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!

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!

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)`

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boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestI had a really good one once but I forgot it. I hate that.

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

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:-) 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.

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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 ? .

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Ah yes, that's a really important property of roots if unity :)

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?

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

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This is my submission for the Power Mean Inequality... And my first submission for the problem writing parties...

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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 :)

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Here is a question on functions ( inverse ) . Log inverse

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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?

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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.

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Here is my question for Rectangular grid walk. I edited the previous one.

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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.

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Ok, I will add one soon.

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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! :)

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TARDISSSSSS! =D =D

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

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Haha, I'm a Doctor Who fan!

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 :)

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Here is mine for Roots of unity

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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 interesting

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A problem for Rectangular Grid Walk:

Heist of the Diamond

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Woah! Very nice question! +1 for storytelling! Reshared

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Thanks!

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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!

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Same here, thats why I cant contribute nowadays :(

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I would like to submit these problems for Newton's Law of Gravity: Entry 1, Entry 2, and Entry 3.

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Oh, I really like question 1. That same thought occurred to me as I was reading the book and thinking about the environmental differences.

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?

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Here are my entries for Triangle Centres :

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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 :)

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

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Here is a first problem for Classification of Triangles

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Great. I've improved the phrasing of the problem. Old version

into

Can you add a solution to it?

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

And a simple one on Newton's Law of Universal Gravitation: Rock.

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Thanks! I combined your posts into 1, to keep this note cleaner.

The first problem could definitely benefit from an image, which will remove the need to define the streets and avenues.

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On Markov Chain :

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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.

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Roots of unity!. will contribute to it

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Looking forward to it!

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

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For Classification of Triangles: That's all?

For Roots of Unity: Unification

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The first question seems computational / tedious, as it's just memorization of an angle. It also doesn't help explain how/why we care about classifying triangles.

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 :)

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

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Here is one on rectangular grid walk: Paths

My problem on Classification of Triangles: Get It Right

Problems on functions: Fitting Functions, Flipping Functions

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Ah yes, that's pretty interesting. At first glance, it seems almost impossible to proceed and we have to resort to the old method of listing out paths to every single node. But as it turns out, there is a nice way to interpret the problem and play with it. Thanks for sharing! Could you add a solution to the problem?

The second problem is good too. Ideally, we want to avoid trigonometry in this basic chapter. I have moved the problem into trigonometry instead.

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I've just posted a solution.

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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.

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The first problem is really interesting! It doesn't fit under Rectangular grid walks, but I've placed it into the Grid puzzles quiz.

The second problem is pretty fun too. I see that it's been placed in the Functions chapter, and will review it later :)

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Thanks. The first one is one of my favorite detective question. :)

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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.

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FYI I combined your posts into 1, to keep this note cleaner.

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!

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Than you, sir, for the invitation, I just posted my problems under the community page. I do not know how to add them here.

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Well write the syntax:-

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

is my submission for xxx section.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.

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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.

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Not sure if this one counts as a Markov chain?

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Very tangentially. It is more of linearity of expectation, then it has to do with understanding a Markov chain. Great question BTW.

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

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Here is my question about Triangle Centers. :>

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

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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.

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Thank you! I enjoyed solving the problems :) They are easy to understand, and slightly tricky to solve.

I am looking forward to your problems in roots of unity!

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Thank you for the compliment, Pranshu! :D

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A set on Markov Chains :

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Winnie the Poo!!!!!!!!!!

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Here is another rectangular grid walk problem.

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Here is mine for functions

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Well u learnt hoe to link!!! (+1)

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Ya I refered to the latex help page :>

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How

doyou link?Log in to reply

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

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Here is my fourth submission for triangle centers section.

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Here's my problem for Function( Sorry i was a little bit late ;) )

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Can i post Similar Triangle Problem for Classification Triangle ?

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Hmmmm, I don't think so. They are two different stuffs.

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;(, that's mean i only have one posted problem

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And if you are not busy, try to write solution in this problem. Yes i know the answer but i don't know how to prove it.

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coupling a few 1008 roots!!

problem on roots of unity i just made !!! :)

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Doesn't your expression of \( \omega\omega^{2n} + \omega^2 \omega^{2n-1} + \cdots + \omega^{2n} \omega \) simplifies to just \((2n+1)\omega^{2n+1} \)? Or am I interpreting your question wrongly

Interesting question nonetheless! +1

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according to me, it adds upto \(2n\omega^{2n+1}\) which is nothing but \(2n\omega\) which can be expressed as

\(2ne^{\frac{2\pi i}{2n}}\) 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

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Here are my entries for the topics: Functions

Maps to itself... eventually and Use a telescope.

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function problem

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Cute question! I thought sinusoidal = periodic only. +1

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An easy one on Classification of Triangles: Tri-Max.

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Another Function Problem

Click Here

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

Enjoy! ;)

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Two easy (I think) problems for functions:

Not many solutions? Part 1

Not many solutions? Part 2

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

Should be pretty easy though. ;)

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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?.

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

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Here's one for Roots of Unity: Odd Powers Only.

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Another one on Roots of Unity: Prime Power Roots.

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Welcome to my dazzling problem on Triangle Centers: Tangling Circles.

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That's interesting (and colorful)!

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Ahh i'm late, need to work fast ;)

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There's still lots of time, don't worry.

And lots of parties too!

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This is my question on Markov's Chain: Sun & Beaches.

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

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

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My entry for roots of unity

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

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Thanks!

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Here's a link to a problem I wrote for Newton's Law of Gravity: Splitting the Sun in Two

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Here's another Gravity problem: A Gloopelhopper Problem

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

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Here's another problem I wrote for Newton's Law of Gravity: Voyage from the Sun

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Thank you, Aaron! It is a lovely problem with a nice diagram.

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.

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Hi Pranshu,

Thank you for your helpful comment! I totally agree with your rephrasing. I will change the problem to incorporate your suggestion.

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Here is my rectangular grid walk question... Enjoy! :^)

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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

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Man you come up with the craziest questions, Pi! ;-)

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Here's my entry for triangle centers

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Final entries for this party::::

Triangle centers:

Centroid?

Some other center?

Grid walk::::

Sudoku

Tron

Limit

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I have one more question to add to this party! I just created it today, for functions: Inseparable

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Do it by algebra

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Hm, after our discussion, I don't see what makes this problem interesting / special.

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.

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@Calvin Lin sir what about this? Will it work for the AP quiz: Just, AP

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I did review the question as I was putting together the AP set, and it's interesting in it's own way. However, the community didn't find it interesting and wasn't excited to work on it, which is why I didn't place it into the Level 4 quiz.

Here are some guidelines to help you improve the quality of your problems, and I would love to feature them :)

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