Problem Writing Party 8 was a great success, and we had so many comments that the page started loading slowly for some people. Thanks for being part of the conversation!

I'm working on creating the quizzes, and will update the following list ASAP. Some of you would also have received B-notifications that your problems were added to the quizzes over the course of the previous week. Keep it up! We value your submissions, and would love to feature more of them.

Here are the quizzes that the Brilliant community helped create:

31 New Brilliant Challenge QuizzesArithmetic Progressions: Level 1, Level 2, Level 3

GCD/LCM: Level 1, Level 2, Level 3, Level 4, Level 5

Conditional Probability: Level 2, Level 3, Level 4, Level 5

Euler's Theorem: Level 2, Level 3, Level 4, Level 5

Distribution into Bins: Level 2, Level 3, Level 4, Level 5

Limits of Functions: Level 1, Level 2, Level 3, Level 4

Chess Tactical: Level 2, Level 3, Level 4

Chess Abstract: Level 2, Level 3

Pattern Recognition:

Let's kick off our **9th** Problem Writing Party!

## How it Works

The party starts right now (June 6th, 2016) and will last for the next two weeks. Throughout the two weeks, we will be focusing on writing awesome problems for the topics listed in quizzes that need your help on the **publish** page. The topics are:

All levels: | Chess Tactical | Rectangular Grid Walk | Power Mean inequality | Roots of Unity |

Low levels: | Functions | Classification of Triangles | Newton's Law of Gravity | |

High levels: | Triangle Centers | Markov Chains |

To join, submit as many problems as you want to these listed topics. At the end of the party, Brilliant staff will be picking the best 5-10 problems for each topic. These problems will then be immortalized and formed into a challenge quiz. If we pick your problem, then you can brag to your friends because it will be displayed on Brilliant forever! Your problem has a better chance of being selected if you include a graphic (when appropriate) and a solution.

Happy writing and keep the party alive!

## Use this note to

Ask questions about the party or brainstorming ideas from Brilliant staff.

Share links to great relevant problems.

Bounce your ideas off each other to help formulate the best problem you can.

If you're posting your problems, please keep it to one rooted comment (and I will be merging such comments from the same person). This helps us keep the page more orderly.

You can link to your own problems by using the markdown syntax of`[text](url link)`

.

## Comments

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TopNewestI had a really good one once but I forgot it. I hate that. – Whitney Clark · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Is it like a fabulous proof for which this comment is too small to contain? I hate that too.Log in to reply

– Whitney Clark · 1 year, 3 months ago

:-) I have a bad memory for some things. Some of my best ideas come when I don't have a pen and paper on hand, it seems.Log in to reply

This is my submission for the Power Mean Inequality... And my first submission for the problem writing parties... – Manuel Kahayon · 1 year, 3 months ago

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– Pranshu Gaba · 1 year, 3 months ago

This is an interesting geometric application of the Power Mean Inequality! It is well presented, and the diagram helps too. I am looking forward to more of your problems :)Log in to reply

Hey guys, check out my new problems for the PWP. Hope you like it :) .

Roots of Unity - Let's get United.

Classical Inequalities - Classic ! , Classical ! .

Law of Gravity - Who are A and B ? . – Anish Harsha · 1 year, 3 months ago

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Note that it's the "Power Mean inequalities" chapter instead of all classical inequalities. Yes, we're developing out this section and splitting up the chapter! Finally! So, the IMO question doesn't quite count, but the other one is great!

The phrasing of the gravitational question could be improved on. Right now, it sounds quite forced / unnatural. Can you tweak it slightly? – Calvin Lin Staff · 1 year, 3 months ago

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– Anish Harsha · 1 year, 3 months ago

Ok, sir. I'll work on the question on Law of gravity. Anyways, thanks.Log in to reply

Thanks for inviting me to this party but I am currently facing crisis in my school that my free time is totally cut off. I will see to that I can add something good if I can! – Akhash Raja Raam · 1 year, 2 months ago

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– Ashish Siva · 1 year, 2 months ago

Same here, thats why I cant contribute nowadays :(Log in to reply

A problem for Rectangular Grid Walk:

Heist of the Diamond – Tarmo Taipale · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

Woah! Very nice question! +1 for storytelling! ResharedLog in to reply

– Tarmo Taipale · 1 year, 3 months ago

Thanks!Log in to reply

Here is mine for Roots of unity – Akeel Howell · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

I think asking for the minimum number of sides was a good question if the point wasn't already of the form \( ( \cos \frac{2\pi}{n}, \sin \frac{2\pi}{n} \). Giving the 3rd vertex of a 7-gon would have made it more interestingLog in to reply

Here is another rectangular grid walk program. It has to do with a random walk in four dimension, where time is the fourth dimension... Enjoy! :) – Geoff Pilling · 1 year, 3 months ago

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Your question brings up a loophole in the Doctor Who universe, where events are "time locked". They could have just travelled to \(T-1\) and then wait it out, or travel to a nearby city and then walk over :) – Calvin Lin Staff · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

TARDISSSSSS! =D =DLog in to reply

– Geoff Pilling · 1 year, 3 months ago

Hahahaha... Yup, an inside joke for Dr. Who fans! :) (Apropos for a time traveling problem!)Log in to reply

Here is my question for Rectangular grid walk. I edited the previous one. – Arkodipto Dutta · 1 year, 3 months ago

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– Pranshu Gaba · 1 year, 3 months ago

Thanks, the final answer is in a much simpler form now. It would be great if you could add a diagram to your problem; it would make the problem easier to visualize.Log in to reply

– Arkodipto Dutta · 1 year, 3 months ago

Ok, I will add one soon.Log in to reply

– Calvin Lin Staff · 1 year, 3 months ago

Thanks for the image! I've edited it to make it clearer, and to also show an example of a possible path.Log in to reply

Here is a question on functions ( inverse ) . Log inverse – Prince Loomba · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

The final answer format of \( \ln(\log_a e)^{6}\) is very contrived. Can we simplify that further? It might be better to ask what the constant \(a\) is, and provide options like \( e^e, e^{ \frac{1}{e}, e^ 1 , e^2 \). Thoughts?Log in to reply

– Prince Loomba · 1 year, 3 months ago

Sir I cannot change the options but you can. Surely it will be better then. But then the question can be solved by hit and trial. Thats why I did this. Anyways as you wish.Log in to reply

– Calvin Lin Staff · 1 year, 3 months ago

I've edited the problem. Let me know what you think of it.Log in to reply

– Aaron Miller Staff · 1 year, 2 months ago

This is an excellent question that was fun to solve. However, I wonder if replacing the two choices that you can immediately eliminate because they are <1, violating the first assumption in the question, would partially address Prince Loomba's concern about trial and error. Perhaps \(e^{e-1}\) and \(e^{e^{-2}}\) can replace \(e^{-1}\) and \(e^{-e}\)?Log in to reply

Welcome to my dazzling problem on Triangle Centers: Tangling Circles. – Worranat Pakornrat · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

That's interesting (and colorful)!Log in to reply

Another one on Roots of Unity: Prime Power Roots. – Worranat Pakornrat · 1 year, 3 months ago

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Here's one for Roots of Unity: Odd Powers Only. – Worranat Pakornrat · 1 year, 3 months ago

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Triangle problem: It's a whole number!. \[\] Triangle centers: It's a Triangle!.\[\] Powers: Powers of 2.\[\] Roots of Unity: What value does the area approach?. – Akeel Howell · 1 year, 3 months ago

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– Pranshu Gaba · 1 year, 2 months ago

Short and simple problems. These problems test basic understanding of the concepts. Thanks for sharing these problems, Akeel :)Log in to reply

This is my new question on Power-Mean Inequality: Yummy Jelly.

Should be pretty easy though. ;) – Worranat Pakornrat · 1 year, 3 months ago

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Two easy (I think) problems for functions:

Not many solutions? Part 1

Not many solutions? Part 2 – Tarmo Taipale · 1 year, 3 months ago

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Here's the applied question for Classical Inequality: Rectangular Inequality.

Enjoy! ;) – Worranat Pakornrat · 1 year, 3 months ago

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Another Function Problem

Click Here – Jason Chrysoprase · 1 year, 3 months ago

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An easy one on Classification of Triangles: Tri-Max. – Worranat Pakornrat · 1 year, 3 months ago

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function problem – Margaret Zheng · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

Cute question! I thought sinusoidal = periodic only. +1Log in to reply

Here are my entries for the topics: Functions

Maps to itself... eventually and Use a telescope. – Pi Han Goh · 1 year, 3 months ago

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coupling a few 1008 roots!!

problem on roots of unity i just made !!! :) – Rohith M.Athreya · 1 year, 3 months ago

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Interesting question nonetheless! +1 – Pi Han Goh · 1 year, 3 months ago

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\(2ne^{\frac{2\pi i}{2n}}\) which finally yields an answer of 2

but a moderator(perhaps) editted the question and the answer has been changed to 1 which i cant account for – Rohith M.Athreya · 1 year, 3 months ago

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Can i post Similar Triangle Problem for Classification Triangle ? – Jason Chrysoprase · 1 year, 3 months ago

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two different stuffs. – Pi Han Goh · 1 year, 3 months ago

Hmmmm, I don't think so. They areLog in to reply

this problem. Yes i know the answer but i don't know how to prove it. – Jason Chrysoprase · 1 year, 3 months ago

And if you are not busy, try to write solution inLog in to reply

– Jason Chrysoprase · 1 year, 3 months ago

;(, that's mean i only have one posted problemLog in to reply

Here's my problem for Function( Sorry i was a little bit late ;) ) – Jason Chrysoprase · 1 year, 3 months ago

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Here is my fourth submission for triangle centers section. – Ashish Siva · 1 year, 3 months ago

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Here is mine for functions – Abc Xyz · 1 year, 3 months ago

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– Ashish Siva · 1 year, 3 months ago

Well u learnt hoe to link!!! (+1)Log in to reply

doyou link? – Finn C · 1 year, 3 months agoLog in to reply

`[Text you want to link](url of the page you want to link)`

– Ashish Siva · 1 year, 3 months agoLog in to reply

– Abc Xyz · 1 year, 3 months ago

Ya I refered to the latex help page :>Log in to reply

– Prince Loomba · 1 year, 3 months ago

Actually it is mentioned in the note tooLog in to reply

Here is another rectangular grid walk problem. – Geoff Pilling · 1 year, 3 months ago

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A set on Markov Chains :

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– Akeel Howell · 1 year, 3 months ago

Winnie the Poo!!!!!!!!!!Log in to reply

I have posted two more problems, both relating to classification of triangles. I hope that these two problems are more suitable than my last two:

Stubborn triangles

Believe in yourself, Tommy!

I am also planning to create some better problems for roots of unity, keeping in mind how Euler's formula can be used as a means of simplifying trigonometric functions. – Jonas Katona · 1 year, 3 months ago

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I am looking forward to your problems in roots of unity! – Pranshu Gaba · 1 year, 3 months ago

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– Jonas Katona · 1 year, 3 months ago

Thank you for the compliment, Pranshu! :DLog in to reply

Here is my question about Triangle Centers. :> – Nowras Otmen · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Thanks for making your first problem contribution to Brilliant! I look forward to seeing more :)Log in to reply

Not sure if this one counts as a Markov chain? – Geoff Pilling · 1 year, 3 months ago

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linearity of expectation, then it has to do with understanding a Markov chain. Great question BTW. – Calvin Lin Staff · 1 year, 3 months ago

Very tangentially. It is more ofLog in to reply

– Geoff Pilling · 1 year, 3 months ago

Yeah, that's kinda what I figured... Still trying to think of a good Markov Chain one... Oh, and thanks! :)Log in to reply

Here is my question for Rectangle grid walk

Here is my question for Rectangular grid walk. I edited the previous one. – Arkodipto Dutta · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Thank you! Can you add a solution to the problem? To me, it's more natural to ask for the total number of ways, in part because the \( Z! ^3 \) in the denominator seems out of place.Log in to reply

Than you, sir, for the invitation, I just posted my problems under the community page. I do not know how to add them here. – Hana Nakkache · 1 year, 3 months ago

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`[word you want to link](the url of the webpage)`

is my submission for xxx section. – Ashish Siva · 1 year, 3 months agoLog in to reply

Here is my first entry for classification of triangles section.

Here is my entry for triangle centers section.

Here is my third submission for triangle centers section.

Thanks. Here is that \({91}^°\) question. – Ashish Siva · 1 year, 3 months ago

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Great question about triangle classifications :) A follow up question could be "Which non-degenerate triangle cannot have \( 91^\circ \) as one of its angles.

I like the triangle centers question too. It's kept simple, and interesting to play around with.

The third problem seems like tedious computation, and I'm not excited to get started with it. You can also tell that from the low attempt rate of the community.

Overall, great improvement in the problems that you're posting, especially in comparison to what you started out from. Keep it up! – Calvin Lin Staff · 1 year, 3 months ago

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Not sure if it fits, but this is my question for Rectangular Grid Walk: Dark Room Hunt.

And for function: Fibonacci Reversed. – Worranat Pakornrat · 1 year, 3 months ago

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The second problem is pretty fun too. I see that it's been placed in the Functions chapter, and will review it later :) – Calvin Lin Staff · 1 year, 3 months ago

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– Worranat Pakornrat · 1 year, 3 months ago

Thanks. The first one is one of my favorite detective question. :)Log in to reply

Here is one on rectangular grid walk: Paths

My problem on Classification of Triangles: Get It Right

Problems on functions: Fitting Functions, Flipping Functions – Lee Care Gene · 1 year, 3 months ago

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The second problem is good too. Ideally, we want to avoid trigonometry in this basic chapter. I have moved the problem into trigonometry instead. – Calvin Lin Staff · 1 year, 3 months ago

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– Lee Care Gene · 1 year, 3 months ago

I've just posted a solution.Log in to reply

For Classification of Triangles: That's all?

For Roots of Unity: Unification – Jonas Katona · 1 year, 3 months ago

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Similarly for the second question, which doesn't yet showcase the beauty of roots of unity. It would have been nicer if final form was \( \cos \frac{pi}{n} \times e^{ i \theta } \), which starts to get at the usefulness of the identities.

Here are some suggestions for writing a great problem. I look forward to seeing your improvements over time :) – Calvin Lin Staff · 1 year, 3 months ago

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– Jonas Katona · 1 year, 3 months ago

Thank you for the advice! I will keep this in mind for next time.Log in to reply

Roots of unity!. will contribute to it – Prakhar Bindal · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Looking forward to it!Log in to reply

– Prakhar Bindal · 1 year, 3 months ago

Sir like gravitation requires low level problems but i have some level 4-5 problems can i still contribute?Log in to reply

– Calvin Lin Staff · 1 year, 3 months ago

Sure of course!Log in to reply

On Markov Chain :

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– Calvin Lin Staff · 1 year, 3 months ago

Great! I've added both of these to the Markov Chains chapter. I really like Otto's problem, and the discussion. I was pleasantly surprised at the result.Log in to reply

Here is one for rectangular grids: Avoiding the accident sites.

And a simple one on Newton's Law of Universal Gravitation: Rock. – Arjen Vreugdenhil · 1 year, 3 months ago

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The first problem could definitely benefit from an image, which will remove the need to define the streets and avenues. – Calvin Lin Staff · 1 year, 3 months ago

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Here is a first problem for Classification of Triangles – Hjalmar Orellana Soto · 1 year, 3 months ago

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into

Can you add a solution to it? – Calvin Lin Staff · 1 year, 3 months ago

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Here are my entries for Triangle Centres :

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– Calvin Lin Staff · 1 year, 3 months ago

Thanks! These are great problems that the community likes and will be in the list that I review. In fact, the first problem was already added to a challenge quiz :)Log in to reply

– Deeparaj Bhat · 1 year, 3 months ago

Oh! I didn't get a notification about it though. Thanks for selecting it. :)Log in to reply

– Calvin Lin Staff · 1 year, 3 months ago

Yea, that happened back in the day before we started sending out notifications lol. I'm so glad that we do it now.Log in to reply

I would like to submit these problems for Newton's Law of Gravity: Entry 1, Entry 2, and Entry 3. – Pranshu Gaba · 1 year, 3 months ago

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For question 2, I'm not quite sure that 5N of gravitational force between 2 stones that we're holding is a reasonable estimate. It might be better to just say "N newtons" and express the options in terms of that.

For question 3, one potential thought experiment is to ask what happens as \( r \rightarrow 0 \). If the gravitational force goes to infinity, why am I allowed to touch something and release it? – Calvin Lin Staff · 1 year, 3 months ago

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I have one more question to add to this party! I just created it today, for functions: Inseparable – Jonas Katona · 1 year, 3 months ago

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Final entries for this party::::

Triangle centers:

Centroid?

Some other center?

Grid walk::::

Sudoku

Tron

Limit – Pi Han Goh · 1 year, 3 months ago

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Here's my entry for triangle centers – Pi Han Goh · 1 year, 3 months ago

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Hope I'm not late to the party. Here's my entries for Power mean inequality::

Do I need to expand it all?

Maximum value is not as big as you think – Pi Han Goh · 1 year, 3 months ago

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– Geoff Pilling · 1 year, 3 months ago

Man you come up with the craziest questions, Pi! ;-)Log in to reply

Here is my rectangular grid walk question... Enjoy! :^) – Geoff Pilling · 1 year, 3 months ago

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Here's a link to a problem I wrote for Newton's Law of Gravity: Splitting the Sun in Two – Aaron Miller Staff · 1 year, 3 months ago

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A Gloopelhopper Problem – Aaron Miller Staff · 1 year, 3 months ago

Here's another Gravity problem:Log in to reply

– Pranshu Gaba · 1 year, 2 months ago

Interesting problems, Aaron! The scenarios are described in great detail, and the solutions are excellently written. Awesome!Log in to reply

Voyage from the Sun – Aaron Miller Staff · 1 year, 3 months ago

Here's another problem I wrote for Newton's Law of Gravity:Log in to reply

I have a suggestion; the problem statement was long and slightly difficult to follow:

It can be simplified to:

By using shorter sentences, we can make the problem more easy to understand. – Pranshu Gaba · 1 year, 3 months ago

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Thank you for your helpful comment! I totally agree with your rephrasing. I will change the problem to incorporate your suggestion. – Aaron Miller Staff · 1 year, 3 months ago

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My entry for roots of unity – Joao Miguel Coelho · 1 year, 3 months ago

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– Pranshu Gaba · 1 year, 3 months ago

Cool problem, Joao! It is simply stated, and clear and concise. Keep it up! :)Log in to reply

– Joao Miguel Coelho · 1 year, 3 months ago

Thanks!Log in to reply

This is my question on Markov's Chain: Sun & Beaches. – Worranat Pakornrat · 1 year, 3 months ago

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– Pranshu Gaba · 1 year, 3 months ago

Nice problem, Dr. Warm. I have added a diagram so it's easier to see what is happening.Log in to reply

– Worranat Pakornrat · 1 year, 3 months ago

Thanks. I was so busy with my work that I didn't have time to draw the diagram.Log in to reply

Ahh i'm late, need to work fast ;) – Jason Chrysoprase · 1 year, 3 months ago

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And lots of parties too! – Calvin Lin Staff · 1 year, 3 months ago

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Do it by algebra – Aditya Narayan Sharma · 1 year, 3 months ago

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The problem is not in any of the chapters that I listed out. These chapters will get special attention over the next 2 weeks, and thus contributing into those chapters now would increase the likelihood that it makes it into the quizzes. – Calvin Lin Staff · 1 year, 3 months ago

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@Calvin Lin sir what about this? Will it work for the AP quiz: Just, AP – Rishabh Sood · 1 year, 3 months ago

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Here are some guidelines to help you improve the quality of your problems, and I would love to feature them :) – Calvin Lin Staff · 1 year, 3 months ago

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