Problem Writing Party: June 27th - July 10th - Calvin Lin

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:

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).

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
list


1. numbered
2. list

numbered
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"

Math

Appears 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}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered 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"

Math	Appears 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

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

Mehul Arora - 4 years, 11 months ago

Nice problems. I personally like #3 the best.

Agnishom Chattopadhyay - 4 years, 11 months ago

Number 3 is from a past NTSE :P

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

Pranshu Gaba - 4 years, 11 months ago

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

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

Pi Han Goh - 4 years, 11 months ago

Thanks! These are indeed fun to solve :)

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 - 4 years, 10 months ago

SCAA Logo on composite figures

Lolly Lau - 4 years, 11 months ago

Wow! This is very simplistic and interesting! Reshared!

Thank you :)

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

Calvin Lin Staff - 4 years, 11 months ago

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

Hobart Pao - 4 years, 11 months ago

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.

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

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.

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.

Too many twos! for Simplifying Expressions.

Sam Bealing - 4 years, 11 months ago

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

Doubling Dragon for Arithmetic Puzzles.

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.

Percentages - That's really strong
Convergence of Sequences - Vercongence?!
Operator Search - Not as many as I expected
(Probably not?) Syllogism - Matrix Syllogism
Work-Energy Theorem - Work-Energy in a non-inertial frame

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?

I added a solution. I hope this is helpful

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 :)

Here's mine for Composite Figure: Love Circles.

Worranat Pakornrat - 4 years, 11 months ago

<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.

Oh, thanks for the advice. ;)

Wow nice, I spot a reuleaux triangle there!

Thanks! ;)

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

sanyam goel - 4 years, 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 :)

@Mehul Arora, you got a competitor! =D

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 – well, i will also be posting more problems after 4 july :-)

@Sanyam Goel – LOL okay, good to know!

hehehehe !!!!

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

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

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

Can you show that the answer is unique?

Here is my submission:- Percentages and Simplifying Expressions

Anuj Shikarkhane - 4 years, 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!

I'm happy that u guys liked my problems!

I enjoyed your problem on Simplifying Expressions.

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

Thanks! Both of these questions are great :)

Here's mine on operator search.

Eight $8$ 's

BTW the new comments system make me dizzy.

Lee Care Gene - 4 years, 11 months ago

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

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 Jain - 4 years, 11 months ago

@Rishabh Jain – 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 Menon - 4 years, 11 months ago

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

@Agnishom Chattopadhyay – *Rishabh

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

Here are my contributions

Simplifying Expressions

Percentages

Composite Figures

Chung Kevin - 4 years, 11 months ago

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

Thanks, these are interesting problems, and tricky too!

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)

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.

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

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

@Ashish Menon – Do not worry. I took care of it.

@Agnishom Chattopadhyay – Thanks!!

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

Haha, my first impression was to differentiate it and show that it's a constant!

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

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

There is one and only one answer to this

Swimming Pool Complex Construction (also part of 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 - 4 years, 11 months 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 :)

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

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

Woah! Captain America! Best question here!

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

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

I really enjoyed the operator search questions that you posted!

An easy one on Percentages: Summer Sale.

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

Margaret Zheng - 4 years, 11 months ago

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.

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 - 4 years, 11 months 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, now

Thanks $\ddot\smile$

This is a very simple setup! Likedddd

Here is a first problem for Work

Hjalmar Orellana Soto - 4 years, 11 months ago

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

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

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 - 4 years, 11 months ago

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

They sure are!

Ayyy alright then, that's great! Here are my many entries for convergence of a series:

I hope that you guys enjoy! :)

@Jonas Katona – OMG!

@Ashish Menon – 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 – Great way to go!

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

@Pi Han Goh – THANKS PI HAN!! :D

Here's my entry for Simplifying Expressions.

Joao Miguel Coelho - 4 years, 11 months 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?

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.

What is this problem writing party i need explanation please

sudoku subbu - 4 years, 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.

Area of the Medial Triangle for Length and Area.

Indeed, a useful fact to know :)

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

W Rose - 4 years, 11 months ago

Well going party :). I am sad that I cant take part due to burden of exams and homeworks at school :(

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

Thanks, yh i will be back.

Here's my entry for Convergence of Sequences.

Here is another entry for Simplifying expressions.

Cool

Ayanlaja Adebola - 4 years, 11 months ago

Here is my other entry for Composite figures.

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 years, 11 months ago

Hi, here are mine:

Simplifyable.

16%

Stanislava Sojáková - 4 years, 11 months ago

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

Thanks, the problems seem understandable now

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

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

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

Concave/Convex

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

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

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

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?

I'm equally confused. Can you explain further?

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

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 - 4 years, 11 months ago

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

Math	Appears 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}`	$\boxed{123}$