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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 / LCMPattern RecognitionEuler's Theorem
Conditional ProbabilityDistribution into BinsChess

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
4 months ago

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28 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! Calvin Lin Staff · 4 months ago

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@Calvin Lin Thank you, sir. :) Soumava Pal · 3 months, 4 weeks ago

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@Calvin Lin Thanks @Calvin Lin Akshay Sharma · 4 months ago

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@Calvin Lin Thank you sir, And even thank you for selecting my problem :D Keerthi Reddy · 4 months ago

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@Calvin Lin Thank you for selecting my problem and I will keep it up😃 Margaret Zheng · 4 months ago

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@Calvin Lin Thank you sir ;) Sparsh Sarode · 4 months ago

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@Calvin Lin Thank you sir , for selecting My problem :) Sambhrant Sachan · 4 months ago

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@Calvin Lin Thank you for selecting our problems. ;) Worranat Pakornrat · 4 months ago

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@Calvin Lin Amazing .!!!congrats sir & every contributor...! Rishabh Tiwari · 4 months ago

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Here's one for Conditional Probability: Mark Hennings · 4 months ago

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@Mark Hennings Ah, that's beautiful. I'm always amazed that it works out so nicely. Calvin Lin Staff · 4 months ago

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@Seth-Riley Adams Here is one: Mate in 3, not 4. Patrick Corn · 4 months ago

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@Seth-Riley Adams Ah yes, I love your chess problems!! Calvin Lin Staff · 4 months ago

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@Calvin Lin Thank you for the compliment! Seth-Riley Adams · 4 months ago

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Here is a question on AP .

These Questions are on Limits of functions

1st ,2nd ,3rd ,4th ,5th ,6th ,7th Sambhrant Sachan · 4 months ago

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@Sambhrant Sachan 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 Pi Han Goh · 4 months ago

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@Sambhrant Sachan Thanks! Those are good suggestions :) Calvin Lin Staff · 4 months ago

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@Calvin Lin These three are good questions on limit of functions @Calvin Lin : 1st , 2nd , 3rd Sambhrant Sachan · 3 months, 4 weeks ago

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@Calvin Lin What should be done for pattern recognition? Just number theory patterns or counting triangle patterns too? Ashish Siva · 4 months ago

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@Ashish Siva 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. Calvin Lin Staff · 4 months ago

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@Calvin Lin 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. Ashish Siva · 4 months ago

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@Ashish Siva Those are good. They are similar to problems in the Pattern Recognition chapter. Calvin Lin Staff · 4 months ago

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Here is a problem on Pattern Recognition. Pranshu Gaba · 3 months, 3 weeks ago

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@Pranshu Gaba Nice problem Pranshu! Ashish Siva · 3 months, 3 weeks ago

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My question on chess.

Attack The White Squares Lee Care Gene · 3 months, 4 weeks ago

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@Lee Care Gene Great picture. It really makes it easy to visualize your question. Keep posting more!! =D Pi Han Goh · 3 months, 4 weeks ago

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@Lee Care Gene I loved this question! Thanks for sharing :) Pranshu Gaba · 3 months, 4 weeks ago

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Here is my entry on Euler's Theorem.

Last Two Digits Soumava Pal · 3 months, 4 weeks ago

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@Soumava Pal Intriguing problem! I solved it in a different way, and have added it as a solution. Pranshu Gaba · 3 months, 4 weeks ago

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@Pranshu Gaba @Pranshu Gaba

Thanks, I saw your solution, and have up voted it. It is easier. :) Soumava Pal · 3 months, 4 weeks ago

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@Soumava Pal Your solution = My method. Modular inverse is an underrated method. NIce solution Pi Han Goh · 3 months, 4 weeks ago

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@Pi Han Goh @Pi Han Goh

Yes, modular inverse is a really interesting part of number theory. :D Soumava Pal · 3 months, 4 weeks ago

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

Enjoy! Worranat Pakornrat · 4 months ago

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@Worranat Pakornrat This question is adorable! Pi Han Goh · 4 months ago

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Here is my thirteenth one for AP Ashish Siva · 4 months ago

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@Ashish Siva 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. Pi Han Goh · 4 months ago

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@Pi Han Goh 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? Calvin Lin Staff · 4 months ago

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@Pi Han Goh Hmmm, thanks will keep in mind for more questions. Ashish Siva · 4 months ago

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Here is my chess entry Geoff Pilling · 4 months ago

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@Geoff Pilling All the chess problems have their own unique way to submit a solution.. Christopher Boo · 4 months ago

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@Christopher Boo Haha.... Yup! Geoff Pilling · 4 months ago

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@Geoff Pilling 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. Calvin Lin Staff · 3 months, 3 weeks ago

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@Calvin Lin 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! :^) Geoff Pilling · 3 months, 3 weeks ago

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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 . Anish Harsha · 4 months ago

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@Anish Harsha Thanks! I really like Part 2. I think it could benefit from an image of how the logs are placed. Calvin Lin Staff · 3 months, 3 weeks ago

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@Calvin Lin Your welcome, sir ! Anish Harsha · 3 months, 3 weeks ago

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Here are my questions on limits Limit of composition 1 and Limit of composition 2 Prince Loomba · 4 months ago

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@Prince Loomba Ah yes, proving that the limit actually exists (or fails to exists) is the challenging part. Nice! Pi Han Goh · 4 months ago

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@Pi Han Goh Thanks Prince Loomba · 4 months ago

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A Brand New Problem On Limits is here Sambhrant Sachan · 4 months ago

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@Sambhrant Sachan I'm so lucky to be the first solver of this problem! Christopher Boo · 4 months ago

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@Christopher Boo Try This one Sambhrant Sachan · 4 months ago

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@Sambhrant Sachan Got it!

UPDATE : Woah your solution is much faster than mine! Christopher Boo · 4 months ago

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@Sambhrant Sachan Ah, that's really interesting! Can you add a solution to it? Thanks :) Calvin Lin Staff · 4 months ago

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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 Geoff Pilling · 4 months ago

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@Geoff Pilling Woah! You got a knack for writing simple engaging questions! Pi Han Goh · 4 months ago

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@Pi Han Goh Thanks... I do my best... Glad you like them... You too! :) Geoff Pilling · 4 months ago

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My submission to conditional probability See you again Rohit Ner · 4 months ago

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@Rohit Ner 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? Calvin Lin Staff · 4 months ago

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@Calvin Lin I am a bit poor at clarity + grammar + punctuation. :P thanks for the edit . Rohit Ner · 4 months ago

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Does this one count as conditional probability? Geoff Pilling · 4 months ago

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@Geoff Pilling Conditionally speaking, yes :) Calvin Lin Staff · 4 months ago

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@Calvin Lin OK, sounds good, I'll go ahead and submit it then! :) Geoff Pilling · 4 months ago

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This one and this one are two more for conditional probability. Geoff Pilling · 4 months ago

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@Geoff Pilling 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. Pi Han Goh · 4 months ago

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@Pi Han Goh Ah yes, thats a good one... Having two halves of a $10,000 bill was a cool twist! :^) Geoff Pilling · 4 months ago

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Here is one for arithmetic progressions. Aaron Tsai · 4 months ago

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@Aaron Tsai Oh, that's a nice one. Calvin Lin Staff · 4 months ago

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Here is one for limits of functions. Deeparaj Bhat · 4 months ago

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@Deeparaj Bhat 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 \(e\). Calvin Lin Staff · 4 months ago

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@Calvin Lin Thanks! Didn't think of the irrational part.

Thank you! Deeparaj Bhat · 4 months ago

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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 ? Anish Harsha · 4 months ago

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@Anish Harsha Where did you go on vacation?

People really like these chess puzzles, so we're starting to build a chapter around them :) Calvin Lin Staff · 4 months ago

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@Calvin Lin To my native, Goa sir . Anish Harsha · 4 months ago

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Here is one for Arithmetic progression. Ashish Siva · 4 months ago

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@Ashish Siva 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! Pi Han Goh · 4 months ago

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@Pi Han Goh Thanks! Ashish Siva · 4 months ago

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One more question on limits Prince Loomba · 3 months, 3 weeks ago

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@Prince Loomba Hm, can you add a solution to that? The units doesn't seem quite right to me. Calvin Lin Staff · 3 months, 3 weeks ago

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@Calvin Lin I have added but image is small to be clearly visible @Calvin Lin Prince Loomba · 3 months, 2 weeks ago

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My fifth question on chess.

Roomy Rooks Lee Care Gene · 3 months, 3 weeks ago

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problem about lcm and gcd Margaret Zheng · 3 months, 3 weeks ago

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@Margaret Zheng Ah, that's a nice one! Calvin Lin Staff · 3 months, 3 weeks ago

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Here is a problem for Limits of Functions Hjalmar Orellana Soto · 3 months, 3 weeks ago

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@Hjalmar Orellana Soto Thanks for fixing the problem. It's a good one, and not many people are used to such a denominator. Calvin Lin Staff · 3 months, 3 weeks ago

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Fourth question on chess.

Queenly Queens Lee Care Gene · 3 months, 3 weeks ago

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Third question on chess.

Kingly Kings Lee Care Gene · 3 months, 3 weeks ago

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@Lee Care Gene This is nice! Pi Han Goh · 3 months, 3 weeks ago

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@Pi Han Goh Thanks! I will post more questions like this. Lee Care Gene · 3 months, 3 weeks ago

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A more complicated one on Combinatorics-Conditional Probability: Date with a Psychic. Worranat Pakornrat · 3 months, 3 weeks ago

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@Worranat Pakornrat Ah, be careful of division by zero! Calvin Lin Staff · 3 months, 3 weeks ago

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Here's the easy one on Combinatorics-Conditional Probability: Rain or Shine. Worranat Pakornrat · 3 months, 3 weeks ago

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Second question on chess.

Fill It Up With Pawns Lee Care Gene · 3 months, 3 weeks ago

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Here's my problem for GCD/LCM! Pranshu Gaba · 3 months, 3 weeks ago

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@Pranshu Gaba Short and sweet setup! Reshared! Pi Han Goh · 3 months, 3 weeks ago

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Here is my different sequence Akash Shukla · 3 months, 3 weeks ago

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@Akash Shukla Hmmm, what chapter does this question falls into? Pi Han Goh · 3 months, 3 weeks ago

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@Pi Han Goh At first its from number theory,then it comes from sequence. Akash Shukla · 3 months, 3 weeks ago

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@Akash Shukla Shouldn't this fall under Diophantine equations? Pi Han Goh · 3 months, 3 weeks ago

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@Pi Han Goh I don't know about this. But if you say so, then it must be. Akash Shukla · 3 months, 3 weeks ago

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Hello! Here is my Chess problem: The new knight Arul Kolla · 3 months, 4 weeks ago

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@Arul Kolla That's known as the elongated knight, or a camel (in Quatrochess). Calvin Lin Staff · 3 months, 3 weeks ago

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@Arul Kolla Cute question. I'm still wondering how to prove that the answer is indeed minimal. Pi Han Goh · 3 months, 3 weeks ago

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@Arul Kolla Great problem! Seth-Riley Adams · 3 months, 4 weeks ago

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Here is my twenty-third entry for GCD/LCM section. Ashish Siva · 3 months, 4 weeks ago

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@Ashish Siva Nice problem, Ashish, although I think this is more suited for principle of inclusion and exclusion than GCD and LCM. Pranshu Gaba · 3 months, 4 weeks ago

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@Pranshu Gaba Hmm. Thanks :) :) Ashish Siva · 3 months, 4 weeks ago

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@Calvin Lin sir is arithmetic progressions, limits removed drom the problem writing party? Ashish Siva · 3 months, 4 weeks ago

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@Ashish Siva 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. Calvin Lin Staff · 3 months, 3 weeks ago

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Here is my twenty second entry for AP section. Ashish Siva · 3 months, 4 weeks ago

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Here is my twentieth entry for AP section. Ashish Siva · 3 months, 4 weeks ago

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here is my another problem on limits, Limit of intercept Prince Loomba · 3 months, 4 weeks ago

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My entries will be posted here.

Limits:

Pattern Recognition:

Arithmetic progessions:

Hobart Pao · 3 months, 4 weeks ago

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Here is a problem on limits... Sparsh Sarode · 3 months, 4 weeks ago

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Here is a problem:

3 in 1 Soumava Pal · 3 months, 4 weeks ago

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@Soumava Pal Hmmmm, it seems that you have posted 3 questions into one question. I think it's better to solve them all separately. Pi Han Goh · 3 months, 4 weeks ago

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Here is my nineteenth entry for AP section. Ashish Siva · 4 months ago

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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. Ashish Siva · 4 months ago

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Another problem on limits: can u limit the floor? Sparsh Sarode · 4 months ago

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My entries:

AP & GP - Here, here and here Hung Woei Neoh · 4 months ago

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Here is a problem on limts Sparsh Sarode · 4 months ago

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@Sparsh Sarode Thanks for using latex in the problem.

It would be great if the solution was in Latex too :) Calvin Lin Staff · 3 months, 3 weeks ago

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Here is my seventeenth entry for AP section. Ashish Siva · 4 months ago

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Can this one be useful for the problem writing party? Alex Spagnoletti · 4 months ago

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@Alex Spagnoletti 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. Pi Han Goh · 4 months ago

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@Pi Han Goh Thank you. I'll post something with fermat's Little theorem soon. Then I'll post it here ok? Alex Spagnoletti · 4 months ago

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@Alex Spagnoletti Sure thing!! =D Pi Han Goh · 4 months ago

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Here is my seventeenth submission for AP Ashish Siva · 4 months ago

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@Ashish Siva 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 \((S_2 + S_4 + S_6 + \cdots + S_{n} ) - (S_1 + S_3 + S_5 + \cdots + S_{n-1} ) = (S_2 - S_1) + (S_4 - S_3) + (S_6-S_5) \cdots + (S_n - S{n-1}) \). Pi Han Goh · 4 months ago

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@Pi Han Goh 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. Ashish Siva · 4 months ago

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@Ashish Siva Unfortunately, your comment is not necessarily. Consider the case when the common difference is negative. Pi Han Goh · 4 months ago

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@Pi Han Goh I have indicated that it is a positive integer. Ashish Siva · 4 months ago

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@Ashish Siva Oh right. My bad. Pi Han Goh · 4 months ago

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@Pi Han Goh 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? Ashish Siva · 4 months ago

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@Ashish Siva I would consider rephrasing your question such that the phrase "common difference is a positive integer" is (almost) at the start of the sentence. Pi Han Goh · 4 months ago

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@Pi Han Goh Thanks! I did that one. Ashish Siva · 4 months ago

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Here is my sixteenth entry for AP Ashish Siva · 4 months ago

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@Ashish Siva Wonderful question + solution. I've added bullet points to make it neater. Pi Han Goh · 4 months ago

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@Pi Han Goh Thank you very much. :) :) Ashish Siva · 4 months ago

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Here is my fifteenth submission for AP section. Ashish Siva · 4 months ago

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@Ashish Siva You don't require the 2nd part of the question, sum to n-1 terms... Sparsh Sarode · 4 months ago

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@Sparsh Sarode Yes I know, I thought it would make calculation easier by just subtracting them and obtaining the nth term. Ashish Siva · 4 months ago

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i didnt understand can u plz explain?(abt thiz party) Palepu Tarun Sathwik · 4 months ago

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@Palepu Tarun Sathwik 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. Calvin Lin Staff · 4 months ago

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a towering limit a moderate level problem on limits that i just created ! :) Rohith M.Athreya · 4 months ago

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@Rohith M.Athreya 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! Pi Han Goh · 4 months ago

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@Pi Han Goh yeah its great!!thanks:) Rohith M.Athreya · 4 months ago

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Here is my fourteenth submission for arithmetic progressions, pattern recognition and to some extent logical reasoning. Ashish Siva · 4 months ago

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@Ashish Siva 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. Calvin Lin Staff · 4 months ago

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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? Sachin Vishwakarma · 4 months ago

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@Sachin Vishwakarma 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. Pi Han Goh · 4 months ago

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@Sachin Vishwakarma These problems could be cleaned up slightly. Also, several of them do not have good solutions. Can you add a clear solution to them? Calvin Lin Staff · 4 months ago

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Here is my fourteenth submission both for pattern recognition and arithmetic progression. Ashish Siva · 4 months ago

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@Ashish Siva 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. Calvin Lin Staff · 4 months ago

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@Calvin Lin O didnt try breaking it up like that. I just mixed up 3 APs alright I will poat easy and simple questions in future. Ashish Siva · 4 months ago

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Where will you add this question @Calvin Lin :P Sambhrant Sachan · 4 months ago

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@Sambhrant Sachan 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. Pi Han Goh · 4 months ago

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@Pi Han Goh I think you are right , I will split the questions . By the way , the limit exists . Hint : Sandwich theorm Sambhrant Sachan · 4 months ago

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@Abhay Kumar 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! Calvin Lin Staff · 4 months ago

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@Calvin Lin Thank you sir.For 3rd I have posted the solution.You can see it and make it correct accordingly.I will re-view it. :) Abhay Kumar · 4 months ago

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@Abhay Kumar 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 \( \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16} \ldots \)? Calvin Lin Staff · 4 months ago

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Here is my twelfth one for AP Ashish Siva · 4 months ago

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@Ashish Siva I've offered a much cleaner solution. Can you figure that out? Calvin Lin Staff · 4 months ago

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@Calvin Lin 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. Ashish Siva · 4 months ago

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A new one on LCM-GCD: GCD vs LCM Worranat Pakornrat · 4 months ago

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@Worranat Pakornrat Ah yes, that's a nice basic fact. Certainly one to add to the L1/2 collection :) Calvin Lin Staff · 4 months ago

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@Calvin Lin Thanks. It's a basic fact that many may overlook. Worranat Pakornrat · 4 months ago

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Here is a question on arithmetic progression..algebra it Sparsh Sarode · 4 months ago

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@Sparsh Sarode I've suggested a change to the problem that removes the condition \(a+b+c \neq 0 \). Calvin Lin Staff · 4 months ago

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@Calvin Lin Changed it.. Thank you Sparsh Sarode · 4 months ago

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My question on GCD/LCM.

Cubic Cuboids (Updated) Lee Care Gene · 4 months ago

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@Lee Care Gene Hm, can you add a solution to that problem? I think you're making an assumption about how the cuboids stack up. Calvin Lin Staff · 4 months ago

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@Calvin Lin Really sorry. I carelessly got the answer messed up. Updated the question. Lee Care Gene · 4 months ago

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@Calvin Lin sir, question for AP and GP together:Just, AP Rishabh Sood · 4 months ago

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@Rishabh Sood 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. Calvin Lin Staff · 4 months ago

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Here goes my 11th one. Ashish Siva · 4 months ago

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Here's my problem Find It Without Plugging Values Anuj Shikarkhane · 4 months ago

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@Anuj Shikarkhane That's a nice one to play around with :) Calvin Lin Staff · 4 months ago

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@Calvin Lin Thanks! Anuj Shikarkhane · 4 months ago

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Here is my tenth submission for AP section. Ashish Siva · 4 months ago

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My problem on conditional probability-The Luck Www Www · 4 months ago

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@Www Www Hm, that problem could be edited for clarity, which would make it more engaging for others. Would you like help with that? Calvin Lin Staff · 4 months ago

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Here is my limit submission. Geoff Pilling · 4 months ago

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@Geoff Pilling 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 Pi Han Goh · 4 months ago

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@Pi Han Goh Ha ha ha... Thanks Pi! ;-) Geoff Pilling · 4 months ago

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Here and here are my conditional probability submissions... Enjoy! :^) Geoff Pilling · 4 months ago

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Here is my seventh submission for AP section Ashish Siva · 4 months ago

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@Ashish Siva 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! Pi Han Goh · 4 months ago

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Here is my sixth submission for arithmetic progression section. Ashish Siva · 4 months ago

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@Ashish Siva Haha! This reminds me of heron's formula and brahmagupta's fomula! Do post more questions! =D Pi Han Goh · 4 months ago

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@Pi Han Goh Herons formula! LOL Ashish Siva · 4 months ago

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Second Floor Rishabh Deep Singh · 4 months ago

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@Rishabh Deep Singh 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. Calvin Lin Staff · 4 months ago

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Here's my question on Combinatorics-Conditional Probability: Fighting Fish. Worranat Pakornrat · 4 months ago

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@Worranat Pakornrat That's a killer question! Calvin Lin Staff · 4 months ago

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@Calvin Lin Thanks. That's the way it is. ;) Worranat Pakornrat · 4 months ago

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Here is my fifth submission for arithmetic progression part. Ashish Siva · 4 months ago

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@Ashish Siva Oh nice.

The question could be tidied up slightly by simply asking:

Is it true that \( a^3 + c^3 + 6 abc = 8 b^3 \)?

Calvin Lin Staff · 4 months ago

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@Calvin Lin Thanks, I have edited it accordingly. Ashish Siva · 4 months ago

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Here is my fourth one on Arithmetic progression- Ashish Siva · 4 months ago

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Here is my third submission for pattern recognition part. Ashish Siva · 4 months ago

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It just so happened that I published a chess problem yesterday :) Here it is. Svatejas Shivakumar · 4 months ago

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@Svatejas Shivakumar Perfect timing :) Calvin Lin Staff · 4 months ago

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Here is a problem for Arithmetic Progressions Hjalmar Orellana Soto · 3 months, 3 weeks ago

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Here is my twentyfirst entry for AP section. Ashish Siva · 3 months, 4 weeks ago

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Here's my limits of functions entry! Pi Han Goh · 4 months ago

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And here's my entry for Euler's theorem! Pi Han Goh · 4 months ago

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Here's my entry for GCD/LCM! Pi Han Goh · 4 months ago

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@Pi Han Goh Nice problem, Pi! Geoff Pilling · 4 months ago

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@Geoff Pilling Hahah I know thanks! I never saw​ any Number Theory questions from you before.... would you like to post some? Pi Han Goh · 4 months ago

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@Pi Han Goh 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... Geoff Pilling · 4 months ago

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

But great questions nonetheless! Pi Han Goh · 4 months ago

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@Pi Han Goh Ah... Number theory... OK, lemme see what I can come up with. Geoff Pilling · 4 months ago

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@Pi Han Goh Oh nice one. I wonder if we can relate the method of differences with this "method of sums". Calvin Lin Staff · 4 months ago

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Try this Abhi Kumbale · 4 months ago

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@Abhi Kumbale Try this https://brilliant.org/profile/abhi-pwu19k/sets/my-creations-check-them-out/413351/problem/interesting-polynomial/ Abhi Kumbale · 4 months ago

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@Abhi Kumbale 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! Pi Han Goh · 4 months ago

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

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Here is my ninth submission for lcm section. Ashish Siva · 4 months ago

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@Ashish Siva Ops it seems like you don't agree with my answer, and people are arguing. You might want to clarify and define everything precisely! Christopher Boo · 4 months ago

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@Christopher Boo @Christopher Boo you are absolutely correct , I have requested @Ashish Siva to edit the solution. Rishabh Sood · 4 months ago

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Here is one for Euler's theorem. Aaron Tsai · 4 months ago

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@Aaron Tsai 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? Pi Han Goh · 4 months ago

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@Pi Han Goh 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! Aaron Tsai · 4 months ago

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@Aaron Tsai Hm, but your solution doesn't use Euler's Theorem ... Calvin Lin Staff · 4 months ago

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@Calvin Lin sir I think this question would be terrifically for the logic quiz: logic challenge 1 Rishabh Sood · 4 months ago

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@Rishabh Sood 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. Calvin Lin Staff · 4 months ago

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@Calvin Lin Ok,sir whenever you find a relevant topic for it, please try to consider my question Rishabh Sood · 4 months ago

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@Rishabh Sood This problem reminds me of a game I played during elementary school, but now a harder version! Christopher Boo · 4 months ago

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@Christopher Boo Thank you, :D Rishabh Sood · 4 months ago

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Expected value level 5 leave me please! Akul Agrawal · 4 months ago

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@Akul Agrawal 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. Calvin Lin Staff · 4 months ago

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good luck Calvin Lin .. I will do . Mohamed Aboalamayem · 4 months ago

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@Mohamed Aboalamayem Thanks! Calvin Lin Staff · 4 months ago

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Here is my second submission for GCD section. Ashish Siva · 4 months ago

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@Ashish Siva I think it's quite simple. I expect your problems to be more towards thinking rather than straightforward... Christopher Boo · 4 months ago

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@Christopher Boo Hmmm it was intended to be simple. Or how about this one? Ashish Siva · 4 months ago

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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 Rishabh Sood · 4 months ago

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@Rishabh Sood Not sure these are arithmetic progression problems... Alex Li · 4 months ago

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@Alex Li @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 Rishabh Sood · 4 months ago

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@Rishabh Sood 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. Christopher Boo · 4 months ago

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@Christopher Boo Very well noticed 👍👍👍👍👍 Rishabh Sood · 4 months ago

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@Rishabh Sood Right, so that solution indicates it's much more about finding the recursive nature, instead of the "arithmetic progression" aspect of the problem. Calvin Lin Staff · 4 months ago

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@Calvin Lin 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. Rishabh Sood · 4 months ago

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@Rishabh Sood 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. Calvin Lin Staff · 4 months ago

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@Calvin Lin Alright sir, Thsi is the 3rd time, I tried and did not get a problem in the quizzes. Will try next time Rishabh Sood · 4 months ago

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@Rishabh Sood 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. Calvin Lin Staff · 4 months ago

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@Calvin Lin Thank you sir Rishabh Sood · 4 months ago

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@Rishabh Sood Congrats! Ashish Siva · 4 months ago

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@Ashish Siva Thank Rishabh Sood · 4 months ago

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@Rishabh Sood You bro Rishabh Sood · 4 months ago

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@Rishabh Sood This is an example for 100 people in a circle Rishabh Sood · 4 months ago

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@Rishabh Sood 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. Calvin Lin Staff · 4 months ago

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@Rishabh Sood Uh @Calvin Lin sir are these questions fine? Please at least see them once you never appreciate my questions Rishabh Sood · 4 months ago

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@Rishabh Sood 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. Calvin Lin Staff · 4 months ago

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@Calvin Lin 😂😂😂😂😂😂, sorry sir. Rishabh Sood · 4 months ago

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@Rishabh Sood More AP questions: Just, AP Just, AP 2 Rishabh Sood · 4 months ago

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@Rishabh Sood "Just AP" is NOT an AP.

I do not understand what "Just AP 2" refers to. Calvin Lin Staff · 4 months ago

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@Calvin Lin 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. Rishabh Sood · 4 months ago

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@Rishabh Sood 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! Calvin Lin Staff · 4 months ago

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Sir please view my posted questions, if you find any one good , then. PLease include them in the quiz Rishabh Sood · 4 months ago

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