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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:

TopicDescriptionsGreat 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 InequalitiesWe know that \(1 < 2\), but is it also true that \(x<2x\)?Level 1, 2, 3
Radical ExpressionsIs it true that \( \sqrt a \times \sqrt b = \sqrt{ab} \)?Level 1, 2, 3
Uniform Circular MotionUniform circular motion describes objects that move along a curve of a constant radius at constant speed.Level 1, 2, 3
VarianceI have two distributions. Which distributions is more sparse than the other?Level 2, 3
Discrete Random VariablesWould you rather flip 10 fair coins or 10 biased coins in hopes of getting 5 heads and 5 tails?Level 2, 3, 4
HeapsHeaps 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 months, 3 weeks ago

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Here 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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@Geoff Pilling These are simple and nice questions. I'm still wondering how you solve the 5 equations simultaneously in Flipping A Binary Coin. Pi Han Goh · 4 months, 3 weeks ago

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@Pi Han Goh I used an online linear equations solver! :) Geoff Pilling · 4 months, 3 weeks ago

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@Geoff Pilling DO share with us! What app is that? Pi Han Goh · 4 months, 3 weeks ago

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@Pi Han Goh This is my favorite one

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

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@Geoff Pilling Or you can Google "Linear Equation System Calculator". I found another one that can enter 4×4 all the way to 12×12 Hung Woei Neoh · 4 months, 3 weeks ago

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@Hung Woei Neoh SHARE SHARE! =D Pi Han Goh · 4 months, 3 weeks ago

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@Pi Han Goh Lol! Ashish Siva · 4 months, 3 weeks ago

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@Ashish Siva 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 Hung Woei Neoh · 4 months, 3 weeks ago

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@Geoff Pilling Wow, the link you gave is good! Hung Woei Neoh · 4 months, 3 weeks ago

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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. :) Jonas Katona · 4 months, 1 week ago

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

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

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@Pi Han Goh 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). Jonas Katona · 4 months, 1 week ago

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@Jonas Katona Don't worry about it. We're all helping each other here! =D Pi Han Goh · 4 months, 1 week ago

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

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@Anuj Shikarkhane 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! Pi Han Goh · 4 months, 3 weeks ago

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@Pi Han Goh Thanks! Anuj Shikarkhane · 4 months, 3 weeks ago

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@Hobart Pao 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. Pi Han Goh · 4 months, 3 weeks ago

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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. Sal Gard · 4 months, 1 week ago

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@Sal Gard 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. Pi Han Goh · 4 months, 1 week ago

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

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@Snehal Shekatkar Hmmmm. I'm curious. Which topic does this question fit inside? Pi Han Goh · 4 months, 2 weeks ago

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@Pi Han Goh I am not sure. May be you can guide me :) Snehal Shekatkar · 4 months, 2 weeks ago

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@Snehal Shekatkar 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. 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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@Worranat Pakornrat The set up of the problem makes it interesting! I liked it :) Pranshu Gaba · 4 months, 2 weeks ago

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@Pranshu Gaba Thanks. I was about to draw children at first, but my graphic skills are not that great. Worranat Pakornrat · 4 months, 2 weeks ago

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@Pranshu Gaba I really liked it too :) Calvin Lin Staff · 4 months, 2 weeks ago

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@Calvin Lin Thanks. Took me a while to draw the flowers though. LOL... Worranat Pakornrat · 4 months, 2 weeks ago

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@Worranat Pakornrat Nice problem! How did you manage to generate the graphics? Agnishom Chattopadhyay · 4 months, 2 weeks ago

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@Agnishom Chattopadhyay Thanks. I drew it myself. Still far from Van Gogh's Sun flowers. Lol... Worranat Pakornrat · 4 months, 2 weeks ago

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

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@Louie Dy Hmmm, I think you're missing a lot of steps in your solution. How did you prove that it converges? Pi Han Goh · 4 months, 2 weeks ago

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@Pi Han Goh 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 \(x = 0 \). Calvin Lin Staff · 4 months, 2 weeks ago

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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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@Worranat Pakornrat Nice questions, providing a scenario where the distribution occurs makes it more enticing for people to think about. Calvin Lin Staff · 4 months, 2 weeks ago

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@Calvin Lin Thanks. I was busy with my new work lately. I'll try to come up with new ones soon. ;) Worranat Pakornrat · 4 months, 2 weeks ago

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

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@Hjalmar Orellana Soto Ah! This is cute. I love how the positions of the absolute value signs change everything! Pi Han Goh · 4 months, 2 weeks ago

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@Pi Han Goh Indeed, that was a fun question to work on :) Calvin Lin Staff · 4 months, 2 weeks ago

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@Pi Han Goh One for Radical Expresions Hjalmar Orellana Soto · 4 months, 2 weeks ago

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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 Snehal Shekatkar · 4 months, 3 weeks ago

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@Snehal Shekatkar 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. Agnishom Chattopadhyay · 4 months, 3 weeks ago

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

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@Snehal Shekatkar Alright then :). How many letters would you find tedious yourself? Agnishom Chattopadhyay · 4 months, 3 weeks ago

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@Snehal Shekatkar Hmmm, this does not look like a heaps question. Am I mistaken? Pi Han Goh · 4 months, 2 weeks ago

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

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@Snehal Shekatkar Sorry. Autocorrect. Fixed. Pi Han Goh · 4 months, 2 weeks ago

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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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@Hung Woei Neoh 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. Pi Han Goh · 4 months, 3 weeks ago

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@Pi Han Goh 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 :) Calvin Lin Staff · 4 months, 2 weeks ago

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@Hung Woei Neoh In my humble opinion, it does. I also think it is a good problem Agnishom Chattopadhyay · 4 months, 3 weeks ago

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

Uniform Circular Motion

Absolute Value

Radicals

Wee Xian Bin · 4 months, 3 weeks ago

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@Wee Xian Bin 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... Pi Han Goh · 4 months, 3 weeks ago

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@Pi Han Goh @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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Michael Fuller · 4 months, 3 weeks ago

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

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@Tommy Li I was wondering: How did you find the square root of that large number in your penultimate step so easily? Pi Han Goh · 4 months, 3 weeks ago

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@Pi Han Goh I used calculator to do some calculation . No trick is involved . Tommy Li · 4 months, 3 weeks ago

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  • 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.
Ashish Siva · 4 months, 3 weeks ago

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@Ashish Siva Wow! You really have a cool collection of radical problems Agnishom Chattopadhyay · 4 months, 3 weeks ago

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@Agnishom Chattopadhyay Thanks! :) Ashish Siva · 4 months, 3 weeks ago

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@Ashish Siva Ah, the Fun with Exponents set. Brings back memories Hung Woei Neoh · 4 months, 3 weeks ago

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@Hung Woei Neoh Do you want more of those? Ashish Siva · 4 months, 3 weeks ago

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@Ashish Siva Only if you have free time. Let me know when there's a new question. I'll check for typos again XD Hung Woei Neoh · 4 months, 3 weeks ago

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@Hung Woei Neoh Same. I used to look forward to those. Sal Gard · 4 months, 3 weeks ago

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@Agnishom Chattopadhyay The plot is not showing properly Hung Woei Neoh · 4 months, 3 weeks ago

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@Hung Woei Neoh Thanks. Fixed. Agnishom Chattopadhyay · 4 months, 3 weeks ago

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@Agnishom Chattopadhyay 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!! Pi Han Goh · 4 months, 3 weeks ago

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@Chung Kevin Nice set of questions. This got me thinking: What is the shape of the graph \( |x_1 | + |x_2| + |x_3| + \cdots + |x_n| = 1\)? Pi Han Goh · 4 months, 3 weeks ago

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

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@Geoff Pilling 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. Calvin Lin Staff · 4 months, 2 weeks ago

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@Geoff Pilling This is a really cool problem. I bet many of your other problems regarding coin flippings also fit into this category. Agnishom Chattopadhyay · 4 months, 3 weeks ago

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@Agnishom Chattopadhyay Hey thanks, @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

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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. Worranat Pakornrat · 4 months, 3 weeks ago

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@Worranat Pakornrat 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) Calvin Lin Staff · 4 months, 2 weeks ago

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@Calvin Lin Thanks for the feedback. Yes, maybe I'll add that x,y are not zeros. Worranat Pakornrat · 4 months, 2 weeks ago

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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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@Pi Han Goh 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. Calvin Lin Staff · 4 months, 2 weeks ago

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@Calvin Lin Oh right. Thanks for pointing it out. I've fixed it! =D Pi Han Goh · 4 months, 2 weeks ago

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

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