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

- Function Graphs: Level 2, Level 4
- Displacement Velocity Acceleration: Level 2, Level 3
- Floor and ceiling functions: Level 1, Level 2, Level 3, Level 4
- Expected Value: Level 2, Level 3, Level 4, Level 5
- Distribution into Bins: Level 2, Level 3, Level 4, Level 5
- Decimals: Level 1, Level 2, Level 4
- Logical Reasoning: Level 1, Level 2, Level 3, Level 4, Level 5
- Curve Sketching: Level 4
- Intro to Recursion: Level 2, Level 3, Level 4

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!

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.

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!

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.

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1 vote

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewest28 quizzes! Oh wow, that's a world record, or something.

@Elisabeth Bonnell @Saurav Yadav @Sparsh Sarode @Keerthi Reddy @Margaret Zheng @Geoff Pilling @Eli Ross @Chan Lye Lee @Alex Li @Worranat Pakornrat @Robert Melville @Mark Hennings @Andy Hayes @Sambhrant Sachan @Gautam Sharma @David Klein @Pranshu Gaba @Pi Han Goh @Ayush Rai @Ammarah Ehsan @Abhay Tiwari @Akshay Sharma @Andrew Christian @Soumava Pal

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!

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

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Thank you for selecting our problems. ;)

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Thank you sir , for selecting My problem :)

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Thank you sir ;)

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

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

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Thanks @Calvin Lin

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Thank you, sir. :)

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Here is a question on AP .

These Questions are on Limits of functions

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

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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

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Thanks! Those are good suggestions :)

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

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

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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.

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Pattern Recognition chapter.

Those are good. They are similar to problems in theLog in to reply

Here are a few problems I posted on chess: Hopeless position, Chess Scenario, Ridiculous Chess Puzzle, How many moves?, Mate in 3, How Did The Pawns Move So Far?, Mate in 2, How Can You Advance So Much?.

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Here is one: Mate in 3, not 4.

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Ah yes, I love your chess problems!!

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Thank you for the compliment!

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Here's one for Conditional Probability:

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

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Here is one for Arithmetic progression.

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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!

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Thanks!

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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 ?

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Where did you go on vacation?

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

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To my native, Goa sir .

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Here is one for limits of functions.

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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 \(e\).

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Thanks! Didn't think of the irrational part.

Thank you!

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Here is one for arithmetic progressions.

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Oh, that's a nice one.

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

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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.

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

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Does this one count as conditional probability?

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Conditionally speaking, yes :)

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

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My submission to conditional probability See you again

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

Original version:

New version:

Do you see how this makes the problem clearer?

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

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

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

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

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A Brand New Problem On Limits is here

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

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Try This one

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UPDATE : Woah your solution is much faster than mine!

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

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

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

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Thanks

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

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

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

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Your welcome, sir !

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Here is my chess entry

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

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Haha.... Yup!

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

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Here is my thirteenth one for AP

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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.

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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?

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Hmmm, thanks will keep in mind for more questions.

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

Enjoy!

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This question is adorable!

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Here is my entry on Euler's Theorem.

Last Two Digits

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

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@Pi Han Goh

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

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

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@Pranshu Gaba

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

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My question on chess.

Attack The White Squares

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I loved this question! Thanks for sharing :)

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

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Here is a problem on Pattern Recognition.

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Nice problem Pranshu!

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

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Perfect timing :)

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Here is my third submission for pattern recognition part.

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Here is my fourth one on Arithmetic progression-

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Here is my fifth submission for arithmetic progression part.

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Oh nice.

The question could be tidied up slightly by simply asking:

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Thanks, I have edited it accordingly.

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

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That's a killer question!

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

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Second Floor

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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.

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Here is my sixth submission for arithmetic progression section.

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

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Herons formula! LOL

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Here is my seventh submission for AP section

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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!

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

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Here is my limit submission.

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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

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

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My problem on conditional probability-The Luck

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

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Here is my tenth submission for AP section.

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Here's my problem Find It Without Plugging Values

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

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Thanks!

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Here goes my 11th one.

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

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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.

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My question on GCD/LCM.

Cubic Cuboids (Updated)

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

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

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Here is a question on arithmetic progression..algebra it

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

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Changed it.. Thank you

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A new one on LCM-GCD: GCD vs LCM

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

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

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Here is my twelfth one for AP

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

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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.

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Here we go:

Arithematic progression 1

Arithematic progression 2

Arithematic progession 3

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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!

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

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Where will you add this question @Calvin Lin :P

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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.

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

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

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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.

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

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Problem 1 Problem 2 Problem 3 Problem 4

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

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

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

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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.

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

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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.

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

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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!

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yeah its great!!thanks:)

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

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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.

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Here is my fifteenth submission for AP section.

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

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

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Here is my sixteenth entry for AP

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

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Thank you very much. :) :)

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Here is my seventeenth submission for AP

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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 \((S_2 + S_4 + S_6 + \cdots + S_{n} ) - (S_1 + S_3 + S_5 + \cdots + S_{n-1} ) = (S_2 - S_1) + (S_4 - S_3) + (S_6-S_5) \cdots + (S_n - S{n-1}) \).Log in to reply

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.

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Can this one be useful for the problem writing party?

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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.

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

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Here is my seventeenth entry for AP section.

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Here is a problem on limts

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Thanks for using latex in the problem.

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

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My entries:

AP & GP - Here, here and here

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Another problem on limits: can u limit the floor?

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

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Here is my nineteenth entry for AP section.

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Here is a problem:

3 in 1

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

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Here is a problem on limits...

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My entries will be posted here.

Limits:

Pattern Recognition:

Arithmetic progessions:

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here is my another problem on limits, Limit of intercept

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Here is my twentieth entry for AP section.

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Here is my twenty second entry for AP section.

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

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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.

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

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

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Hmm. Thanks :) :)

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Hello! Here is my Chess problem: The new knight

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Great problem!

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

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

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Here is my different sequence

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Hmmm, what chapter does this question falls into?

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

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Here's my problem for GCD/LCM!

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Short and sweet setup! Reshared!

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Second question on chess.

Fill It Up With Pawns

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

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

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Ah, be careful of division by zero!

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Third question on chess.

Kingly Kings

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This is nice!

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Thanks! I will post more questions like this.

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Fourth question on chess.

Queenly Queens

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Here is a problem for Limits of Functions

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

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problem about lcm and gcd

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Ah, that's a nice one!

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My fifth question on chess.

Roomy Rooks

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One more question on limits

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

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

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Here is one for Euler's theorem.

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

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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?

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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!

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Here is my ninth submission for lcm section.

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

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

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Try this

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

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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!

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Here's my entry for arithmetic progression.

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

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Here's my entry for GCD/LCM!

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Nice problem, Pi!

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

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@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...

Two problems forLog in to reply

But great questions nonetheless!

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

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Here's my limits of functions entry!

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Here is my twentyfirst entry for AP section.

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Here is a problem for Arithmetic Progressions

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Here is my second submission for GCD section.

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

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Hmmm it was intended to be simple. Or how about this one?

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good luck Calvin Lin .. I will do .

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Thanks!

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Expected value level 5 leave me please!

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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.

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

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

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Thank you, :D

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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.

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

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Arithematic Progressions? I have a whole set:

last one alive

last one alive 2

last one alive 3

last one alive 4

last one alive x

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Not sure these are arithmetic progression problems...

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@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

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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.

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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.

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Josephus problem which is exactly the same as yours! The coincidence, haha.

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 calledLog in to reply

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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.

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

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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.

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More AP questions: Just, AP Just, AP 2

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