Welcome to RadMaths! We will update popular maths problems and discussions to help you learn, think more and advance in Maths.
Science(and programming!) to be included in MadScience :)
MATHATHON by Percy Jackson
Mathathon 2020
Mathathon 2021

COURSES:
Calculus
Science

Problems:

Discussions:

Formatting:

• Brilliant
• Percy Jackson
• Páll Márton (A Former Brilliant Member)

Note by Jeff Giff
11 months, 3 weeks 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.
• Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. 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 1paragraph 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} $\boxed{123}$

Sort by:

- 4 months, 2 weeks ago

It doesn't work.

- 4 months, 2 weeks ago

But it is working in my PC Right now!

- 4 months, 2 weeks ago

Ya, it works now, I submitted :)

- 4 months, 2 weeks ago

Nice and very simple quiz

$10/10$ for the interesting thought for making the question

- 4 months, 2 weeks ago

Ah but I can’t access it in mainland China :P

- 4 months, 2 weeks ago

A new one!

- 4 months, 2 weeks ago

- 4 months, 2 weeks ago

I suppose I’m the only person still awake yet I cannot access to Google! :P

- 4 months, 2 weeks ago

Nice quiz! Can you tell me how to solve the second last one? Rest of them felt like I have seen them somewhere in Physics, even though I haven't learnt them in math! Especially the last one, it reminded me directly of equation of a wave. Guessed a few by elimination.

- 4 months, 2 weeks ago

Solution of second last one (with standard notations) : $b_{n+1}=b_n(\frac{1}{a}-n)$ $=b_{n-1}(\frac{1}{a}-(n-1))(\frac{1}{a}-n)$ $=(\frac{1}{a}-n)(\frac{1}{a}-(n-1))...(\frac{1}{a}-1)\frac{1}{a}=\prod_{k=0}^{n}(\frac{1}{a}-k)$ $\Rightarrow b_{n+1}=\prod_{k=0}^{n}(\frac{1}{a}-k)$ $\therefore b_{n}=\prod_{k=0}^{n-1}(\frac{1}{a}-k)$ $\Rightarrow b_na^n=a^n\prod_{k=0}^{n-1}(\frac{1}{a}-k)$ $=\prod_{k=0}^{n-1}a(\frac{1}{a}-k)$ $=\prod_{k=0}^{n-1}(1-ak)$ $\therefore\lim_{a\to 0} b_na^n=\lim_{a\to 0} \prod_{k=0}^{n-1}(1-ak)$ $=\prod_{k=0}^{n-1}\lim_{a\to 0}(1-ak)=\prod_{k=0}^{n-1}1=1$ $\therefore\lim_{a\to 0}b_na^n=1$ $\therefore \red{\lim_{a\to 0}\frac{b_na^n}{n!}}=\frac{1}{n!}$ $\lim_{a\to 0}\sum_{n=0}^{\infty}\frac{b_na^n}{n!}=\sum_{n=0}^{\infty}\red{\lim_{a\to 0}\frac{b_na^n}{n!}}$ $=\sum_{n=0}^{\infty}\frac{1}{n!}=e$

- 4 months, 1 week ago

Wow! Wonderful to see how it collapses after the limit! Loved the solution! :)

- 4 months, 1 week ago

Could any of you make this a quiz or problem set on brilliant? Thanks!

- 4 months, 1 week ago

- 4 months, 1 week ago

@Jeff Giff - You can use buttons in RadMaths to make it more rad. See my note Buttons to learn button formatting :)

- 10 months, 2 weeks ago

I used it in anther note :) I don’t think it is necessary to add buttons here :)

- 10 months, 2 weeks ago

Hi @Tomislav Franov , your problem set has been included to this note! Good job! :)

- 1 month, 1 week ago

Hi, thank you so much!!!

- 1 month, 1 week ago

Nice, @Jeff Giff

- 11 months, 3 weeks ago

What about my Recurring Proof Notes? You think they are useful to your note, @Jeff Giff?

- 11 months, 3 weeks ago

@Jeff Giff- Try my A Pre-RMO question! series, Math also Fails! series.

- 11 months, 3 weeks ago

That's a definite one for @Jeff Giff to try - the Pre-RMO questions.

Also, RMO stands for...?

- 11 months, 3 weeks ago

By the way, try this for Math Also Fails - $e^{i\pi} =-1, (e^\pi)^i =-1,$ then $i=\log_{e^\pi} -1?!$

- 11 months, 3 weeks ago

No actually, definition of log clearly states that $log_ab$ is defined only when

• $a \gt 0 and a \neq 1$

• $b \gt 0$

- 11 months, 3 weeks ago

Well it is correct, and not surprising if you know the Taylor series of $\ln$ and this

- 11 months, 3 weeks ago

If you want a big and detailed explanation you can ask for that (can even write a note!)

- 11 months, 3 weeks ago

Oops.. that’s logarithm for negative numbers :/

- 11 months, 3 weeks ago

Good idea! I’ll add them :)

- 11 months, 3 weeks ago

@Jeff Giff, Thanks for the mention for my $\LaTeX{}$ Guide but, it is a work in progress and I can suggest you better ones - Daniel Liu's Guide and Hamza Anushath's Guide.

- 11 months, 3 weeks ago

Ok! Thanks!

- 11 months, 3 weeks ago

Thanks for the mention of Mathathon 2020 too!

- 11 months, 3 weeks ago

And please add mine too @Jeff Giff (I am Hamza Anushath)

- 11 months, 3 weeks ago

@Hamza Anushath - He still didn't add your Latex note, LOL

Yeah, it has been two weeks @Percy Jackson @Jeff Giff

- 11 months ago

Correction - 2 weeks and 3 days LOL

Mathathon started, start posting solutions @Hamza Anushath

Yeah, if I post solutions for past questions, will I still get points @Percy Jackson

Deduct five points from the total due to late submission if you'd like as well

- 11 months ago

Cuz I didn't see the Mathathon problems till just now @Percy Jackson...

- 11 months ago

No deduction for past questions go post the solutions!

Thnx @Percy Jackson!

- 11 months ago

Try my When two lines meet series, it is a series of hard questions for learning to solve questions using graph. Is this useful for your note?

- 11 months, 3 weeks ago

@Jeff Giff Add this sreies also, of @Aryan Sanghi

- 11 months, 3 weeks ago

Thanks a lot @Zakir Husain

- 11 months, 3 weeks ago

Thanks to @Jeff Giff for adding this in the note

- 11 months, 3 weeks ago

Yes, @Jeff Gift great initiative this is like Percky Jackson.

- 11 months, 3 weeks ago

@Jeff Giff Also try to add polyfon series by @Aryan Sanghi

- 11 months, 3 weeks ago

Yes,thanku. I'll try to make the polyfun series more vast by adding more problems to it.

- 11 months, 3 weeks ago

@Jeff Giff- Kindly mention this note instead of my feed for Pre-RMO question series.

- 11 months, 3 weeks ago

👌 OK!

- 11 months, 3 weeks ago

@Jeff Giff, could you $\color{#333333}\text{add my note}$ too as a $\LaTeX$ guide, it has many new facts and features which may only have been mentioned by me

- 11 months, 3 weeks ago

Click the $\text{add my note}$ to access my note @Jeff Giff

- 11 months, 3 weeks ago

@Jeff Giff, if you need anything from me, check out my profile and choose the series (i.e. if you choose one problem, you have to have the rest of the problems with that title.)

- 11 months, 2 weeks ago

@Jeff Giff - Kindly add this in RadMaths ''Late Events''

- 11 months, 2 weeks ago

@Jeff Giff Thanks!

- 11 months, 1 week ago

Check this out, @Páll Márton :)

- 11 months ago

Thank you!

- 11 months ago

Wowie!!!!!! RadMaths has become even better! Good work @Jeff Giff! You'll have to organize it a bit though, like removing the Mathathon as it is over, adding more space between 2 different series, etc.

@Jeff Giff it is Vinayak Srivastavsa not Yinayak @Vinayak Srivastava ?

- 11 months ago

Yes @Jeff Giff!

- 11 months ago

Uh oh. Typo ^@^

- 11 months ago

@Jeff Giff, check out this:

- 11 months ago

@Jeff Giff you might like to add my Coordinate geometry series. All of its questions are popular and level 5. :)

- 8 months, 4 weeks ago

The link is level 4 actually lol

- 8 months, 3 weeks ago

Yes, this question didn't live to the expectations, but it's atleast popular. :)

- 8 months, 3 weeks ago

Yes, it is a very good problem. I like all your problems, they are new and different, pretty cool according to me.

- 8 months, 3 weeks ago

Thanku very much for your appreciation. :)

- 8 months, 3 weeks ago

@Jeff Giff, I think the actual PRMO discussion is this, so please change the link, that one has only sample questions. :)

- 4 months, 1 week ago

very nice collection. thank you

- 4 months ago

Hey everyone! I just found a way to nest buttons!!! All we have to do is to quote in a button and make a button in the quote! Only we can’t nest tables :( @Frisk Dreemurr , @Yajat Shamji
Test: (Failed)

[[show-hide-button|+]] [[start-hidden]] whoa I can button comments [[end-hidden]]

- 3 months, 3 weeks ago

Páll Márton would love this awww... but he is removed :(

- 3 months, 3 weeks ago

You used > to make a quote right

- 3 months, 3 weeks ago

How did you make it, I can create the nested button but can’t hide stuff in it

- 3 months, 3 weeks ago

Oh I forgot! You have to put the nested button frame behind the last button instead of in it :P I found that by accident actually and it turns out you can’t put line breaks though :)

- 3 months, 3 weeks ago

Is it okay if I remake this note to make it more... accessible? I will give credit + link to this note as well if you do

- 3 months, 3 weeks ago

Ok :) but a better way would be to link this note in the daily problem solutions :) or would you just want the code for this note?

- 3 months, 3 weeks ago

You see, num IC has accessed this note from my daily solution :)

- 3 months, 3 weeks ago

Look:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Welcome to RadMaths! We will update popular maths problems and discussions to help you learn, think more and advance in Maths. **_[list of 1000 primes](https://brilliant.org/discussions/thread/list-of-primes/)_** **_COURSES:_** [Calculus](https://brilliant.org/discussions/thread/calculus-notes/?ref_id=1610121) **_LATE EVENTS:_** [approximating a slice of pi](https://brilliant.org/discussions/thread/least-operations-and-numbers-possible/?ref_id=1610787) [simplifying trigonometric values into (nested) radicals](https://brilliant.org/discussions/thread/how-to-find-trigonometric-values-that-radical/) **Problems:** *- Alice Smith* 1. [SAT 1000 series](https://brilliant.org/discussions/thread/sat-1000-problems-series-upcoming-frequently/) 2. [Luogu series](https://brilliant.org/discussions/thread/luogu-problem-set/) 3. [reach the summit series](https://brilliant.org/discussions/thread/reach-for-the-summit-problem-set-mathematics/) *- Zakir Husain* 1. [Pre-RMO questions](https://brilliant.org/discussions/thread/a-pre-rmo-question-whole-series/) 2. [The e-day quiz](https://brilliant.org/discussions/thread/happy-e-day/) *- Jeff Giff* 1. Dr Fiendish series [1](https://brilliant.org/problems/dr-fiendish/?ref_id=1591979),[2](https://brilliant.org/problems/dr-fiendish-2/?ref_id=1592533),[3](https://brilliant.org/problems/dr-fiendish-3/?ref_id=1592894),[4](https://brilliant.org/problems/dr-fiendish-4/?ref_id=1593218) *- Aryan Sanghi* 1. [When two lines meet series](https://brilliant.org/problems/when-two-lines-meet-7/) 2. [Coordinate geometry series](https://brilliant.org/problems/ellipses-circular-mask/?ref_id=1602635) *- Valentin Duringer* 1. Dynamic Geometry series [1](https://brilliant.org/problems/dynamic-geometry-level-1/?ref_id=1610351),[2](https://brilliant.org/problems/dynamic-geometry-level-2/?ref_id=1610354),[3](https://brilliant.org/problems/dynamic-geometry-level-3/?ref_id=1610360),[4](https://brilliant.org/problems/dynamic-geometry-level-4/?ref_id=1610363),[5](https://brilliant.org/problems/dynamic-geometry-level-5/?ref_id=1610385),[6](https://brilliant.org/problems/dynamic-geometry-level-6/?ref_id=1610388),[7](https://brilliant.org/problems/dynamic-geometry-level-7/?ref_id=1610400),[8](https://brilliant.org/problems/dynamic-geometry-level-8/?ref_id=1610408),[9](https://brilliant.org/problems/dynamic-geometry-level-9/?ref_id=1610427),[10](https://brilliant.org/problems/dynamic-geometry-level-10/?ref_id=1610469),[11](https://brilliant.org/problems/dynamic-geometry-level-11/?ref_id=1610472),[12](https://brilliant.org/problems/dynamic-geometry-level-12/?ref_id=1610475),[13](https://brilliant.org/problems/dynamic-geometry-level-13/?ref_id=1610479),[14](https://brilliant.org/problems/dynamic-geometry-level-14/?ref_id=1610541),[15](https://brilliant.org/problems/dynamic-geometry-level-15/),[16](https://brilliant.org/problems/dynamic-geometry-level-16/),[17](https://brilliant.org/problems/dynamic-geometry-p17/?ref_id=1610607),[18](https://brilliant.org/problems/dynamic-geometry-p18/?ref_id=1610617),[19](https://brilliant.org/problems/dynamic-geometry-p19/?ref_id=1610772),[20](https://brilliant.org/problems/dynamic-geometry-p20/?ref_id=1610775),[21](https://brilliant.org/problems/dynamic-geometry-p21/?ref_id=1610872),[22](https://brilliant.org/problems/dynamic-geometry-p22/?ref_id=1610875),[23](https://brilliant.org/problems/dynamic-geometry-p23/?ref_id=1610878),[24](https://brilliant.org/problems/dynamic-geometry-p24/?ref_id=1610891),[25](https://brilliant.org/problems/dynamic-geometry-p25/?ref_id=1610903),[26](https://brilliant.org/problems/dynamic-geometry-p26/?ref_id=1610909),[27](https://brilliant.org/problems/dynamic-geometry-p27/?ref_id=1611231),[28](https://brilliant.org/problems/dynamic-geometry-p28/?ref_id=1611234),[29](https://brilliant.org/problems/dynamic-geometry-p29/?ref_id=1611237),[30](https://brilliant.org/problems/dynamic-geometry-p30/?ref_id=1611356),[31](https://brilliant.org/problems/dynamic-geometry-p31/?ref_id=1611359),[32](https://brilliant.org/problems/dynamic-geometry-p32/?ref_id=1611389),[33](https://brilliant.org/problems/dynamic-geometry-p33/?ref_id=1611393),[34](https://brilliant.org/problems/dynamic-geometry-p34/?ref_id=1611396),[35](https://brilliant.org/problems/dynamic-geometry-p35/?ref_id=1611399),[36](https://brilliant.org/problems/dynamic-geometry-p36/?ref_id=1611402),[37](https://brilliant.org/problems/dynamic-geometry-p37/?ref_id=1611409),[38](https://brilliant.org/problems/dynamic-geometry-p38/?ref_id=1611471),[39](https://brilliant.org/problems/dynamic-geometry-p39/?ref_id=1611474),[40](https://brilliant.org/problems/dynamic-geometry-p40/?ref_id=1611483),[41](https://brilliant.org/problems/dynamic-geometry-p41/?ref_id=1611486),[42](https://brilliant.org/problems/dynamic-geometry-p42/?ref_id=1611536),[43-sequel to 42](https://brilliant.org/problems/dynamic-geometry-p43/?ref_id=1611539),[44](https://brilliant.org/problems/dynamic-geometry-p44/?ref_id=1611544),[45](https://brilliant.org/problems/dynamic-geometry-p45/),[46](https://brilliant.org/problems/dynamic-geometry-p46/) **Discussions:** *- Zakir Husain* 1. On area percentage series [1](https://brilliant.org/discussions/thread/on-area-percentage/?ref_id=1593918),[2](https://brilliant.org/discussions/thread/on-area-percentage-2/?ref_id=1594187),[3-bonus](https://brilliant.org/discussions/thread/on-area-percentage/?ref_id=1593918) 2. Math also fails series [1](https://brilliant.org/discussions/thread/math-also-fails/?ref_id=1590442),[2](https://brilliant.org/discussions/thread/math-also-fails-2/?ref_id=1592912) 3. [Recurring decimals](https://brilliant.org/discussions/thread/on-recurring-decimals/) *- Yajat Shamji* 1.Recurring proof notes See [Recurring decimals](https://brilliant.org/discussions/thread/on-recurring-decimals/). 2. Number spy challenges [1](https://brilliant.org/discussions/thread/number-spy-challenge-1/),[2](https://brilliant.org/discussions/thread/number-spy-challenge-2/) [*- Gandoff Tan*](https://brilliant.org/profile/gandoff-5e56fk/) *- Vinayak Srivastava* 1. [10 PRMO sample questions-discussion](https://brilliant.org/discussions/thread/prmo-sample-questions/) 2.[PRMO discussion](https://brilliant.org/discussions/thread/prmo-discussion/) *- Páll Márton (A Former Brilliant Member)* 1. [Proof chain](https://brilliant.org/discussions/thread/math-prove-marathon/) *- Jeff Giff* 1. [Bilingual geometry note](https://brilliant.org/discussions/thread/bilingual-geometry-notebook/?ref_id=1598123) *- Inquisitor Math* 1. [A function whose reciprocal is an inverse](https://brilliant.org/discussions/thread/a-function-whose-reciprocal-is-an-inverse/) **Formatting:** *- Brilliant* 1. [\\$$\\LaTeX\\$$ formatting guides](https://brilliant.org/math-formatting-guide/) *- Percy Jackson* 1. [\\$$\\LaTeX\\$$ formatting guides](https://brilliant.org/discussions/thread/latex-formatting-guide/) *- Daniel Liu* 1. [\\$$\\LaTeX\\$$ formatting guides](https://brilliant.org/discussions/thread/beginner-latex-guide/) *- Hamza Anushath (Frisk Dreemurr)* 1. [\\$$\\LaTeX\\$$ formatting guides](https://brilliant.org/discussions/thread/different-types-of-latex-formatting-methods-that-i/) *- Páll Márton (A Former Brilliant Member)* 1. [\\$$\\LaTeX\\$$ formatting guides](https://brilliant.org/discussions/thread/formatting-guide/) 

- 3 months, 3 weeks ago

@Jeff Giff, the deed is done. Check out my latest note!

- 3 months, 2 weeks ago

@Jeff Giff mention[10101485:Jeff Giff]

- 3 months, 2 weeks ago

Sorry, just wanted to get your mention number tag :)

- 3 months, 2 weeks ago

Check my new mentions page then, here

@Frisk Dreemurr mention[10427613:Frisk Dreemurr] (I need to add your mention Id)

- 3 months, 2 weeks ago

nice!

- 3 months, 2 weeks ago

Line 25 may be my worst creation (holy cow I didn’t click enter) :P

- 3 months, 3 weeks ago

@Jeff Giff Kindly add this

- 3 months, 1 week ago

Done :)

- 3 months, 1 week ago

- 2 months, 3 weeks ago

@Jeff Giff Can you add these?

These are not by me (those in bold)

- 2 months, 2 weeks ago

@Jeff Giff ????

- 2 months, 2 weeks ago

@Jeff Giff What about "It's Mathematics Olympiad" ? and "Trigonometry Everywhere" ?

- 2 months, 1 week ago

At work now :) I’m quite busy :P

- 2 months, 1 week ago

Oh I wasn’t noticed! Now I see :)

- 2 months, 2 weeks ago

Thanks for all that!

- 2 months, 2 weeks ago

Have you edited the note? I am not able to see them right now...

- 2 months, 2 weeks ago