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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
1 year, 4 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. 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 1

paragraph 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} \( \boxed{123} \)

Comments

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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 - 1 year, 4 months ago

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Thanks, Mehul. I had fun solving these problems. :) I have even written solutions to the first two problems.

Pranshu Gaba - 1 year, 4 months ago

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Nice problems. I personally like #3 the best.

Agnishom Chattopadhyay - 1 year, 4 months ago

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Number 3 is from a past NTSE :P

Mehul Arora - 1 year, 4 months ago

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That's great! I am looking forward to solving your problems

Pranshu Gaba - 1 year, 4 months ago

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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 - 1 year, 3 months ago

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Woahh! These are amazing! I find myself drawing up Venn Diagrams every time! LUV THEM

Pi Han Goh - 1 year, 4 months ago

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Thanks! These are indeed fun to solve :)

Mehul Arora - 1 year, 4 months ago

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SCAA Logo on composite figures

Lolly Lau - 1 year, 4 months ago

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Wow! This is very simplistic and interesting! Reshared!

Pi Han Goh - 1 year, 4 months ago

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Thank you :)

Lolly Lau - 1 year, 4 months ago

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Oh wow, I'm amazed at how complicated that got, despite such a simplistic figure!

Calvin Lin Staff - 1 year, 4 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 - 1 year, 4 months ago

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Woah! Captain America! Best question here!

Pi Han Goh - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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I think both are acceptable, I don't see why we need to forbid one in favor of the other.

Pi Han Goh - 1 year, 4 months ago

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@Pi Han Goh Yeap, added new question on series convergence :)

Wee Xian Bin - 1 year, 4 months 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 - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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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 - 1 year, 4 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 - 1 year, 4 months ago

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@Agnishom Chattopadhyay Thanks! :) Sorry for not being able to organize the questions

Ashish Siva - 1 year, 4 months ago

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@Ashish Siva Do not worry. I took care of it.

Agnishom Chattopadhyay - 1 year, 4 months ago

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@Agnishom Chattopadhyay Thanks!!

Ashish Siva - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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:P yeah maybe it is under that topic. Differentiatae! Lol

Ashish Siva - 1 year, 4 months ago

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Here are my contributions

Simplifying Expressions

Percentages

Composite Figures

Chung Kevin - 1 year, 4 months ago

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Thanks, these are interesting problems, and tricky too!

Pranshu Gaba - 1 year, 4 months ago

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Nice questions! I've fixed the answer in "Tedious Multiplication".

Calvin Lin Staff - 1 year, 4 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 - 1 year, 4 months ago

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Thanks, we will see what we can do to make it work better

Agnishom Chattopadhyay - 1 year, 4 months ago

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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 - 1 year, 4 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 - 1 year, 4 months ago

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@Rishabh Cool Thanks Rishav, I will talk to the staff about this

Agnishom Chattopadhyay - 1 year, 4 months ago

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@Agnishom Chattopadhyay *Rishabh

Rishabh Cool - 1 year, 4 months ago

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That's a nice problem. How can we show that is indeed the minimum​?

Calvin Lin Staff - 1 year, 4 months ago

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Here is my submission:- Percentages and Simplifying Expressions

Anuj Shikarkhane - 1 year, 4 months ago

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Thanks, Anuj. These problems are fun to solve. I was almost tricked by the Percentages question.

Pranshu Gaba - 1 year, 4 months ago

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I enjoyed your problem on Simplifying Expressions.

Agnishom Chattopadhyay - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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I'm happy that u guys liked my problems!

Anuj Shikarkhane - 1 year, 4 months ago

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Thanks! Both of these questions are great :)

Calvin Lin Staff - 1 year, 4 months ago

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Thank you :)

Anuj Shikarkhane - 1 year, 4 months ago

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Here's my most challenging problem on Arithmetic Puzzle: Can you fill in these boxes?.

Worranat Pakornrat - 1 year, 4 months ago

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Can you show that the answer is unique?

Pi Han Goh - 1 year, 4 months ago

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I'll try, but it looks pretty complex. :)

Worranat Pakornrat - 1 year, 4 months ago

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Challenging indeed. Can you provide further guidance in the solution so that it's not just a random observation?

Calvin Lin Staff - 1 year, 4 months ago

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I'll try, but it looks pretty complex. :)

Worranat Pakornrat - 1 year, 4 months ago

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Syllogismzz. - 3
Syllogismzz. - 2
Syllogismzz. - 1
Here's mine for syllogism

Sanyam Goel - 1 year, 4 months ago

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@Mehul Arora, you got a competitor! =D

Pi Han Goh - 1 year, 4 months ago

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hehehehe !!!!

Sanyam Goel - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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@Mehul Arora well, i will also be posting more problems after 4 july :-)

Sanyam Goel - 1 year, 4 months ago

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@Sanyam Goel LOL okay, good to know!

Mehul Arora - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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Here's mine for Composite Figure: Love Circles.

Worranat Pakornrat - 1 year, 4 months ago

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Wow nice, I spot a reuleaux triangle there!

Pi Han Goh - 1 year, 4 months ago

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Thanks! ;)

Worranat Pakornrat - 1 year, 4 months ago

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<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 - 1 year, 4 months ago

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Oh, thanks for the advice. ;)

Worranat Pakornrat - 1 year, 4 months ago

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Agnishom Chattopadhyay - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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I added a solution. I hope this is helpful

Agnishom Chattopadhyay - 1 year, 4 months ago

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Doubling Dragon for Arithmetic Puzzles.

Sam Bealing - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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Too many twos! for Simplifying Expressions.

Sam Bealing - 1 year, 4 months ago

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That's fun! Love it. There are several simplifications that come into play.

Calvin Lin Staff - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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Those are good :) Some lower level ones would also be helpful, since that chapter is targeted at introductory​ material.

Calvin Lin Staff - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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Here's my entry for Simplifying Expressions.

Joao Miguel Coelho - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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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 - 1 year, 4 months 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 - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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@Jonas Katona OMG!

Ashish Siva - 1 year, 4 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 - 1 year, 4 months ago

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@Jonas Katona Great way to go!

Ashish Siva - 1 year, 4 months ago

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@Jonas Katona WOAHH! A TREASURE TROVE!!! =DDDDDDD

Pi Han Goh - 1 year, 4 months ago

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@Pi Han Goh THANKS PI HAN!! :D

Jonas Katona - 1 year, 4 months ago

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This is the question in my stock on Length & Area: Weird Land for Sale.

Worranat Pakornrat - 1 year, 4 months ago

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Here is a first problem for Work

Hjalmar Orellana Soto - 1 year, 4 months ago

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Thanks, that was a nice problem. Glad to see someone posting physics problems :)

Agnishom Chattopadhyay - 1 year, 4 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 - 1 year, 4 months ago

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This is a very simple setup! Likedddd

Pi Han Goh - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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Thanks \(\ddot\smile\)

Hung Woei Neoh - 1 year, 4 months ago

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a problem about percentages Somebody please help... I can't get the format right...

Margaret Zheng - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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An easy one on Percentages: Summer Sale.

Worranat Pakornrat - 1 year, 4 months ago

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Here are my entries:
Composite figure
Percentages
Operator Search
Operator Search 2

Pi Han Goh - 1 year, 4 months ago

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I really enjoyed the operator search questions that you posted!

Calvin Lin Staff - 1 year, 4 months ago

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Here we go again on Arithmetic Puzzle: Can you fill in these boxes? (Part II).

Worranat Pakornrat - 1 year, 4 months ago

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I would like more physics topics in next problem writing party :)

Ashish Siva - 1 year, 4 months ago

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Hi, here are mine:

Simplifyable.

16%

Stanislava Sojáková - 1 year, 4 months ago

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I think it'd be helpful if you added a definition for simplifiablity in the second problem

Agnishom Chattopadhyay - 1 year, 4 months ago

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Thanks, the problems seem understandable now

Agnishom Chattopadhyay - 1 year, 4 months ago

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now I maybe see what you meant in the second problem. :)

Stanislava Sojáková - 1 year, 4 months ago

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Did you mean the first problem? I edited the problem statement in that one. Thanks.

Stanislava Sojáková - 1 year, 4 months 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 - 1 year, 4 months ago

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Here is my other entry for Composite figures.

Pi Han Goh - 1 year, 4 months ago

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Cool

Ayanlaja Adebola - 1 year, 4 months ago

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Here is another entry for Simplifying expressions.

Pi Han Goh - 1 year, 4 months ago

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Here's my entry for Convergence of Sequences.

Pi Han Goh - 1 year, 4 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 - 1 year, 4 months ago

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It's alright. Hope to see you back again when burdens are lessened :)

Agnishom Chattopadhyay - 1 year, 4 months ago

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Thanks, yh i will be back.

Ashish Siva - 1 year, 4 months ago

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Basic Mathematics? It's a variation on the So Many Shapes format!

W Rose - 1 year, 4 months ago

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Area of the Medial Triangle for Length and Area.

Sam Bealing - 1 year, 4 months ago

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Indeed, a useful fact to know :)

Calvin Lin Staff - 1 year, 4 months ago

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What is this problem writing party i need explanation please

Sudoku Subbu - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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This is old wine in a new bottle for Length (perimeter) and Area Geometry problems.

W Rose - 1 year, 4 months ago

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I'm equally confused. Can you explain further?

Calvin Lin Staff - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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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 - 1 year, 4 months ago

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Concave/Convex

W Rose - 1 year, 4 months ago

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Hmmm, must all the vertices of "answer" lie on the perimeter of the square? Because I can't get your answer.

Pi Han Goh - 1 year, 4 months ago

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That's an interesting question. Which of the above topics do you think it's related to?

Calvin Lin Staff - 1 year, 4 months 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 - 1 year, 4 months ago

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That's a good point to ponder. How about you create a discussion for us to discuss it?

Agnishom Chattopadhyay - 1 year, 4 months ago

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