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!

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 |

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

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These are simple and nice questions. I'm still wondering how you solve the 5 equations simultaneously in Flipping A Binary Coin.

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I used an online linear equations solver! :)

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This is my favorite one

Enjoy! :)

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Check it out!

It shows results in decimals and fractions both. I used this to write this solution

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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. :)

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"How about 4, 5, 6?" looks like a number theory question. Reshared

Nevertheless, you got very nice set of questions as usual.

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Thank you so much, Pi Han! You always take the time to try solving all of my problems, it seems. I really appreciate that. :)

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).

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Here is my submission -Minimum Value

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Ahh this one is nice!! @Rishabh Cool's solution was unexpected. I thought the only way to solve this is via case by case analysis. Reshared!

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Thanks!

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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.

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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.

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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.

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Here my number theory problem.

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Hmmmm. I'm curious. Which topic does this question fit inside?

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I am not sure. May be you can guide me :)

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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.

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This is my new question on Variance: Sunny Shoot-out.

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The set up of the problem makes it interesting! I liked it :)

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

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I really liked it too :)

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

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

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Here's my submission for radical expressions.

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

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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 \(x = 0 \).

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

And for Radical Expressions: Radical Sums.

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

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

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My contribution for Absolut Value

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

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

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One for Radical Expresions

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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

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I think this problem would be better suited to Level 4. I have changed the level of the problem.

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.Log in to reply

@Agnishom Chattopadhyay: I don't understand. Why? There are only 26 letters.

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Hmmm, this does not look like a heaps question. Am I mistaken?

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@Pi Han Goh : I'm sorry. Didn't get you.

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

Enjoy! Geoff

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Absolute value - Not sure if this qualifies

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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.

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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 :)

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In my humble opinion, it does. I also think it is a good problem

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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

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...

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@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 :)

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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 .

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

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

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Wow! You really have a cool collection of radical problems

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Thanks! :)

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Ah, the Fun with Exponents set. Brings back memories

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Do you want more of those?

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

The plot is not showing properly

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Thanks. Fixed.

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For your first question, I was wondering how you get the number \(1.374 \times 10 ^{284} \). Interesting setup, now I have to go and read the Heaps wiki.

Still, I have no idea what your last question is talking about, though. Reshared anyway!!

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Absolute Value Absolute Value 2

Linear Inequalities Linear Inequalities 2

Variance

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

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For discrete random variables, I have this one

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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.

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

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Hey thanks, @Agnishom Chattopadhyay ! :-) When I get a chance I'll compile a list of links to my other coin flippers!

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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.

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Nice twist on these topics.

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)

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

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How can I join in Slack..??? @Calvin Lin

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Here are my third round of entries

Absolute value 6.

Linear inequality 6.

Radical expressions 6.

Discrete Random Variables 3.

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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.

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I like absolute value 2. I thought it was a nice setup, and am slightly sad that it has no solutions.

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.

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Oh right. Thanks for pointing it out. I've fixed it! =D

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https://brilliant.org/discussions/thread/rolle-theorem/

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