# Problem Writing Party: July 11th - July 24th

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 Quizzes

Properties 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
$\quad$

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

1. Ask questions about the party or brainstorming ideas from Brilliant staff.

2. Share links to great relevant problems.

3. Bounce your ideas off each other to help formulate the best problem you can.

4. 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).

Note by Calvin Lin
4 years, 6 months ago

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.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 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"
MathAppears 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} $\boxed{123}$

Sort by:

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

Enjoy! Geoff

- 4 years, 6 months ago

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

- 4 years, 6 months ago

I used an online linear equations solver! :)

- 4 years, 6 months ago

DO share with us! What app is that?

- 4 years, 6 months ago

This is my favorite one

Enjoy! :)

- 4 years, 6 months ago

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

- 4 years, 6 months ago

SHARE SHARE! =D

- 4 years, 6 months ago

Lol!

- 4 years, 6 months ago

Sorry, I remembered wrongly. It's 2X2 to 11X11

Check it out!

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

- 4 years, 6 months ago

Wow, the link you gave is good!

- 4 years, 6 months ago

- 4 years, 6 months 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.

- 4 years, 6 months ago

Here is my submission -Minimum Value

- 4 years, 6 months ago

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!

- 4 years, 6 months ago

Thanks!

- 4 years, 6 months ago

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. :)

- 4 years, 6 months ago

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

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

- 4 years, 6 months ago

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).

- 4 years, 6 months ago

Don't worry about it. We're all helping each other here! =D

- 4 years, 6 months ago

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.

- 4 years, 6 months ago

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 $xy$?

Staff - 4 years, 6 months ago

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

- 4 years, 6 months ago

For discrete random variables, I have this one

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months 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.

Staff - 4 years, 6 months ago

- 4 years, 6 months ago

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

- 4 years, 6 months ago

The plot is not showing properly

- 4 years, 6 months ago

Thanks. Fixed.

- 4 years, 6 months ago

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!!

- 4 years, 6 months ago

• Here is my first submission for variance.
• Here is my second submission for unoform circular motion.
• Here is my third submission for circular motion.
• Here is my fourth submission for radical expressions.
• Here is my fifth submission for radical expressions.
• Here is my sixth submission for radical expressions.
• Here is my seventh submission for radical expressions.
• Here is my eight submission for radical expressions.
• Here is my ninth submission for radical expressions.
• Here is my tenth submission for radical expressions.

- 4 years, 6 months ago

Wow! You really have a cool collection of radical problems

- 4 years, 6 months ago

Thanks! :)

- 4 years, 6 months ago

Ah, the Fun with Exponents set. Brings back memories

- 4 years, 6 months ago

Do you want more of those?

- 4 years, 6 months ago

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

- 4 years, 6 months ago

Same. I used to look forward to those.

- 4 years, 6 months ago

Absolute value and complex number is my question about absolute value .

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months ago

- 4 years, 6 months ago

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

Uniform Circular Motion

Absolute Value

- 4 years, 6 months 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...

- 4 years, 6 months ago

@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 :)

- 4 years, 6 months ago

Absolute value - Not sure if this qualifies

- 4 years, 6 months ago

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

- 4 years, 6 months 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.

- 4 years, 6 months 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 :)

Staff - 4 years, 6 months ago

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

Enjoy! Geoff

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

The convert number to number name problem seems interesting. However, I think counting up the number of straightlines in each letter makes it a little tedious.

- 4 years, 6 months ago

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

- 4 years, 6 months ago

Alright then :). How many letters would you find tedious yourself?

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months ago

Sorry. Autocorrect. Fixed.

- 4 years, 6 months ago

My contribution for Absolut Value

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

Staff - 4 years, 6 months ago

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

Staff - 4 years, 6 months ago

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

- 4 years, 6 months ago

Here's my submission for radical expressions.

- 4 years, 6 months ago

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

- 4 years, 6 months 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 $x = 0$.

Staff - 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months ago

I really liked it too :)

Staff - 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months ago

Here are my second round of entries

- 4 years, 6 months ago

Here my number theory problem.

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months 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.

- 4 years, 6 months ago

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.

- 4 years, 6 months 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.

- 4 years, 6 months ago

Here are my entries::::

- 4 years, 6 months ago

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.

Staff - 4 years, 6 months ago

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

- 4 years, 6 months ago

Here are my third round of entries

- 4 years, 6 months ago

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

- 4 years, 5 months ago