most of the time on Facebook or 9GAG or Omegle :3

4) Future? What's that? A new Pokemon that I haven't heard of?

5) Yeah... I can eat almost anything that's edible, given that it's cooked properly.

- 6 years, 7 months ago

Awesome. I loved the answers to #1) and #4). Your answer to #2) doesn't make any sense because "claim to fame" refers to something which you have already achieved! My question was what would you call as your claim to fame, and not what would you want to be called as your claim to fame.

- 6 years, 7 months ago

Ooh, sorry for that. Damn my poor sense of English! Anyway, the answer to your question #2 would then be, "Absolutely nothing, because I haven't done anything worthwhile in my entire life till now."

- 6 years, 7 months ago

XD. I would've answered the same too :P

- 6 years, 7 months ago

Nobody likes to praise himself except politicians, etc.

There are exceptions you know... for them there's a idiom in Hindi

"Apne muh miya miththu" :D

And that's the base reason why most people don't like to praise themselves or their achievements. :)

- 6 years, 4 months ago

Oh Really?!

- 6 years, 7 months ago

Yes.

- 6 years, 7 months ago