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 QuizzesChess 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:

Topic | Descriptions |

Simplifying Expressions | Can you simplify \( \dfrac{(x^2-3x+2)(x^2-7x+12)}{(x^2-5x+4)(x^2-5x+6)} \)? |

Operator Search | Can you find the necessary math operators that represents the boxes in \( 10 \; \square \; 10 \; \square \; 10 \; \square \; 10 = 101 \)? |

Percentages | Is 23% of 45 equal to 45% of 23? |

Syllogistic Logic | All X are Y, All Y are Z. Is it true that all Z are X? |

Composite Figures | Find the area of this crecsent shaped region |

Convergence of Sequences | If \(f\) 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 Theorem | How 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

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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## Comments

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

Syllogisms 1

Syllogisms 2

Syllogisms 3

Syllogisms 4 – Mehul Arora · 11 months ago

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– Pranshu Gaba · 10 months, 4 weeks ago

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

– Agnishom Chattopadhyay · 11 months ago

Nice problems. I personally like #3 the best.Log in to reply

– Mehul Arora · 11 months ago

Number 3 is from a past NTSE :PLog in to reply

– Pranshu Gaba · 11 months ago

That's great! I am looking forward to solving your problemsLog in to reply

– Akiva Weinberger · 9 months, 2 weeks ago

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.Log in to reply

– Pi Han Goh · 11 months ago

Woahh! These are amazing! I find myself drawing up Venn Diagrams every time! LUV THEMLog in to reply

– Mehul Arora · 11 months ago

Thanks! These are indeed fun to solve :)Log in to reply

SCAA Logo on

composite figures– Lolly Lau · 11 months agoLog in to reply

– Pi Han Goh · 11 months ago

Wow! This is very simplistic and interesting! Reshared!Log in to reply

– Lolly Lau · 11 months ago

Thank you :)Log in to reply

– Calvin Lin Staff · 11 months ago

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

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

Simplifying ExpressionsThere is one and only one answer to this

PercentagesSwimming Pool Complex Construction (also part of Composite Figures)

Composite FiguresCaptain America's Shield

Vicious Circles & Savage Shapes

Inscribe-ception

Work-Energy TheoremLiquid in a tin can

Projectile Motion With Air Resistance

Conservation of Energy in Suspended Spring System

Other Classical Mechanics ProblemsAutomatic Clothes Dryer

Acceleration-time graphs in 1D kinematics

Sequence & Series ConvergenceWhat diverges?

List to be expanded. – Wee Xian Bin · 10 months, 4 weeks ago

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– Pi Han Goh · 10 months, 3 weeks ago

Woah! Captain America! Best question here!Log in to reply

– Wee Xian Bin · 10 months, 4 weeks ago

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 :)Log in to reply

– Pi Han Goh · 10 months, 3 weeks ago

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

– Wee Xian Bin · 10 months, 3 weeks ago

Yeap, added new question on series convergence :)Log in to reply

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Could you please organize your problems into one comment or it's replies? That is usually helpful for us for bookkeeping. – Agnishom Chattopadhyay · 10 months, 3 weeks ago

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Sometimeswritingcommentsof 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 · 10 months, 3 weeks agoLog in to reply

– Agnishom Chattopadhyay · 10 months, 3 weeks ago

I do agree with you. We told the staff about this. I hope they'll fix them in the earliest.Log in to reply

– Ashish Siva · 10 months, 3 weeks ago

Thanks! :) Sorry for not being able to organize the questionsLog in to reply

– Agnishom Chattopadhyay · 10 months, 3 weeks ago

Do not worry. I took care of it.Log in to reply

– Ashish Siva · 10 months, 3 weeks ago

Thanks!!Log in to reply

Haha, my first impression was to differentiate it and show that it's a constant! – Pi Han Goh · 10 months, 3 weeks ago

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– Ashish Siva · 10 months, 3 weeks ago

:P yeah maybe it is under that topic. Differentiatae! LolLog in to reply

Here are my contributions

Simplifying Expressions

Percentages

Composite Figures – Chung Kevin · 11 months ago

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– Pranshu Gaba · 10 months, 4 weeks ago

Thanks, these are interesting problems, and tricky too!Log in to reply

– Calvin Lin Staff · 11 months ago

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

Here's mine on operator search.

Eight \(8\)'s

BTW the new comments system make me dizzy. – Lee Care Gene · 11 months ago

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– Agnishom Chattopadhyay · 11 months ago

Thanks, we will see what we can do to make it work betterLog in to reply

– Rishabh Cool · 11 months ago

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)Log in to reply

– Ashish Siva · 11 months ago

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.Log in to reply

– Agnishom Chattopadhyay · 11 months ago

Thanks Rishav, I will talk to the staff about thisLog in to reply

– Rishabh Cool · 11 months ago

*RishabhLog in to reply

– Calvin Lin Staff · 11 months ago

That's a nice problem. How can we show that is indeed the minimum?Log in to reply

Here is my submission:- Percentages and Simplifying Expressions – Anuj Shikarkhane · 11 months ago

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– Pranshu Gaba · 10 months, 4 weeks ago

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

– Agnishom Chattopadhyay · 11 months ago

I enjoyed your problem on Simplifying Expressions.Log in to reply

– Pi Han Goh · 11 months ago

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!Log in to reply

– Anuj Shikarkhane · 11 months ago

I'm happy that u guys liked my problems!Log in to reply

– Calvin Lin Staff · 11 months ago

Thanks! Both of these questions are great :)Log in to reply

– Anuj Shikarkhane · 11 months ago

Thank you :)Log in to reply

Here's my most challenging problem on Arithmetic Puzzle: Can you fill in these boxes?. – Worranat Pakornrat · 11 months ago

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– Pi Han Goh · 11 months ago

Can you show that the answer is unique?Log in to reply

– Worranat Pakornrat · 11 months ago

I'll try, but it looks pretty complex. :)Log in to reply

– Calvin Lin Staff · 11 months ago

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

– Worranat Pakornrat · 11 months ago

I'll try, but it looks pretty complex. :)Log in to reply

Syllogismzz. - 3

Syllogismzz. - 2

Syllogismzz. - 1

Here's mine for syllogism – Sanyam Goel · 11 months ago

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@Mehul Arora, you got a competitor! =D – Pi Han Goh · 11 months ago

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– Sanyam Goel · 11 months ago

hehehehe !!!!Log in to reply

@sanyam goel better be on his heels ;) – Mehul Arora · 11 months ago

Hahaha I love competition. And I'm up for it :P I'll probably be posting more soon, soLog in to reply

– Sanyam Goel · 11 months ago

well, i will also be posting more problems after 4 july :-)Log in to reply

– Mehul Arora · 11 months ago

LOL okay, good to know!Log in to reply

– Calvin Lin Staff · 11 months ago

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 :)Log in to reply

Here's mine for Composite Figure: Love Circles. – Worranat Pakornrat · 11 months ago

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– Pi Han Goh · 11 months ago

Wow nice, I spot a reuleaux triangle there!Log in to reply

– Worranat Pakornrat · 11 months ago

Thanks! ;)Log in to reply

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 · 11 months ago

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– Worranat Pakornrat · 11 months ago

Oh, thanks for the advice. ;)Log in to reply

Percentages- That's really strongConvergence of Sequences- Vercongence?!Operator Search- Not as many as I expectedSyllogism- Matrix SyllogismWork-Energy Theorem- Work-Energy in a non-inertial frameLog in to reply

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 · 11 months ago

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And I don't understand why your last post is related to syllogistic logic. Isn't it just some matrix misconception? – Pi Han Goh · 11 months ago

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– Agnishom Chattopadhyay · 11 months ago

I added a solution. I hope this is helpfulLog in to reply

Doubling Dragon for

Arithmetic Puzzles. – Sam Bealing · 11 months agoLog in to reply

Also, this party is focused on Operator Search, and we will pull that out as a separate chapter. – Calvin Lin Staff · 11 months ago

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Too many twos! for

Simplifying Expressions. – Sam Bealing · 11 months agoLog in to reply

– Calvin Lin Staff · 11 months ago

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

I have plenty of rational expression problems from my former teacher's Russian problem sheet :) I will put them here.

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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 · 11 months ago

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– Hobart Pao · 11 months ago

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.Log in to reply

– Calvin Lin Staff · 11 months ago

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

Here are some suggestions for making great problems. – Pranshu Gaba · 11 months ago

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Here's my entry for Simplifying Expressions. – Joao Miguel Coelho · 10 months, 3 weeks ago

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– Pi Han Goh · 10 months, 3 weeks ago

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?Log in to reply

– Joao Miguel Coelho · 10 months, 3 weeks ago

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.Log in to reply

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:

Circle, triangle, circle, triangle, etc

Colored Tiles And Tangent Circles

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 · 10 months, 4 weeks ago

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They sure are! – Agnishom Chattopadhyay · 10 months, 4 weeks ago

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I hope that you guys enjoy! :) – Jonas Katona · 10 months, 4 weeks ago

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– Ashish Siva · 10 months, 4 weeks ago

OMG!Log in to reply

– Jonas Katona · 10 months, 4 weeks ago

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.Log in to reply

– Ashish Siva · 10 months, 4 weeks ago

Great way to go!Log in to reply

– Pi Han Goh · 10 months, 3 weeks ago

WOAHH! A TREASURE TROVE!!! =DDDDDDDLog in to reply

– Jonas Katona · 10 months, 3 weeks ago

THANKS PI HAN!! :DLog in to reply

This is the question in my stock on Length & Area: Weird Land for Sale. – Worranat Pakornrat · 10 months, 4 weeks ago

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Here is a first problem for Work – Hjalmar Orellana Soto · 10 months, 4 weeks ago

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– Agnishom Chattopadhyay · 10 months, 4 weeks ago

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

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 · 11 months ago

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– Pi Han Goh · 10 months, 4 weeks ago

This is a very simple setup! LikeddddLog in to reply

– Agnishom Chattopadhyay · 10 months, 4 weeks ago

This is a nice puzzle. The first question that came to my mind was if 0 is obtainable. But that doesn't seem so, nowLog in to reply

– Hung Woei Neoh · 10 months, 4 weeks ago

Thanks \(\ddot\smile\)Log in to reply

a problem about percentages Somebody please help... I can't get the format right... – Margaret Zheng · 11 months ago

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Very cute setup! Reshared. – Pi Han Goh · 11 months ago

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An easy one on Percentages: Summer Sale. – Worranat Pakornrat · 11 months ago

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Here are my entries:

Composite figure

Percentages

Operator Search

Operator Search 2 – Pi Han Goh · 11 months ago

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– Calvin Lin Staff · 11 months ago

I really enjoyed the operator search questions that you posted!Log in to reply

Here we go again on Arithmetic Puzzle: Can you fill in these boxes? (Part II). – Worranat Pakornrat · 11 months ago

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I would like more physics topics in next problem writing party :) – Ashish Siva · 10 months, 3 weeks ago

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Hi, here are mine:

Simplifyable.

16% – Stanislava Sojáková · 10 months, 3 weeks ago

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– Agnishom Chattopadhyay · 10 months, 3 weeks ago

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

– Agnishom Chattopadhyay · 10 months, 3 weeks ago

Thanks, the problems seem understandable nowLog in to reply

– Stanislava Sojáková · 10 months, 3 weeks ago

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

– Stanislava Sojáková · 10 months, 3 weeks ago

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

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 · 10 months, 3 weeks ago

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Here is my other entry for Composite figures. – Pi Han Goh · 10 months, 3 weeks ago

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Cool – Ayanlaja Adebola · 10 months, 3 weeks ago

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Here is another entry for Simplifying expressions. – Pi Han Goh · 10 months, 3 weeks ago

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Here's my entry for Convergence of Sequences. – Pi Han Goh · 10 months, 4 weeks 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 · 11 months ago

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– Agnishom Chattopadhyay · 11 months ago

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

– Ashish Siva · 11 months ago

Thanks, yh i will be back.Log in to reply

Basic Mathematics? It's a variation on the So Many Shapes format! – W Rose · 11 months ago

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Area of the Medial Triangle for

Length and Area. – Sam Bealing · 11 months agoLog in to reply

– Calvin Lin Staff · 11 months ago

Indeed, a useful fact to know :)Log in to reply

What is this problem writing party i need explanation please – Sudoku Subbu · 11 months ago

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– Mehul Arora · 11 months ago

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.Log in to reply

This is old wine in a new bottle for Length (perimeter) and Area Geometry problems. – W Rose · 11 months ago

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– Calvin Lin Staff · 11 months ago

I'm equally confused. Can you explain further?Log in to reply

– W Rose · 11 months ago

The lower legs form +/- 135 degree angle(s) with the shorter upper leg. The centroid formula is the scribble written above the polygon figure.Log in to reply

– Pi Han Goh · 11 months ago

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?Log in to reply

Concave/Convex – W Rose · 11 months ago

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– Pi Han Goh · 11 months ago

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

– Calvin Lin Staff · 11 months ago

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

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 · 11 months ago

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discussion for us to discuss it? – Agnishom Chattopadhyay · 11 months ago

That's a good point to ponder. How about you create aLog in to reply