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Problem Writing Party: June 27th - July 10th

Problem Writing Party 9 lead to a lot of contributions. There are 200 problems contributed in the past 3 weeks, and another 200 popular problems created in the past, that we will start to sort through. Once again, 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:

New Brilliant Challenge Quizzes

Chess Tactical: Level 3, Level 4
Rectangular Grid Walk: Level 3, Level 4
Power Mean Inequality: Level 2, Level 3, Level 4, Level 5
Roots of Unity: Level 3, Level 4, Level 5
Functions: Level 1, Level 2, Level 3, Level 4, Level 5
Classification of Triangles: Level 1, Level 2, Level 3
Newton's Law of Gravity
Triangle Centers: Level 2, Level 3, Level 4
Distribution Into Bins: Level 4

Let's kick off our 10th Problem Writing Party!

How it Works

The party starts right now (June 27th, 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:

TopicDescriptions
Simplifying ExpressionsCan you simplify \( \dfrac{(x^2-3x+2)(x^2-7x+12)}{(x^2-5x+4)(x^2-5x+6)} \)?
Operator SearchCan you find the necessary math operators that represents the boxes in \( 10 \; \square \; 10 \; \square \; 10 \; \square \; 10 = 101 \)?
PercentagesIs 23% of 45 equal to 45% of 23?
Syllogistic LogicAll X are Y, All Y are Z. Is it true that all Z are X?
Composite FiguresFind the area of this crecsent shaped region
Convergence of SequencesIf \(f\) is non-increasing function, is it true that \(f(1) + f(2) + f(3)+ \cdots \) converges if and only if \( 2^1 f(1) + 2^2 f(2^2) + 2^3 f(2^3) + \cdots \) converges?
Work-Energy TheoremHow much force is acting on me if If I move down an inclined plane?

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.

Use this note to

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

  2. Share links to great relevant problems.

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

  4. 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).

Note by Calvin Lin
5 months, 1 week ago

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I have a lottt of problems on Syllogistic logic, I can sure add some! :D

Syllogisms 1

Syllogisms 2

Syllogisms 3

Syllogisms 4 Mehul Arora · 5 months, 1 week ago

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@Mehul Arora Thanks, Mehul. I had fun solving these problems. :) I have even written solutions to the first two problems. Pranshu Gaba · 5 months ago

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@Mehul Arora Nice problems. I personally like #3 the best. Agnishom Chattopadhyay · 5 months, 1 week ago

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@Agnishom Chattopadhyay Number 3 is from a past NTSE :P Mehul Arora · 5 months, 1 week ago

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@Mehul Arora That's great! I am looking forward to solving your problems Pranshu Gaba · 5 months, 1 week ago

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@Mehul Arora I think #1 is wrong. It should be neither. If there are no pens, roads, or houses, then both hypotheses are true (all zero pens are roads and all zero roads are houses) but the second conclusion is false (zero houses are pens). You forgot to think about the empty set case. Akiva Weinberger · 3 months, 2 weeks ago

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@Mehul Arora Woahh! These are amazing! I find myself drawing up Venn Diagrams every time! LUV THEM Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh Thanks! These are indeed fun to solve :) Mehul Arora · 5 months, 1 week ago

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SCAA Logo on composite figures Lolly Lau · 5 months, 1 week ago

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@Lolly Lau Wow! This is very simplistic and interesting! Reshared! Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh Thank you :) Lolly Lau · 5 months, 1 week ago

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@Lolly Lau Oh wow, I'm amazed at how complicated that got, despite such a simplistic figure! Calvin Lin Staff · 5 months ago

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I'll be continue to add more problems (will edit/update this comment accordingly), but here is what I have at the moment:

Simplifying Expressions

There is one and only one answer to this

Percentages

Swimming Pool Complex Construction (also part of Composite Figures)

Composite Figures

Captain America's Shield

Vicious Circles & Savage Shapes

Inscribe-ception

Work-Energy Theorem

Liquid in a tin can

Projectile Motion With Air Resistance

Conservation of Energy in Suspended Spring System

Other Classical Mechanics Problems

Automatic Clothes Dryer

Acceleration-time graphs in 1D kinematics

Sequence & Series Convergence

What diverges?

List to be expanded. Wee Xian Bin · 5 months ago

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@Wee Xian Bin Woah! Captain America! Best question here! Pi Han Goh · 5 months ago

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@Wee Xian Bin By the way, are we looking out for problems related to sequence convergence or also series convergence as well? Because that will definitely widen the scope of problems to write :) Wee Xian Bin · 5 months ago

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@Wee Xian Bin I think both are acceptable, I don't see why we need to forbid one in favor of the other. Pi Han Goh · 5 months ago

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@Pi Han Goh Yeap, added new question on series convergence :) Wee Xian Bin · 4 months, 4 weeks ago

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  • Here is my first submission for work-energy theorem part.
  • Here is my second entry for work-energy theorem section.
  • Here is my third submission for simplifying expressions section.
  • Here is my fourth submission on percentages.
  • Here is my fifth submission for syllogistic logic section.
  • Here is my sixth submission for operator search section.
  • Here is my seventh submission for work-energy theorem section.
(edited by a Moderator) Ashish Siva · 5 months ago

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@Ashish Siva Nice problems as always :)

Could you please organize your problems into one comment or it's replies? That is usually helpful for us for bookkeeping. Agnishom Chattopadhyay · 5 months ago

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@Agnishom Chattopadhyay Thanks for your conpliments. I would have done the organization in the first place, but there is a problem due to the new chat system. I works wierdly on the phone. Sometimes writing comments of 5-6 lines makes the whole work go. It didnt used to happen in the old system. So, I didnt want to lose my work like that :/ We cant even preview the comments before posting. The edit and reply buttons are invisible :O and usually i press reply instead of edit and you know what happens. The worst part is that the place for writing comments is placed down we have to scroll all the way down -_- Replying to a comment is hilarious now. Ashish Siva · 5 months ago

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@Ashish Siva I do agree with you. We told the staff about this. I hope they'll fix them in the earliest. Agnishom Chattopadhyay · 5 months ago

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@Agnishom Chattopadhyay Thanks! :) Sorry for not being able to organize the questions Ashish Siva · 5 months ago

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@Ashish Siva Do not worry. I took care of it. Agnishom Chattopadhyay · 5 months ago

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@Agnishom Chattopadhyay Thanks!! Ashish Siva · 5 months ago

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@Ashish Siva Hmmm, isn't this under "proving trigonometric identities"?

Haha, my first impression was to differentiate it and show that it's a constant! Pi Han Goh · 5 months ago

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@Pi Han Goh :P yeah maybe it is under that topic. Differentiatae! Lol Ashish Siva · 5 months ago

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Here are my contributions

Simplifying Expressions

Percentages

Composite Figures Chung Kevin · 5 months ago

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@Chung Kevin Thanks, these are interesting problems, and tricky too! Pranshu Gaba · 5 months ago

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@Chung Kevin Nice questions! I've fixed the answer in "Tedious Multiplication". Calvin Lin Staff · 5 months ago

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Here's mine on operator search.

Eight \(8\)'s

BTW the new comments system make me dizzy. Lee Care Gene · 5 months, 1 week ago

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@Lee Care Gene Thanks, we will see what we can do to make it work better Agnishom Chattopadhyay · 5 months, 1 week ago

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@Agnishom Chattopadhyay Exactly the new system isn't very friendly(as before) and on mobile things are even worse... Maybe you should write a note about new changes being made and what opinions do people have... (Just a suggestion) Rishabh Cool · 5 months ago

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@Rishabh Cool Yep agreed, this system looks wierd. Maybe we would get used to it a few weeks later. But, I'm still not sure. Everything is so compact! But I like rhe view/hide comments part in solutions. Thats a nice feature. Ashish Siva · 5 months ago

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@Rishabh Cool Thanks Rishav, I will talk to the staff about this Agnishom Chattopadhyay · 5 months ago

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@Agnishom Chattopadhyay *Rishabh Rishabh Cool · 5 months ago

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@Lee Care Gene That's a nice problem. How can we show that is indeed the minimum​? Calvin Lin Staff · 5 months ago

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Here is my submission:- Percentages and Simplifying Expressions Anuj Shikarkhane · 5 months, 1 week ago

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@Anuj Shikarkhane Thanks, Anuj. These problems are fun to solve. I was almost tricked by the Percentages question. Pranshu Gaba · 5 months ago

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@Anuj Shikarkhane I enjoyed your problem on Simplifying Expressions. Agnishom Chattopadhyay · 5 months, 1 week ago

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@Anuj Shikarkhane Your second problem is very nice. I was about to use my calculator but then I realized how it should be done. Thanks for sharing! Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh I'm happy that u guys liked my problems! Anuj Shikarkhane · 5 months, 1 week ago

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@Anuj Shikarkhane Thanks! Both of these questions are great :) Calvin Lin Staff · 5 months ago

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@Calvin Lin Thank you :) Anuj Shikarkhane · 5 months ago

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Here's my most challenging problem on Arithmetic Puzzle: Can you fill in these boxes?. Worranat Pakornrat · 5 months, 1 week ago

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@Worranat Pakornrat Can you show that the answer is unique? Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh I'll try, but it looks pretty complex. :) Worranat Pakornrat · 5 months, 1 week ago

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@Worranat Pakornrat Challenging indeed. Can you provide further guidance in the solution so that it's not just a random observation? Calvin Lin Staff · 5 months, 1 week ago

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@Calvin Lin I'll try, but it looks pretty complex. :) Worranat Pakornrat · 5 months, 1 week ago

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Syllogismzz. - 3
Syllogismzz. - 2
Syllogismzz. - 1
Here's mine for syllogism Sanyam Goel · 5 months, 1 week ago

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@Sanyam Goel @Mehul Arora, you got a competitor! =D Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh hehehehe !!!! Sanyam Goel · 5 months, 1 week ago

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@Pi Han Goh Hahaha I love competition. And I'm up for it :P I'll probably be posting more soon, so @sanyam goel better be on his heels ;) Mehul Arora · 5 months, 1 week ago

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@Mehul Arora well, i will also be posting more problems after 4 july :-) Sanyam Goel · 5 months, 1 week ago

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@Sanyam Goel LOL okay, good to know! Mehul Arora · 5 months, 1 week ago

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@Sanyam Goel Thanks for posting them across different levels. I think we can simplify it so that there isn't the constant intro of "take these statements as fact even though you might not believe them". Having them be presented in the Syllogistic logic section would help with that too :) Calvin Lin Staff · 5 months, 1 week ago

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Here's mine for Composite Figure: Love Circles. Worranat Pakornrat · 5 months, 1 week ago

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@Worranat Pakornrat Wow nice, I spot a reuleaux triangle there! Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh Thanks! ;) Worranat Pakornrat · 5 months ago

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@Worranat Pakornrat <3 it!

There are ways to simplify the solution so that we're not making repeated calculations. Essentially, you just need to find the overlap areas when two circles pass through each other's centers. That would help make the solution less frightening. Calvin Lin Staff · 5 months, 1 week ago

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@Calvin Lin Oh, thanks for the advice. ;) Worranat Pakornrat · 5 months ago

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Agnishom Chattopadhyay · 5 months, 1 week ago

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@Agnishom Chattopadhyay Nice convergence question! We would like to develop some more advanced calculus on Brilliant for the community to improve further :)

The matrix question is great! I don't think it really qualifies under Syllogism. We will have to develop out the linear algebra section even more :) Calvin Lin Staff · 5 months ago

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@Agnishom Chattopadhyay Hmmm, your Operator search looks like a standard CS problem. Why do you think that this is an interesting question?
And I don't understand why your last post is related to syllogistic logic. Isn't it just some matrix misconception? Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh I added a solution. I hope this is helpful Agnishom Chattopadhyay · 5 months, 1 week ago

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Doubling Dragon for Arithmetic Puzzles. Sam Bealing · 5 months, 1 week ago

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@Sam Bealing Hm, that's not an arithmetic puzzle in Logic. It's more of Geometric Progressions / Setting up equations.

Also, this party is focused on Operator Search, and we will pull that out as a separate chapter. Calvin Lin Staff · 5 months, 1 week ago

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Too many twos! for Simplifying Expressions. Sam Bealing · 5 months, 1 week ago

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@Sam Bealing That's fun! Love it. There are several simplifications that come into play. Calvin Lin Staff · 5 months, 1 week ago

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@Hobart Pao Hmmm, you seem to forget to post "Spoooooooky" Russian rational expressions 3, 5, 6, 7, 8, 9 , ... , 29, 30 ;)

I think your "31" can be greatly improved if you replaced \(n\) with 2016 directly into the expression, so there appears to to no algebra involved, which makes this so much more interesting. Pi Han Goh · 5 months, 1 week ago

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@Pi Han Goh Thanks for your comment! Some of the expressions on that sheet I deemed to be too easy so I skipped them. As for 31, I'll take that under consideration. Hobart Pao · 5 months, 1 week ago

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@Hobart Pao Those are good :) Some lower level ones would also be helpful, since that chapter is targeted at introductory​ material. Calvin Lin Staff · 5 months, 1 week ago

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@Hobart Pao These problems are really spooky! The expressions are long, and would seem intimidating to members who are level 1-2 in Algebra. I would suggest you share problems with simpler expressions; people are more likely to solve them and such problems will become more popular!

Here are some suggestions for making great problems. Pranshu Gaba · 5 months, 1 week ago

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Here's my entry for Simplifying Expressions. Joao Miguel Coelho · 5 months ago

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@Joao Miguel Coelho Hmmm, it seems that I need to factorize that large number first. It appears to be a somewhat tedious job to do. How do you factorize that number so quickly? Pi Han Goh · 4 months, 4 weeks ago

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@Pi Han Goh When i sarted learning maths, one of the "base" thins i learnt to do was factorizing numbers. I start by divinding the number by 2, since it is even, and then, when the sum of all the digits is a multiple of 3, i divide it by 3. It`ll end up with only 2 and 3 powers, making it not that hard to factor out. Joao Miguel Coelho · 4 months, 4 weeks ago

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I already have a few problems for some of these topics, but I am definitely planning to make some more in the coming week! :D

Composite Figures/Length and Area:

I also have a ton of problems which deal with the convergence of a series, but only what it converges to, rather than testing for convergence (so the limit of the series or summation). Are these kinds of problems allowed for this problem writing party, or must they deal directly with conditions for convergence? Jonas Katona · 5 months ago

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@Jonas Katona

Are these kinds of problems allowed for this problem writing party, or must they deal directly with conditions for convergence?

They sure are! Agnishom Chattopadhyay · 5 months ago

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@Jonas Katona OMG! Ashish Siva · 5 months ago

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@Ashish Siva LOL you don't know how long I have been waiting for a problem writing party in which I could use these problems. As you can tell, I really enjoy studying series. Jonas Katona · 5 months ago

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@Jonas Katona Great way to go! Ashish Siva · 5 months ago

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@Jonas Katona WOAHH! A TREASURE TROVE!!! =DDDDDDD Pi Han Goh · 5 months ago

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@Pi Han Goh THANKS PI HAN!! :D Jonas Katona · 5 months ago

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This is the question in my stock on Length & Area: Weird Land for Sale. Worranat Pakornrat · 5 months ago

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Here is a first problem for Work Hjalmar Orellana Soto · 5 months ago

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@Hjalmar Orellana Soto Thanks, that was a nice problem. Glad to see someone posting physics problems :) Agnishom Chattopadhyay · 5 months ago

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Finally, my turn to join this party!

Operator Search - Here!

Simplifying Expressions - Here! and Here! (Not sure if the second question qualifies for this category)

Percentages - Here!

Last updated - 6 July 2016 Hung Woei Neoh · 5 months ago

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@Hung Woei Neoh This is a very simple setup! Likedddd Pi Han Goh · 5 months ago

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@Hung Woei Neoh This is a nice puzzle. The first question that came to my mind was if 0 is obtainable. But that doesn't seem so, now Agnishom Chattopadhyay · 5 months ago

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@Agnishom Chattopadhyay Thanks \(\ddot\smile\) Hung Woei Neoh · 5 months ago

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a problem about percentages Somebody please help... I can't get the format right... Margaret Zheng · 5 months ago

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@Margaret Zheng Oh this question is nice. My instinct tells me it's "the other answer". I've formatted the question for you.

Very cute setup! Reshared. Pi Han Goh · 5 months ago

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An easy one on Percentages: Summer Sale. Worranat Pakornrat · 5 months ago

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@Pi Han Goh I really enjoyed the operator search questions that you posted! Calvin Lin Staff · 5 months ago

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Here we go again on Arithmetic Puzzle: Can you fill in these boxes? (Part II). Worranat Pakornrat · 5 months, 1 week ago

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I would like more physics topics in next problem writing party :) Ashish Siva · 4 months, 3 weeks ago

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Hi, here are mine:

Simplifyable.

16% Stanislava Sojáková · 4 months, 3 weeks ago

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@Stanislava Sojáková I think it'd be helpful if you added a definition for simplifiablity in the second problem Agnishom Chattopadhyay · 4 months, 3 weeks ago

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@Agnishom Chattopadhyay Thanks, the problems seem understandable now Agnishom Chattopadhyay · 4 months, 3 weeks ago

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@Agnishom Chattopadhyay now I maybe see what you meant in the second problem. :) Stanislava Sojáková · 4 months, 3 weeks ago

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@Agnishom Chattopadhyay Did you mean the first problem? I edited the problem statement in that one. Thanks. Stanislava Sojáková · 4 months, 3 weeks ago

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I have two problem of function :) 2001 problem!

2016 problem!

And a triangle problem a median of triangle

Simplifying expressions 1 2016

Simplifying expressions 2 2016 2016 2016!

Simplifying expressions 3 Simplify 2016 and 2015 factorial !

Percentages 1 2016 percentage!

Percentages 2 2016 percentage #2

percentages 3 Adding percentages ! True or False? Novril Razenda · 4 months, 4 weeks ago

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Here is my other entry for Composite figures. Pi Han Goh · 5 months ago

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Cool Ayanlaja Adebola · 5 months ago

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Here is another entry for Simplifying expressions. Pi Han Goh · 5 months ago

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Here's my entry for Convergence of Sequences. Pi Han Goh · 5 months ago

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Well going party :). I am sad that I cant take part due to burden of exams and homeworks at school :( Ashish Siva · 5 months ago

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@Ashish Siva It's alright. Hope to see you back again when burdens are lessened :) Agnishom Chattopadhyay · 5 months ago

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@Agnishom Chattopadhyay Thanks, yh i will be back. Ashish Siva · 5 months ago

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Basic Mathematics? It's a variation on the So Many Shapes format! W Rose · 5 months, 1 week ago

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Area of the Medial Triangle for Length and Area. Sam Bealing · 5 months, 1 week ago

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@Sam Bealing Indeed, a useful fact to know :) Calvin Lin Staff · 5 months ago

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What is this problem writing party i need explanation please Sudoku Subbu · 5 months, 1 week ago

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@Sudoku Subbu Hi, Problem Writing Parties aim towards users making more problems on specific topics to create new quizzes. Each fortnight, new topics are decided, and we have Wiki Writing Parties too, relating to these topics. You can contribute by creating new problems pertaining to the topics given above :) The topics can also be seen on the Publish Page. Mehul Arora · 5 months, 1 week ago

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This is old wine in a new bottle for Length (perimeter) and Area Geometry problems. W Rose · 5 months, 1 week ago

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@W Rose I'm equally confused. Can you explain further? Calvin Lin Staff · 5 months ago

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@Calvin Lin The lower legs form +/- 135 degree angle(s) with the shorter upper leg. The centroid formula is the scribble written above the polygon figure. W Rose · 5 months ago

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@W Rose I confused. How do you construct the "Y" figure? Or more precisely: how what the angle between each of the 3 rectangles that form the "Y" shape figure. And what is the tiny scribbles at the top of the picture? Pi Han Goh · 5 months, 1 week ago

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Concave/Convex W Rose · 5 months, 1 week ago

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@W Rose Hmmm, must all the vertices of "answer" lie on the perimeter of the square? Because I can't get your answer. Pi Han Goh · 5 months, 1 week ago

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@W Rose That's an interesting question. Which of the above topics do you think it's related to? Calvin Lin Staff · 5 months, 1 week ago

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Sir; I want to ask a physics problem on electrostatics. Dipoles have minimum seperation between them ; then why they don't get attract to each other and collide? Dev Rajyaguru · 5 months, 1 week ago

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@Dev Rajyaguru That's a good point to ponder. How about you create a discussion for us to discuss it? Agnishom Chattopadhyay · 5 months, 1 week ago

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