×

Problem Writing Party: May 23rd to June 5th

Problem Writing Party number 7 was a resounding success! We have 28 quizzes created! I'm flabbergasted.

Here are the quizzes that the Brilliant community helped create:

New Brilliant Challenge Quizzes

You may also have noticed that when we add your problem to a challenge quiz, you will also receive a B-notification about it. That's our way to say "THANKS!" with a capital T. Your contributions are greatly appreciated, and the community loves these quizzes that challenge their problem-solving abilities. Keep it up!

Let's kick off our 8th Problem Writing Party!

How it Works

The party starts right now (May 23rd, 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. The topics are:

 GCD / LCM Pattern Recognition Euler's Theorem Conditional Probability Distribution into Bins Chess

To join, submit as many problems as you want to these listed topics. At the end of the party, Brilliant staff will be picking the best 5-10 problems for each topic. These problems will then be immortalized and formed into a challenge quiz. If we pick your problem, then you can brag to your friends because it will be displayed on Brilliant forever! Your problem has a better chance of being selected if you include a graphic (when appropriate) and a solution.

This Party's Topic Listing

The topics of problem submission for this party can be found by navigating over to the Brilliant publish page and checking under the quizzes that need your help section. Just click the contribute button next to the topic you want to make a submission to.

Happy writing and keep the party alive!

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.

Note by Calvin Lin
1 year, 6 months ago

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:

28 quizzes! Oh wow, that's a world record, or something.

Thanks so much for your contributions, and making this such a great success.

I'm sure I missed out a ton of people too. Sorry for not getting everyone!

Staff - 1 year, 6 months ago

Thank you, sir. :)

- 1 year, 5 months ago

Thanks @Calvin Lin

- 1 year, 6 months ago

Thank you sir, And even thank you for selecting my problem :D

- 1 year, 6 months ago

Thank you for selecting my problem and I will keep it up😃

- 1 year, 6 months ago

Thank you sir ;)

- 1 year, 6 months ago

Thank you sir , for selecting My problem :)

- 1 year, 6 months ago

Thank you for selecting our problems. ;)

- 1 year, 6 months ago

Amazing .!!!congrats sir & every contributor...!

- 1 year, 6 months ago

Here's one for Conditional Probability:

- 1 year, 6 months ago

Ah, that's beautiful. I'm always amazed that it works out so nicely.

Staff - 1 year, 6 months ago

Here is one: Mate in 3, not 4.

- 1 year, 6 months ago

Ah yes, I love your chess problems!!

Staff - 1 year, 6 months ago

Thank you for the compliment!

- 1 year, 6 months ago

Here is a question on AP .

These Questions are on Limits of functions

1st ,2nd ,3rd ,4th ,5th ,6th ,7th

- 1 year, 6 months ago

I like your very first question because, from a glance, it looks like an arithmetic progression and geometric progression, but it is a combination of them! Excellent!

This question is also good! There are many ways of approaching this question. I favorite method is to take the log of the exponential function first. Given that your limit has a nice form, I would have phrased the question to "$$L = \dfrac AB e$$, find $$A+B$$".

Overall, very diverse and exciting questions! Do post more! =D

- 1 year, 6 months ago

Thanks! Those are good suggestions :)

Staff - 1 year, 6 months ago

These three are good questions on limit of functions @Calvin Lin : 1st , 2nd , 3rd

- 1 year, 5 months ago

What should be done for pattern recognition? Just number theory patterns or counting triangle patterns too?

- 1 year, 6 months ago

When replying, make sure your comment is related to the threaded comment. Otherwise, it seems like you're hijacking someone else's comment.

Recursive descriptions, Explicit descriptions, Predicting terms, Visual patterns, etc. NT patterns are fine (e.g. $$n!$$, $$n^n-1$$ etc).
I'm not sure what you mean by "Counting triangle patterns". If you are thinking of the problems that you posted long time ago with "draw 40 points and connect them to another 40 points", then no, those are not under pattern recognition.

Staff - 1 year, 6 months ago

First of all sorry I wont reply somewhere unrelated. Second of all not those long ago questions. Just simple ones like in one figure there are 4 squares, in the next there are 9 of them, in the next there are 16 of them, so how many squares will be there in the 10th figure.

- 1 year, 6 months ago

Those are good. They are similar to problems in the Pattern Recognition chapter.

Staff - 1 year, 6 months ago

Here is a problem on Pattern Recognition.

- 1 year, 5 months ago

Nice problem Pranshu!

- 1 year, 5 months ago

My question on chess.

- 1 year, 5 months ago

Great picture. It really makes it easy to visualize your question. Keep posting more!! =D

- 1 year, 5 months ago

I loved this question! Thanks for sharing :)

- 1 year, 5 months ago

Here is my entry on Euler's Theorem.

- 1 year, 5 months ago

Intriguing problem! I solved it in a different way, and have added it as a solution.

- 1 year, 5 months ago

Thanks, I saw your solution, and have up voted it. It is easier. :)

- 1 year, 5 months ago

Your solution = My method. Modular inverse is an underrated method. NIce solution

- 1 year, 5 months ago

Yes, modular inverse is a really interesting part of number theory. :D

- 1 year, 5 months ago

This is my new question on Number Theory-Sweet Building.

Enjoy!

- 1 year, 6 months ago

- 1 year, 6 months ago

Here is my thirteenth one for AP

- 1 year, 6 months ago

I think this is nice. But do try to mix up the denominators in each of these terms, otherwise, it's much easy to figure out the common difference.

- 1 year, 6 months ago

That's a good question to ask. Suppose we want a AP of (positive) rational terms where all of the denominators are distinct. What is the minimum value of the largest denominator?

Staff - 1 year, 6 months ago

Hmmm, thanks will keep in mind for more questions.

- 1 year, 6 months ago

Here is my chess entry

- 1 year, 6 months ago

All the chess problems have their own unique way to submit a solution..

- 1 year, 6 months ago

Haha.... Yup!

- 1 year, 6 months ago

We should figure out a way to standardize the answer in chess problems.

Wouldn't it be nice if you could actually move the chess pieces around? Oh, such dreams.

Staff - 1 year, 5 months ago

Definitely... The thing I don't like about some of them is that they don't always define unique moves... If we could standardize, that would be great! :^)

- 1 year, 5 months ago

Here are some problems to motivate your progress in Arithmetic Progressions .

Progress your way : Part 1 , Part 2 , Part 3 , Part 4 .

- 1 year, 6 months ago

Thanks! I really like Part 2. I think it could benefit from an image of how the logs are placed.

Staff - 1 year, 5 months ago

- 1 year, 5 months ago

Here are my questions on limits Limit of composition 1 and Limit of composition 2

- 1 year, 6 months ago

Ah yes, proving that the limit actually exists (or fails to exists) is the challenging part. Nice!

- 1 year, 6 months ago

Thanks

- 1 year, 6 months ago

A Brand New Problem On Limits is here

- 1 year, 6 months ago

I'm so lucky to be the first solver of this problem!

- 1 year, 6 months ago

Try This one

- 1 year, 6 months ago

Got it!

UPDATE : Woah your solution is much faster than mine!

- 1 year, 6 months ago

Ah, that's really interesting! Can you add a solution to it? Thanks :)

Staff - 1 year, 6 months ago

For distribution into bins I have: 9 balls 3 colors, Egg Hunt, I come bearing gifts, and 3 colors of paint

- 1 year, 6 months ago

Woah! You got a knack for writing simple engaging questions!

- 1 year, 6 months ago

Thanks... I do my best... Glad you like them... You too! :)

- 1 year, 6 months ago

My submission to conditional probability See you again

- 1 year, 6 months ago

I've edited your problem for clarity + grammar + punctuation.

Original version:

Dom and Brian decide to race along the streets of Brazil. However, they know that the cops may get behind them. Dom being a fussy driver, the probability of him being intercepted by the police is 0.7, whereas as that of Brian being intercepted is 0.3. The probability of there cars being impounded (after being intercepted) are equal i.e 0.5. What is the probability of Brian's car is impounded.

New version:

Dom and Brian decided to race along the streets of Brazil, where the cops may chase after them. The probability of being intercepted by the police is 0.7 for Dom and 0.3 for Brian. After being intercepted, the probability that their cars get impounded is 0.5.
What is the probability that Brians's car gets impounded?

Do you see how this makes the problem clearer?

Staff - 1 year, 6 months ago

I am a bit poor at clarity + grammar + punctuation. :P thanks for the edit .

- 1 year, 6 months ago

Does this one count as conditional probability?

- 1 year, 6 months ago

Conditionally speaking, yes :)

Staff - 1 year, 6 months ago

OK, sounds good, I'll go ahead and submit it then! :)

- 1 year, 6 months ago

This one and this one are two more for conditional probability.

- 1 year, 6 months ago

Ah! A generalization of monty hall problem! I love both of them! Keep them coming Mr Geoff!

Here's another problem written by the legend @Brian Charlesworth $$\Longrightarrow$$ Monty Hall revisited.

- 1 year, 6 months ago

Ah yes, thats a good one... Having two halves of a \$10,000 bill was a cool twist! :^)

- 1 year, 6 months ago

Here is one for arithmetic progressions.

- 1 year, 6 months ago

Oh, that's a nice one.

Staff - 1 year, 6 months ago

Here is one for limits of functions.

- 1 year, 6 months ago

I added the case for the limit to be irrational, just in case :)

That's a great question, relating $$(1 + x) ^ \frac{1}{x}$$ with $$e$$.

Staff - 1 year, 6 months ago

Thanks! Didn't think of the irrational part.

Thank you!

- 1 year, 6 months ago

I missed the last PWP ( because I went to vacation :D ) , but this time I won't !

Here are some of my problems :
Pattern Recognition - Those Golden Shapes .
Chess - Is this a party or a war ?

- 1 year, 6 months ago

Where did you go on vacation?

People really like these chess puzzles, so we're starting to build a chapter around them :)

Staff - 1 year, 6 months ago

To my native, Goa sir .

- 1 year, 6 months ago

Here is one for Arithmetic progression.

- 1 year, 6 months ago

This is great! Your question didn't explicit tell us what the common difference or even the number of terms in this progression. It's less common to find these variables because most of them we are told to find the sum of the progression where all the relevant data are already given. Nice question!

- 1 year, 6 months ago

Thanks!

- 1 year, 6 months ago

One more question on limits

- 1 year, 5 months ago

Hm, can you add a solution to that? The units doesn't seem quite right to me.

Staff - 1 year, 5 months ago

I have added but image is small to be clearly visible @Calvin Lin

- 1 year, 5 months ago

My fifth question on chess.

- 1 year, 5 months ago

- 1 year, 5 months ago

Ah, that's a nice one!

Staff - 1 year, 5 months ago

Here is a problem for Limits of Functions

- 1 year, 5 months ago

Thanks for fixing the problem. It's a good one, and not many people are used to such a denominator.

Staff - 1 year, 5 months ago

Fourth question on chess.

- 1 year, 5 months ago

Third question on chess.

- 1 year, 5 months ago

This is nice!

- 1 year, 5 months ago

Thanks! I will post more questions like this.

- 1 year, 5 months ago

A more complicated one on Combinatorics-Conditional Probability: Date with a Psychic.

- 1 year, 5 months ago

Ah, be careful of division by zero!

Staff - 1 year, 5 months ago

Here's the easy one on Combinatorics-Conditional Probability: Rain or Shine.

- 1 year, 5 months ago

Second question on chess.

- 1 year, 5 months ago

Here's my problem for GCD/LCM!

- 1 year, 5 months ago

Short and sweet setup! Reshared!

- 1 year, 5 months ago

Here is my different sequence

- 1 year, 5 months ago

Hmmm, what chapter does this question falls into?

- 1 year, 5 months ago

At first its from number theory,then it comes from sequence.

- 1 year, 5 months ago

Shouldn't this fall under Diophantine equations?

- 1 year, 5 months ago

- 1 year, 5 months ago

Hello! Here is my Chess problem: The new knight

- 1 year, 5 months ago

That's known as the elongated knight, or a camel (in Quatrochess).

Staff - 1 year, 5 months ago

Cute question. I'm still wondering how to prove that the answer is indeed minimal.

- 1 year, 5 months ago

Great problem!

- 1 year, 5 months ago

Here is my twenty-third entry for GCD/LCM section.

- 1 year, 5 months ago

Nice problem, Ashish, although I think this is more suited for principle of inclusion and exclusion than GCD and LCM.

- 1 year, 5 months ago

Hmm. Thanks :) :)

- 1 year, 5 months ago

@Calvin Lin sir is arithmetic progressions, limits removed drom the problem writing party?

- 1 year, 5 months ago

We've got a bunch of problems in those chapters. So for those who are looking at the note, I would like for them to focus on the others.

Staff - 1 year, 5 months ago

Here is my twenty second entry for AP section.

- 1 year, 5 months ago

Here is my twentieth entry for AP section.

- 1 year, 5 months ago

here is my another problem on limits, Limit of intercept

- 1 year, 5 months ago

My entries will be posted here.

Limits:

Pattern Recognition:

Arithmetic progessions:

- 1 year, 5 months ago

Here is a problem on limits...

- 1 year, 5 months ago

Here is a problem:

- 1 year, 6 months ago

Hmmmm, it seems that you have posted 3 questions into one question. I think it's better to solve them all separately.

- 1 year, 5 months ago

Here is my nineteenth entry for AP section.

- 1 year, 6 months ago

Here is my eighteenth submission for AP section. I have tried my best to make the phrasing as clear as possible. Please comment.

- 1 year, 6 months ago

Another problem on limits: can u limit the floor?

- 1 year, 6 months ago

My entries:

AP & GP - Here, here and here

- 1 year, 6 months ago

Here is a problem on limts

- 1 year, 6 months ago

Thanks for using latex in the problem.

It would be great if the solution was in Latex too :)

Staff - 1 year, 5 months ago

Here is my seventeenth entry for AP section.

- 1 year, 6 months ago

Can this one be useful for the problem writing party?

- 1 year, 6 months ago

Hmmm, it seems that you only applied properties of modular arithmetic. So, unfortunately, I don't think this counts. =(

For starters, you can post some simple Euler's theorem questions that uses fermat's little theorem.

- 1 year, 6 months ago

Thank you. I'll post something with fermat's Little theorem soon. Then I'll post it here ok?

- 1 year, 6 months ago

Sure thing!! =D

- 1 year, 6 months ago

Here is my seventeenth submission for AP

- 1 year, 6 months ago

This is cute. There are a few issues, though:

You should mention that the number of odd terms and the number of even terms are equal. Otherwise, we wouldn't have known whether the last term is odd or even. Do you know how to rephrase your question?

Plus, looking at your solution tells us that you applied the arithmetic progression sum formula. Which is correct, but much longer than necessary. There's a much simpler solution.

Hint: The (absolute) difference between these sum can be expressed as $$(S_2 + S_4 + S_6 + \cdots + S_{n} ) - (S_1 + S_3 + S_5 + \cdots + S_{n-1} ) = (S_2 - S_1) + (S_4 - S_3) + (S_6-S_5) \cdots + (S_n - S{n-1})$$.

- 1 year, 6 months ago

In my solution I have proved that it ends with an odd number because sum of ecen numbered termw is more than the sum of odd numbered terms. Since it starts witg a positive odd term and its common difference is a positive integer, it ends with an even number. Anyways thanks! As I said before, my phrasing skills are a bit off. I am working to improve it.

- 1 year, 6 months ago

Unfortunately, your comment is not necessarily. Consider the case when the common difference is negative.

- 1 year, 6 months ago

I have indicated that it is a positive integer.

- 1 year, 6 months ago

- 1 year, 6 months ago

Thanks for your help. Anyways is mentioning this way ok or would you like me to edit the question directly to the question has an even number of terms?

- 1 year, 6 months ago

I would consider rephrasing your question such that the phrase "common difference is a positive integer" is (almost) at the start of the sentence.

- 1 year, 6 months ago

Thanks! I did that one.

- 1 year, 6 months ago

Here is my sixteenth entry for AP

- 1 year, 6 months ago

Wonderful question + solution. I've added bullet points to make it neater.

- 1 year, 6 months ago

Thank you very much. :) :)

- 1 year, 6 months ago

Here is my fifteenth submission for AP section.

- 1 year, 6 months ago

You don't require the 2nd part of the question, sum to n-1 terms...

- 1 year, 6 months ago

Yes I know, I thought it would make calculation easier by just subtracting them and obtaining the nth term.

- 1 year, 6 months ago

i didnt understand can u plz explain?(abt thiz party)

- 1 year, 6 months ago

The community is writing up problems in specific chapters, and the great ones will be put into challenge quizzes for those chapters. You can click on the "Level X" links to see examples of problems generated in the previous party.

Staff - 1 year, 6 months ago

a towering limit a moderate level problem on limits that i just created ! :)

- 1 year, 6 months ago

Woah! This question is best question yet! It's rare to see a power tower limit. I love it!

I've converted your solution to LaTeX. Hope you liked it!

- 1 year, 6 months ago

yeah its great!!thanks:)

- 1 year, 6 months ago

Here is my fourteenth submission for arithmetic progressions, pattern recognition and to some extent logical reasoning.

- 1 year, 6 months ago

This problem is once again very convoluted. Please work on simplifying your statements and making them clear. If you're inventing a phrase, make sure you define it for everyone else.

Staff - 1 year, 6 months ago

These are some from my old problems. ( No idea about levels)

For pattern recognition , can i post numerical patterns? Or graphical only?

- 1 year, 6 months ago

OHhhh I like your sum of sines limit question! It's tempting to say the answer is 0 by assuming all of them are 0.

- 1 year, 6 months ago

These problems could be cleaned up slightly. Also, several of them do not have good solutions. Can you add a clear solution to them?

Staff - 1 year, 6 months ago

Here is my fourteenth submission both for pattern recognition and arithmetic progression.

- 1 year, 6 months ago

I don't quite like "Oh, let's break this up into N sequences, and claim that there is such a pattern for them". Why can't we break it up into 50 sequences with a random pattern in them?

Avoid over-complicating a problem.

Also, a bonus is not a hint.

Staff - 1 year, 6 months ago

O didnt try breaking it up like that. I just mixed up 3 APs alright I will poat easy and simple questions in future.

- 1 year, 6 months ago

Where will you add this question @Calvin Lin :P

- 1 year, 6 months ago

Hmmm.. I think this is unncessarily complicated and it should split into 4 question: search for A, B, C and D. For what it's worth, I think your limit for "L" does not exists.

- 1 year, 6 months ago

I think you are right , I will split the questions . By the way , the limit exists . Hint : Sandwich theorm

- 1 year, 6 months ago

Here we go:

- 1 year, 6 months ago

These are great questions! I really enjoyed 1 and 2. I've edited 2 for clarity.

I have slight difficulty understanding 3, due to the numerous terms which could be ambiguous. I've offered an alternative phrasing for 3. Can you help me review and improve it? Thanks!

Staff - 1 year, 6 months ago

Thank you sir.For 3rd I have posted the solution.You can see it and make it correct accordingly.I will re-view it. :)

- 1 year, 6 months ago

Thanks. I've updated the phrasing accordingly. I removed "An even number of arithmetic means are added" as that is ambiguous. E.g. if $$a = 0, b = 1$$, do we add the AM's of $$\frac{1}{2}$$ an even number of times? Or do we add $$\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16} \ldots$$?

Staff - 1 year, 6 months ago

Here is my twelfth one for AP

- 1 year, 6 months ago

I've offered a much cleaner solution. Can you figure that out?

Staff - 1 year, 6 months ago

Yes, sum of the terms equidistant from the back and end are equal. So, last term + first term = 2 × middle term. Else , middle term is arithmetic mean of first and last term out. So, 2 × middle term = first term - last term.

- 1 year, 6 months ago

A new one on LCM-GCD: GCD vs LCM

- 1 year, 6 months ago

Ah yes, that's a nice basic fact. Certainly one to add to the L1/2 collection :)

Staff - 1 year, 6 months ago

Thanks. It's a basic fact that many may overlook.

- 1 year, 6 months ago

Here is a question on arithmetic progression..algebra it

- 1 year, 6 months ago

I've suggested a change to the problem that removes the condition $$a+b+c \neq 0$$.

Staff - 1 year, 6 months ago

Changed it.. Thank you

- 1 year, 6 months ago

My question on GCD/LCM.

Cubic Cuboids (Updated)

- 1 year, 6 months ago

Hm, can you add a solution to that problem? I think you're making an assumption about how the cuboids stack up.

Staff - 1 year, 6 months ago

Really sorry. I carelessly got the answer messed up. Updated the question.

- 1 year, 6 months ago

@Calvin Lin sir, question for AP and GP together:Just, AP

- 1 year, 6 months ago

For decimal answers, have them be accurate to a 2% margin. This ensures that people who round up or down will still be able to be marked correct.

Staff - 1 year, 6 months ago

Here goes my 11th one.

- 1 year, 6 months ago

Here's my problem Find It Without Plugging Values

- 1 year, 6 months ago

That's a nice one to play around with :)

Staff - 1 year, 6 months ago

Thanks!

- 1 year, 6 months ago

Here is my tenth submission for AP section.

- 1 year, 6 months ago

My problem on conditional probability-The Luck

- 1 year, 6 months ago

Hm, that problem could be edited for clarity, which would make it more engaging for others. Would you like help with that?

Staff - 1 year, 6 months ago

Here is my limit submission.

- 1 year, 6 months ago

But $$\require{cancel} \displaystyle \lim_{n\to\infty} \dfrac{n!}{!n} =\lim_{n\to\infty} \dfrac{ \cancel n \cancel ! }{\cancel ! \cancel n} = \lim_{n\to\infty} 1 = 1$$. haahahaha! Just kidding!

It's weird that derangements and factorials "share the same symbols". I guess that's what this question so good. Nice question! =D

- 1 year, 6 months ago

Ha ha ha... Thanks Pi! ;-)

- 1 year, 6 months ago

Here and here are my conditional probability submissions... Enjoy! :^)

- 1 year, 6 months ago

Here is my seventh submission for AP section

- 1 year, 6 months ago

This is nice! We don't have to find the first term nor the common difference, and yet, we can immediately get the answer!

This inspires me to post an arithmetic progression question of my own!

- 1 year, 6 months ago

Here is my sixth submission for arithmetic progression section.

- 1 year, 6 months ago

Haha! This reminds me of heron's formula and brahmagupta's fomula! Do post more questions! =D

- 1 year, 6 months ago

Herons formula! LOL

- 1 year, 6 months ago

- 1 year, 6 months ago

Hm, can I remove the "mod 2016" condition? That seems really arbitrary to me, and we're just making people jump through hoops to answer it. I think calculating $$A$$ is sufficient.

Staff - 1 year, 6 months ago

Here's my question on Combinatorics-Conditional Probability: Fighting Fish.

- 1 year, 6 months ago

That's a killer question!

Staff - 1 year, 6 months ago

Thanks. That's the way it is. ;)

- 1 year, 6 months ago

Here is my fifth submission for arithmetic progression part.

- 1 year, 6 months ago

Oh nice.

The question could be tidied up slightly by simply asking:

Is it true that $$a^3 + c^3 + 6 abc = 8 b^3$$?

Staff - 1 year, 6 months ago

Thanks, I have edited it accordingly.

- 1 year, 6 months ago

Here is my fourth one on Arithmetic progression-

- 1 year, 6 months ago

Here is my third submission for pattern recognition part.

- 1 year, 6 months ago

It just so happened that I published a chess problem yesterday :) Here it is.

- 1 year, 6 months ago

Perfect timing :)

Staff - 1 year, 6 months ago

Here is a problem for Arithmetic Progressions

- 1 year, 5 months ago

Here is my twentyfirst entry for AP section.

- 1 year, 5 months ago

Here's my limits of functions entry!

- 1 year, 6 months ago

And here's my entry for Euler's theorem!

- 1 year, 6 months ago

Here's my entry for GCD/LCM!

- 1 year, 6 months ago

Nice problem, Pi!

- 1 year, 6 months ago

Hahah I know thanks! I never saw​ any Number Theory questions from you before.... would you like to post some?

- 1 year, 6 months ago

Two problems for @Pi Han Goh : This one and this one. (The closest I've come to a number theory so far, although maybe they are more of "expectation value" problems???) Oh well they're still kinda fun... Enjoy! I'll try to think of some good number theory problems...

- 1 year, 6 months ago

Hmmmm... expected value falls under Combinatorics. And unfortunately, Calvin is not looking for Expected values questions right now.

But great questions nonetheless!

- 1 year, 6 months ago

Ah... Number theory... OK, lemme see what I can come up with.

- 1 year, 6 months ago

- 1 year, 6 months ago

Oh nice one. I wonder if we can relate the method of differences with this "method of sums".

Staff - 1 year, 6 months ago

Try this

- 1 year, 6 months ago

Try this https://brilliant.org/profile/abhi-pwu19k/sets/my-creations-check-them-out/413351/problem/interesting-polynomial/

- 1 year, 6 months ago

Hmmm, I think you're making random connection between different math backgrounds, which will make this question rather cumbersome to solve.

Do post more though!

- 1 year, 6 months ago

I agree with Pi Han. Avoid over-complicating the problem and making people jump through hoops to work on it. If the problem is interesting, you want to keep it simple. If the problem is boring, it doesn't help to add more (boring) parts to it.

Staff - 1 year, 6 months ago

Here is my ninth submission for lcm section.

- 1 year, 6 months ago

Ops it seems like you don't agree with my answer, and people are arguing. You might want to clarify and define everything precisely!

- 1 year, 6 months ago

@Christopher Boo you are absolutely correct , I have requested @Ashish Siva to edit the solution.

- 1 year, 6 months ago

Here is one for Euler's theorem.

- 1 year, 6 months ago

Hi Aaron, your question doesn't fit into Euler's Theorem because it doesn't apply any of the functions in that chapter. It should only be in that chapter if you have applied at least one of the following concepts:

For starters, you can simply write up another question with numbers whose powers are ridiculously large.
Like "What are the last three digits of $$\large 998^{10^6}$$?"
Would you like to post another version of this question?

- 1 year, 6 months ago

I won't post another version. I had commented on it here because one of the moderators had categorized it into Euler's Theorem. Thanks!

- 1 year, 6 months ago

Hm, but your solution doesn't use Euler's Theorem ...

Staff - 1 year, 6 months ago

@Calvin Lin sir I think this question would be terrifically for the logic quiz: logic challenge 1

- 1 year, 6 months ago

For the problem writing party, we are focusing on specific chapters each fortnight. Problems in these chapters will receive more attention, and be used to form the challenge sets from the community.

Currently, there isn't a topic that is relevant for the problem "logic challenge", and I do not think it should be forced into any of these 8 chapters.

Staff - 1 year, 6 months ago

Ok,sir whenever you find a relevant topic for it, please try to consider my question

- 1 year, 6 months ago

This problem reminds me of a game I played during elementary school, but now a harder version!

- 1 year, 6 months ago

Thank you, :D

- 1 year, 6 months ago

Expected value level 5 leave me please!

- 1 year, 6 months ago

I reviewed that problem as I was creating the Expected value set. It was unclear what you meant by "As soon as is distance exceeds X, it will find itself outside the cube with the same distance from the center and can again enter the cube only when distance becomes X". This also seems like a forced construct, which makes it less engaging to others to think about. As such, I passed over adding your problem.

Problems that are engaging, clearly explained, and simplified are much more likely to appeal to the community.

Staff - 1 year, 6 months ago

good luck Calvin Lin .. I will do .

- 1 year, 6 months ago

Thanks!

Staff - 1 year, 6 months ago

Here is my second submission for GCD section.

- 1 year, 6 months ago

I think it's quite simple. I expect your problems to be more towards thinking rather than straightforward...

- 1 year, 6 months ago

- 1 year, 6 months ago

Arithematic Progressions? I have a whole set:

last one alive

last one alive 2

last one alive 3

last one alive 4

- 1 year, 6 months ago

Not sure these are arithmetic progression problems...

- 1 year, 6 months ago

@Alex Li and @Calvin Lin sir as you both have strongly opposed my problems, here is how the last one alive problems can be solved by using AP:

Suppose there are n people in the circle, and we know the answer for all numbers smaller than n. If n=2k

is even, then every second person gets killed, and we are left with the k numbers 1,3,5,…,n−1

. We can reduce this to a problem with k

people, by mapping the numbers 1,3,5,...,n−1

onto 1,2,3,...,k

. If the solution for k

people is the person numbered i

, then the solution for n

people is 2i−1

, since the ith number in the sequence is 2i−1

If n=2k+1

is odd, then we are left with the k numbers 3,5,…,n. If the solution for k people is the person numbered i, then a similar reduction shows the solution for n people is 2i+1 Let Sk be the solution for k people.

Then $$S_{100}$$=$$2S_{50}$$-1

=2($$2S_{25}$$−1)−1=$$4S_{25}$$−3

=4($$2S_{12}$$+1)−3=$$8S_{12}$$+1

=8($$2S_{6}$$−1)+1=$$16S_{6}$$−7

=16($$2S_{3}$$−1)−7=$$32S_{3}$$-23

=32($$2S_{1}$$+1)−23=$$64S_{1}$$+9

=64∗1+9

=73

- 1 year, 6 months ago

Correct me if I'm wrong, but the "last one alive" series differs just in the initial numbers of people right? Although it's solvable by math, it would be more accurate to put it under the Computer Science section. Let the program do the work! In fact, you might not notice, there is a well-studied CS problem called Josephus problem which is exactly the same as yours! The coincidence, haha.

- 1 year, 6 months ago

Very well noticed 👍👍👍👍👍

- 1 year, 6 months ago

Right, so that solution indicates it's much more about finding the recursive nature, instead of the "arithmetic progression" aspect of the problem.

Staff - 1 year, 6 months ago

But sir it's possible to solve them with AP and according to me these questions or even one of them would be great if considered a part of the quizzes. I have got appreciation for these questions from many people on brilliant and other websites I posted these questions on.

- 1 year, 6 months ago

I agree that they are great and interesting problems.

However, I disagree that they are suitable for the Arithmetic Progressions chapter, because of how forced the connection is. At no point in time in your solution was the arithmetic progression nature of the sequence referenced. Instead, it's the recursive nature of calculating $$S_{2k}$$ and $$S_{2k+1}$$ from $$S_k$$ that's important in solving this problem. IE I don't see how an understanding of arithmetic progressions (whether it's the structure, or the sum, or the graph) would help someone solve this problem. Whereas, I see a strong connection between realizing the underlying recursive nature of the setup and being able to solve the problem.

Staff - 1 year, 6 months ago

Alright sir, Thsi is the 3rd time, I tried and did not get a problem in the quizzes. Will try next time

- 1 year, 6 months ago

I can help provide you with more feedback, to improve the relevance of your problems. Taking a quick glance through your problems, I think the main area to improve is to understand what makes the problem exciting for others to engage with, and how to have clear presentation that reflects that. One way to get started is to look at the existing challenge / concept quizzes, and see which questions inspire you, and then create different versions of those.

This problem of yours is in the inscribed and circumscribed figures Level 2 Challenges. The simplicity of it attracts people to want to work through it and figure out how they are related.
This other problem is also pretty engaging to the community, and I've placed it in the circle properties quiz.

Staff - 1 year, 6 months ago

Thank you sir

- 1 year, 6 months ago

Congrats!

- 1 year, 6 months ago

Thank

- 1 year, 6 months ago

You bro

- 1 year, 6 months ago

This is an example for 100 people in a circle

- 1 year, 6 months ago

These are not problems in arithmetic progressions. Yes, for the first $$n/2$$, it follows a pattern of $$2k-1$$. However, that pattern breaks after one loop around the circle, and it is not easily described via an arithmetic progression.

Staff - 1 year, 6 months ago

Uh @Calvin Lin sir are these questions fine? Please at least see them once you never appreciate my questions

- 1 year, 6 months ago

Hang on, I'm in the midst of replying to this thread. I am not an octopus with 8 arms, I only have 2 unfortunately.

Staff - 1 year, 6 months ago

😂😂😂😂😂😂, sorry sir.

- 1 year, 6 months ago

More AP questions: Just, AP Just, AP 2

- 1 year, 6 months ago

"Just AP" is NOT an AP.

I do not understand what "Just AP 2" refers to.

Staff - 1 year, 6 months ago

Alright sir as no one seems to understand any of my problems, I have deleted all of them. Hope that satisfies what you asked for. And by the way, sir we can solve all of the last one alive problems by using AP.

- 1 year, 6 months ago

There was no need to delete "Just AP". It's just that $$a_n = \frac{n}{n+1}$$ is not an arithmetic progression, and so I objected to saying "Consider the AP $$a_n = \frac{n}{n+1}$$".

For "Just AP 2", I was asking you to post a solution, so that I can figure out what you were trying to express.

I know that asking good questions is a skill, that takes time to be developed (and certainly isn't one that's taught in schools). It helps if your problem is interesting, easily understood and unambiguous. Please do not be discouraged, and continue going at it!

Staff - 1 year, 6 months ago

Sir please view my posted questions, if you find any one good , then. PLease include them in the quiz

- 1 year, 6 months ago