Problem Writing Party: July 25th - Aug 14th - Calvin Lin

Problem Writing Party 11 had lots of comments with active back and forth discussion. It's great that the community is helping each other improve posed problems, so that we can collate much better challenge quizzes.

Once again, I'm working on creating the challenge 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

Absolute Value: Level 2, Level 3, Level 4
Linear Inequalities: Level 1, Level 2, Level 3
Radical Expressions: Level 1, Level 2, Level 3, Level 4
Uniform Circular Motion: Level 2, Level 4

New chapters
Operator Search: Level 2, Level 3, Level 4

Let's kick off our 12th Problem Writing Party!

How it Works

The party starts right now (July 25th, 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. We will be picking the best problems for each topic and they will be immortalized and formed into a challenge quiz. By participating, you will improve your presentation skills and learn how to write engaging problems that wow others!

The topics are:

Topic	Descriptions	Great Problems
Partial Fractions	Is it true that $\dfrac{4}{x^2-2^2} = \dfrac1{x-2} -\dfrac1{x+2}$ ?	Level 2, 3, 4
Geometric Progressions	If I run 1 mile every day, and each day I run 10% more than the previous day, on which day onwards would I have run over 2 miles?	Level 1, 2, 3
Vieta's formula	If $P,Q,R$ are roots to the equation $x^3 + 2x^2 + x + 1 = 0$ , then prove that $P^3 + Q^3 + R^3 =-5$ .	Level 3, 4, 5
Momentum	How do the pool balls move after they collide?	Level 2, 3
Taylor Series	Why is $1 -\dfrac13 +\dfrac15 - \dfrac17 + \dfrac19 - \cdots = \dfrac\pi4$ ?	Level 3, 4
Differentiation Rules	True or False? $\dfrac d{dx} \left [ f(x) g(x) \right ] = \left [\dfrac d{dx} f(x) \right ] \left [\dfrac d{dx} g(x) \right ]$	Level 2
Implicit Differentiation	What is the gradient of the curve $x^2 +y^2 = 2$ when $x= 1$ ?	Level 2
Abstract Data Types	How would you maintain a list to facilitate efficient deletion?	Level 3

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 nominate @Jonas Katona's question for Taylor Series.

Pi Han Goh - 4 years, 10 months ago

Thank you for your support!! :) I will definitely post - and come up with some more problems - before this party ends. I totally agree with Rishabh: there are so many great topics for this party!

Jonas Katona - 4 years, 10 months ago

Here's my contribution: Rolling Rugby, Bizarre Hyperbola for Implicit Differentiation

Coyote VS Road Runner, Geometric Mystery for Geometric Progression

Evil 666 for Taylor Series

Power of Derivatives for Differentiation

The Roots Are Right There! for Vieta's formula

The Hidden Prime for partial fractions.

Worranat Pakornrat - 4 years, 10 months ago

Wow your first question is a very creative setup. I tried ot solve it via geometry alone but I failed miserably. Looking forward to more questions!

Thanks. I agree that things will get much easier with calculus. As a matter of fact, I was a bit surprised with the solution myself. 😉

When is the next party coming?

Lee Care Gene - 4 years, 6 months ago

Here's one for Taylor Series (application).

A Former Brilliant Member - 4 years, 10 months ago

Is there any problem with the "Quiz that need help" link? It seems to direct to the list in the last party.

I think it's fixed now.

Geometric Progressions

A Vicious Circle

Taylor/Maclaurin Series

Maclaurin 2015

Partial Fractions

Multiple Partial Fractions

Implicit Differentiation

What's in the Denominator?
Abnormally Normal (Try not to think too hard for this problem)

Wee Xian Bin - 4 years, 10 months ago

Wow! Luv your circle question. I didn't expect that GeometricProgression is essential in solving this quesiton! Reshared!!

Do post moreeeeee

I have two Basic problems on G.P : 1 , 2

one problem on Implicit Differentiation :1

Sabhrant Sachan - 4 years, 10 months ago

I accept! Now, to come up with some new and creative problems...

Denton Young - 4 years, 10 months ago

Remember to post them hereeeeeee! =D

Okay! Here's a simple momentum problem.

All my entries will be here. I will try to write some more problems.

Taylor Series:

Partial fractions:

Geometric progressions:

Differentiation rules:

Implicit differentiation:

Nested radical differentiation

Hobart Pao - 4 years, 10 months ago

Love your partial fractions question. And I thought I need to use the quadratic formula. You got me there. Got more?

I'll have to think of them. Thanks!

TAYLOR SERIES

Prince Loomba - 4 years, 10 months ago

VIETA'S FORMULA

This is nice. Got anymore of these?

No I have posted problem on different logics except my set. Sorry!!

GEOMETRIC PROGRESSION

Partial fraction challenge and Partial fraction challenge (2)

Tommy Li - 4 years, 10 months ago

These are nice! Keep them comingg

Here is one for geometric progressions.

Aaron Tsai - 4 years, 10 months ago

Nice question, I see that there are indeed many ways to solve this question. Not sure why it's in Level 4 though. Hahah

you sure talk a lot ............. i will listen to your babbling after you have solved it . ha ha!!

were you able to solve that ques with even one of your 'methods' haHAHA!!!

i challenge everybody and anybody to do this : " https://brilliant.org/problems/its-level-6-isnt-it/?ref_id=1244287 " let's see if you like that he he !!

Abstract Data Structures: What Abstract Data Structures is this?

Agnishom Chattopadhyay - 4 years, 10 months ago

Here are my contributions

Chung Kevin - 4 years, 10 months ago

my question about partial fraction

and something is wrong with my correct answer choice... P.S. I am back from summer vacation to Brilliant! :)

Margaret Zheng - 4 years, 10 months ago

Another partial fraction question

Hmmmm, that doesn't look like partial fractions, but instead, it should be "long division of polynomials".

Okay... Then I'd love for it to be in "long division of polynomials". I will try to think of another one :)

@Margaret Zheng – Haha, no problem. In the meantime, you can read up the wiki page: partial fractions.

May I add some new and old problems of mine? I think they're somehow overrated though :)

•for Taylor Series

•Vieta's 1

•Geometric Progression

•Geometric Progression 2

•Geometric Progression 3

•Geometric Progression 4

•Vieta's 2

•Vieta's 3

Efren Medallo - 4 years, 10 months ago

Woah! Your last question is great!!!! And I thought I want to find all the roots first =D

New problem on Differentiation Rules:

https://brilliant.org/problems/chained/

Here is my first entry of problems:

Partial Fractions 1
Geometric Progressions 1.

Here is my second entry of problems:
Vieta's formula 1
Implicit Differentiation 1

Here is my third entry of problems:
Partial fractions 2, Partial fractions 3
Geometric progressions 2
Vieta's formula 2, Vieta's formula 3
Taylor series 1, Taylor series 2

Here are my fourth entries of problems:
Vieta's formula 4
Differentiation Rules 1

Here are my fifth entries of problems:
Geometric progression 3
Vieta's formula 5, Vieta's formula 6
Implicit differentiation 2
Differentiation rules 2
Taylor series 4

Here are sixth entries of problems:
Partial fractions 4, Partial fractions 5
Geometric progression 4, Geometric progression 5
Vieta's formula 7
Taylor series 5, Taylor series 6
Implicit differentiation 3

Sorry was busy. Will definitely contribute in next brilliant writing party

Anubhav Tyagi - 4 years, 10 months ago

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}`	$\boxed{123}$