Problem Writing Party 10 had a ton of discussion, and lots of people were contributing various problems to it. You may have noticed that we started adding some new chapters like Operator Search, Syllogistic Logic, Composite Figures and Convergence of Sequences, indicating that we're expanding the availability of material on Brilliant. Unfortunately, this introduced confusion, as it wasn't immediately clear what was / was not allowed into the chapter. As such, we will only be adding existing chapters to the PWP, so that everyone can easily reference the relevant material.

Once again, I'm working on creating the quizzes, and will update the following list ASAP. The new chapters will take a bit more time for us to create, and I am hoping for them to be released at the end of the week.

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 QuizzesProperties of Arithmetic: Level 1, Level 2

Operator Search: Level 2, Level 3, Level 4

Percentages: Level 1, Level 2

Syllogistic Logic

Composite Figures: Level 2, Level 3, Level 4

Convergence of Sequences

Work: Level 2, Level 3

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

## How it Works

The party starts right now (July 12th, 2016) and will last for the next 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 few problems for each topic and they will be immortalized and formed into a challenge quiz.

Do participate in attaining a sense of accomplishment and a growth in problem writing skills!

The topics are:

Topic | Descriptions | Great Problems |

Absolute value | \(|x| \) is the distance from from 0 to \(x\) on the number line. How do we interpret \(|x-y|\)? | Level 2, 3 |

Linear Inequalities | We know that \(1 < 2\), but is it also true that \(x<2x\)? | Level 1, 2, 3 |

Radical Expressions | Is it true that \( \sqrt a \times \sqrt b = \sqrt{ab} \)? | Level 1, 2, 3 |

Uniform Circular Motion | Uniform circular motion describes objects that move along a curve of a constant radius at constant speed. | Level 1, 2, 3 |

Variance | I have two distributions. Which distributions is more sparse than the other? | Level 2, 3 |

Discrete Random Variables | Would you rather flip 10 fair coins or 10 biased coins in hopes of getting 5 heads and 5 tails? | Level 2, 3, 4 |

Heaps | Heaps are data structures which are maintained in a way so that finding the minimum or the maximum is always efficient. | Level 1, 2 |

## 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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TopNewestHere is a collection of my coin flipping problems that could likely be added to the discrete variable problems:

Enjoy! Geoff – Geoff Pilling · 4 months, 3 weeks ago

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Flipping A Binary Coin. – Pi Han Goh · 4 months, 3 weeks ago

These are simple and nice questions. I'm still wondering how you solve the 5 equations simultaneously inLog in to reply

– Geoff Pilling · 4 months, 3 weeks ago

I used an online linear equations solver! :)Log in to reply

– Pi Han Goh · 4 months, 3 weeks ago

DO share with us! What app is that?Log in to reply

This is my favorite one

Enjoy! :) – Geoff Pilling · 4 months, 3 weeks ago

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– Hung Woei Neoh · 4 months, 3 weeks ago

Or you can Google "Linear Equation System Calculator". I found another one that can enter 4×4 all the way to 12×12Log in to reply

– Pi Han Goh · 4 months, 3 weeks ago

SHARE SHARE! =DLog in to reply

– Ashish Siva · 4 months, 3 weeks ago

Lol!Log in to reply

Check it out!

It shows results in decimals and fractions both. I used this to write this solution – Hung Woei Neoh · 4 months, 3 weeks ago

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– Hung Woei Neoh · 4 months, 3 weeks ago

Wow, the link you gave is good!Log in to reply

I have several radical expressions problems here which I would like to be considered for this Problem Writing Party. Here they are!

Enjoy! I apologize that these were posted late, and I really hope that you guys will forgive me. :) – Jonas Katona · 4 months, 1 week ago

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Nevertheless, you got very nice set of questions as usual. – Pi Han Goh · 4 months, 1 week ago

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Btw, for the "Putting it through twice" problem, I looked back and finally understood your frustration; that's why I changed the problem to how you wanted it. I apologize for the trouble; I sometimes make careless mistakes because I forget to look at how everything fits together. I am glad that you take the time to look at things thoroughly, because you would find faults which very few others would notice (as with this one). – Jonas Katona · 4 months, 1 week ago

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– Pi Han Goh · 4 months, 1 week ago

Don't worry about it. We're all helping each other here! =DLog in to reply

Here is my submission -Minimum Value – Anuj Shikarkhane · 4 months, 3 weeks ago

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@Rishabh Cool's solution was unexpected. I thought the only way to solve this is via case by case analysis. Reshared! – Pi Han Goh · 4 months, 3 weeks ago

Ahh this one is nice!!Log in to reply

– Anuj Shikarkhane · 4 months, 3 weeks ago

Thanks!Log in to reply

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– Pi Han Goh · 4 months, 3 weeks ago

I think most of your radical questions are super duper hard because we need to deal with convergence, which is another hard issue to tackle.Log in to reply

As a fairly new member, I am happy to submit Radical Mad. If someone could latex it, it would be appreciated. Thanks and @Calvin Lin sorry for previous inactivity in problem writing parties. – Sal Gard · 4 months, 1 week ago

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– Pi Han Goh · 4 months, 1 week ago

Hmmm, this looks like multiple tedious algebraic manipulation questions merged into one. Have you tried simplifying your question? Because from the looks of it, it's just plain bashing.Log in to reply

Here my number theory problem. – Snehal Shekatkar · 4 months, 2 weeks ago

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– Pi Han Goh · 4 months, 2 weeks ago

Hmmmm. I'm curious. Which topic does this question fit inside?Log in to reply

– Snehal Shekatkar · 4 months, 2 weeks ago

I am not sure. May be you can guide me :)Log in to reply

– Pi Han Goh · 4 months, 2 weeks ago

Calvin wished to have problems in Absolute value, Linear inequalities, Radical expressions, etc (in the table above) only. Your number theory question is nice but I don't think that is what he is looking for right now.Log in to reply

Here are my second round of entries

Absolute value 3, Absolute value 4, Absolute value 5.

Linear inequalities 4, Linear inequalities 5.

Radical expressions 2, Radical expressions 3, Radical expressions 4.

Variance 4, Variance 5.

Discrete Random Variables 1, Discrete Random Variables 2. – Pi Han Goh · 4 months, 2 weeks ago

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This is my new question on Variance: Sunny Shoot-out. – Worranat Pakornrat · 4 months, 2 weeks ago

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– Pranshu Gaba · 4 months, 2 weeks ago

The set up of the problem makes it interesting! I liked it :)Log in to reply

– Worranat Pakornrat · 4 months, 2 weeks ago

Thanks. I was about to draw children at first, but my graphic skills are not that great.Log in to reply

– Calvin Lin Staff · 4 months, 2 weeks ago

I really liked it too :)Log in to reply

– Worranat Pakornrat · 4 months, 2 weeks ago

Thanks. Took me a while to draw the flowers though. LOL...Log in to reply

– Agnishom Chattopadhyay · 4 months, 2 weeks ago

Nice problem! How did you manage to generate the graphics?Log in to reply

– Worranat Pakornrat · 4 months, 2 weeks ago

Thanks. I drew it myself. Still far from Van Gogh's Sun flowers. Lol...Log in to reply

Here's my submission for radical expressions. – Louie Dy · 4 months, 2 weeks ago

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– Pi Han Goh · 4 months, 2 weeks ago

Hmmm, I think you're missing a lot of steps in your solution. How did you prove that it converges?Log in to reply

– Calvin Lin Staff · 4 months, 2 weeks ago

As pointed out, care has to be taken when dealing with infinite sequences. Sometimes, they could tend to infinity, and still satisfy the equation \( x = 2x \), which doesn't imply that \(x = 0 \).Log in to reply

Here's mine on Discrete Variables: Infinity Game, Grab & Guess.

And for Radical Expressions: Radical Sums. – Worranat Pakornrat · 4 months, 2 weeks ago

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– Calvin Lin Staff · 4 months, 2 weeks ago

Nice questions, providing a scenario where the distribution occurs makes it more enticing for people to think about.Log in to reply

– Worranat Pakornrat · 4 months, 2 weeks ago

Thanks. I was busy with my new work lately. I'll try to come up with new ones soon. ;)Log in to reply

My contribution for Absolut Value – Hjalmar Orellana Soto · 4 months, 2 weeks ago

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– Pi Han Goh · 4 months, 2 weeks ago

Ah! This is cute. I love how the positions of the absolute value signs change everything!Log in to reply

– Calvin Lin Staff · 4 months, 2 weeks ago

Indeed, that was a fun question to work on :)Log in to reply

Radical Expresions – Hjalmar Orellana Soto · 4 months, 2 weeks ago

One forLog in to reply

Here is a computer science problem I created. I think this should be placed in level 5 but I was unable to do that because of my own level. @Calvin Lin : Can you kindly do this? Thanks – Snehal Shekatkar · 4 months, 3 weeks ago

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The

convert number to number nameproblem seems interesting. However, I think counting up the number of straightlines in each letter makes it a little tedious. – Agnishom Chattopadhyay · 4 months, 3 weeks agoLog in to reply

@Agnishom Chattopadhyay: I don't understand. Why? There are only 26 letters. – Snehal Shekatkar · 4 months, 3 weeks ago

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– Agnishom Chattopadhyay · 4 months, 3 weeks ago

Alright then :). How many letters would you find tedious yourself?Log in to reply

– Pi Han Goh · 4 months, 2 weeks ago

Hmmm, this does not look like a heaps question. Am I mistaken?Log in to reply

@Pi Han Goh : I'm sorry. Didn't get you. – Snehal Shekatkar · 4 months, 2 weeks ago

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– Pi Han Goh · 4 months, 2 weeks ago

Sorry. Autocorrect. Fixed.Log in to reply

Here are some dice rolling ones which could likely be considered as discrete random variables:

Enjoy! Geoff – Geoff Pilling · 4 months, 3 weeks ago

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Absolute value - Not sure if this qualifies – Hung Woei Neoh · 4 months, 3 weeks ago

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– Pi Han Goh · 4 months, 3 weeks ago

Hmmm, this feels like an amalgamation of absolute values and floor/ceiling functions which require us to know various backgrounds before solving it first. To be honest, this seems more like a ceiling/floor question.Log in to reply

– Calvin Lin Staff · 4 months, 2 weeks ago

Becuase floor/ceiling functions tend to be studied later than absolute values, I'm also inclined to place this under floor/ceiling. This is a great quesiton though :)Log in to reply

– Agnishom Chattopadhyay · 4 months, 3 weeks ago

In my humble opinion, it does. I also think it is a good problemLog in to reply

Here are my problems, list will be expanded as more are added.

Uniform Circular Motion3 masses, 3 strings & 1 pin

Automatic Clothes Dryer

Jupiter Ascending

Circular motion of ions in a magnetic field

Absolute ValueRadicalsLog in to reply

– Pi Han Goh · 4 months, 3 weeks ago

Ahh! I love your second last question. It feels like a mixture of inequalities of polynomials and absolute value properties. I'm still struggling with your last question though...Log in to reply

@Pi Han Goh You may want to try my older radical problem and my Some Brute Force & Luck Needed Part 1 problems first for a feel then :) – Wee Xian Bin · 4 months, 3 weeks ago

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Uniform Circular Motion:"Around and around"Log in to reply

Absolute value and complex number is my question about absolute value . – Tommy Li · 4 months, 3 weeks ago

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– Pi Han Goh · 4 months, 3 weeks ago

I was wondering: How did you find the square root of that large number in your penultimate step so easily?Log in to reply

– Tommy Li · 4 months, 3 weeks ago

I used calculator to do some calculation . No trick is involved .Log in to reply

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– Agnishom Chattopadhyay · 4 months, 3 weeks ago

Wow! You really have a cool collection of radical problemsLog in to reply

– Ashish Siva · 4 months, 3 weeks ago

Thanks! :)Log in to reply

– Hung Woei Neoh · 4 months, 3 weeks ago

Ah, the Fun with Exponents set. Brings back memoriesLog in to reply

– Ashish Siva · 4 months, 3 weeks ago

Do you want more of those?Log in to reply

– Hung Woei Neoh · 4 months, 3 weeks ago

Only if you have free time. Let me know when there's a new question. I'll check for typos again XDLog in to reply

– Sal Gard · 4 months, 3 weeks ago

Same. I used to look forward to those.Log in to reply

Heaps:This is really an addition problem, Towards better heaps, d-ary heapsAbsolute Values:Colorful AbsolutesVariance:Erratic Systematic Wormhole VarianceLog in to reply

– Hung Woei Neoh · 4 months, 3 weeks ago

The plot is not showing properlyLog in to reply

– Agnishom Chattopadhyay · 4 months, 3 weeks ago

Thanks. Fixed.Log in to reply

Still, I have no idea what your last question is talking about, though. Reshared anyway!! – Pi Han Goh · 4 months, 3 weeks ago

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Absolute Value Absolute Value 2

Linear Inequalities Linear Inequalities 2

Variance – Chung Kevin · 4 months, 3 weeks ago

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– Pi Han Goh · 4 months, 3 weeks ago

Nice set of questions. This got me thinking: What is the shape of the graph \( |x_1 | + |x_2| + |x_3| + \cdots + |x_n| = 1\)?Log in to reply

For discrete random variables, I have this one – Geoff Pilling · 4 months, 3 weeks ago

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– Calvin Lin Staff · 4 months, 2 weeks ago

Good setup. The solution should briefly explain how one could arrive at the count. The usage of Markov chains to express the change of states could be a helpful framework.Log in to reply

– Agnishom Chattopadhyay · 4 months, 3 weeks ago

This is a really cool problem. I bet many of your other problems regarding coin flippings also fit into this category.Log in to reply

@Agnishom Chattopadhyay ! :-) When I get a chance I'll compile a list of links to my other coin flippers! – Geoff Pilling · 4 months, 3 weeks ago

Hey thanks,Log in to reply

This is my entry for Absolute number: Zero Sum Game.

My new one on Inequalities: Think Positive.

Here's mine on Discrete variables: Hit the Jackpot. – Worranat Pakornrat · 4 months, 3 weeks ago

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For the absolute value question, my concern is that the origin lies in all 4 quadrants, and so we must be careful to explain how to deal with these cases. Perhaps, we could divide the expression by \(xy\)?

(Note: I've combined your comments) – Calvin Lin Staff · 4 months, 2 weeks ago

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– Worranat Pakornrat · 4 months, 2 weeks ago

Thanks for the feedback. Yes, maybe I'll add that x,y are not zeros.Log in to reply

How can I join in Slack..??? @Calvin Lin – Sudhir Aripirala · 4 months ago

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Here are my third round of entries

Absolute value 6.

Linear inequality 6.

Radical expressions 6.

Discrete Random Variables 3. – Pi Han Goh · 4 months, 2 weeks ago

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Here are my entries::::

Absolute value 1, Absolute value 2

Radical Expressions 1

Linear Inequalities 1, Linear Inequalities 2, Linear Inequalities 3

Variance 1, Variance 2, Variance 3. – Pi Han Goh · 4 months, 3 weeks ago

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For variance 2, you have to be careful to make it such that the rv only takes on those values. Otherwise, we could have (say) \( P(Y = 1000) = 0.1 \), which would affect the variance. – Calvin Lin Staff · 4 months, 2 weeks ago

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– Pi Han Goh · 4 months, 2 weeks ago

Oh right. Thanks for pointing it out. I've fixed it! =DLog in to reply

https://brilliant.org/discussions/thread/rolle-theorem/ – Rishabh Deep Singh · 4 months, 1 week ago

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