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!

## How it Works

The party starts right now (May 23rd, 2016) and will last for the next two weeks. Throughout the two weeks, we will be focusing on writing awesome problems for the topics listed in quizzes that need your help on the **publish** page. The topics are:

GCD / LCM | Pattern Recognition | Euler's Theorem | |

Conditional Probability | Distribution into Bins | Chess |

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

## This Party's Topic Listing

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

Happy writing and keep the party alive!

## Use this note to

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.

## 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! – Calvin Lin Staff · 1 year, 3 months ago

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– Soumava Pal · 1 year, 3 months ago

Thank you, sir. :)Log in to reply

@Calvin Lin – Akshay Sharma · 1 year, 3 months ago

ThanksLog in to reply

– Keerthi Reddy · 1 year, 3 months ago

Thank you sir, And even thank you for selecting my problem :DLog in to reply

– Margaret Zheng · 1 year, 3 months ago

Thank you for selecting my problem and I will keep it up😃Log in to reply

– Sparsh Sarode · 1 year, 3 months ago

Thank you sir ;)Log in to reply

– Sambhrant Sachan · 1 year, 3 months ago

Thank you sir , for selecting My problem :)Log in to reply

– Worranat Pakornrat · 1 year, 3 months ago

Thank you for selecting our problems. ;)Log in to reply

– Rishabh Tiwari · 1 year, 3 months ago

Amazing .!!!congrats sir & every contributor...!Log in to reply

Here's one for Conditional Probability: – Mark Hennings · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Ah, that's beautiful. I'm always amazed that it works out so nicely.Log 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?. – Seth-Riley Adams · 1 year, 3 months ago

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Mate in 3, not 4. – Patrick Corn · 1 year, 3 months ago

Here is one:Log in to reply

– Calvin Lin Staff · 1 year, 3 months ago

Ah yes, I love your chess problems!!Log in to reply

– Seth-Riley Adams · 1 year, 3 months ago

Thank you for the compliment!Log in to reply

Here is a question on AP .

These Questions are on Limits of functions

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

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

I like yourThis 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 · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Thanks! Those are good suggestions :)Log in to reply

@Calvin Lin : 1st , 2nd , 3rd – Sambhrant Sachan · 1 year, 3 months ago

These three are good questions on limit of functionsLog in to reply

– Ashish Siva · 1 year, 3 months ago

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

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 · 1 year, 3 months ago

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– Ashish Siva · 1 year, 3 months ago

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

Pattern Recognition chapter. – Calvin Lin Staff · 1 year, 3 months ago

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

Here is a problem on Pattern Recognition. – Pranshu Gaba · 1 year, 3 months ago

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– Ashish Siva · 1 year, 3 months ago

Nice problem Pranshu!Log in to reply

My question on chess.

Attack The White Squares – Lee Care Gene · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

– Pranshu Gaba · 1 year, 3 months ago

I loved this question! Thanks for sharing :)Log in to reply

Here is my entry on Euler's Theorem.

Last Two Digits – Soumava Pal · 1 year, 3 months ago

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– Pranshu Gaba · 1 year, 3 months ago

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

@Pranshu Gaba

Thanks, I saw your solution, and have up voted it. It is easier. :) – Soumava Pal · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

Your solution = My method. Modular inverse is an underrated method. NIce solutionLog in to reply

@Pi Han Goh

Yes, modular inverse is a really interesting part of number theory. :D – Soumava Pal · 1 year, 3 months ago

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

Enjoy! – Worranat Pakornrat · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

This question is adorable!Log in to reply

Here is my thirteenth one for AP – Ashish Siva · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

– Calvin Lin Staff · 1 year, 3 months ago

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

– Ashish Siva · 1 year, 3 months ago

Hmmm, thanks will keep in mind for more questions.Log in to reply

Here is my chess entry – Geoff Pilling · 1 year, 3 months ago

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– Christopher Boo · 1 year, 3 months ago

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

– Geoff Pilling · 1 year, 3 months ago

Haha.... Yup!Log in to reply

Wouldn't it be nice if you could actually move the chess pieces around? Oh, such dreams. – Calvin Lin Staff · 1 year, 3 months ago

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– Geoff Pilling · 1 year, 3 months ago

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

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

Progress your way : Part 1 , Part 2 , Part 3 , Part 4 . – Anish Harsha · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

– Anish Harsha · 1 year, 3 months ago

Your welcome, sir !Log in to reply

Here are my questions on limits Limit of composition 1 and Limit of composition 2 – Prince Loomba · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

– Prince Loomba · 1 year, 3 months ago

ThanksLog in to reply

A Brand New Problem On Limits is here – Sambhrant Sachan · 1 year, 3 months ago

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– Christopher Boo · 1 year, 3 months ago

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

This one – Sambhrant Sachan · 1 year, 3 months ago

TryLog in to reply

UPDATE : Woah your solution is much faster than mine! – Christopher Boo · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

For distribution into bins I have: 9 balls 3 colors, Egg Hunt, I come bearing gifts, and 3 colors of paint – Geoff Pilling · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

Woah! You got a knack for writing simple engaging questions!Log in to reply

– Geoff Pilling · 1 year, 3 months ago

Thanks... I do my best... Glad you like them... You too! :)Log in to reply

My submission to conditional probability See you again – Rohit Ner · 1 year, 3 months ago

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Original version:

New version:

Do you see how this makes the problem clearer? – Calvin Lin Staff · 1 year, 3 months ago

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– Rohit Ner · 1 year, 3 months ago

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

Does this one count as conditional probability? – Geoff Pilling · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Conditionally speaking, yes :)Log in to reply

– Geoff Pilling · 1 year, 3 months ago

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

This one and this one are two more for conditional probability. – Geoff Pilling · 1 year, 3 months ago

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

Ah! A generalization ofHere's another problem written by the legend @Brian Charlesworth \(\Longrightarrow\) Monty Hall revisited. – Pi Han Goh · 1 year, 3 months ago

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– Geoff Pilling · 1 year, 3 months ago

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

Here is one for arithmetic progressions. – Aaron Tsai · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Oh, that's a nice one.Log in to reply

Here is one for limits of functions. – Deeparaj Bhat · 1 year, 3 months ago

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That's a great question, relating \( (1 + x) ^ \frac{1}{x} \) with \(e\). – Calvin Lin Staff · 1 year, 3 months ago

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Thank you! – Deeparaj Bhat · 1 year, 3 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 · 1 year, 3 months ago

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People really like these chess puzzles, so we're starting to build a chapter around them :) – Calvin Lin Staff · 1 year, 3 months ago

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– Anish Harsha · 1 year, 3 months ago

To my native, Goa sir .Log in to reply

Here is one for Arithmetic progression. – Ashish Siva · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

– Ashish Siva · 1 year, 3 months ago

Thanks!Log in to reply

One more question on limits – Prince Loomba · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

@Calvin Lin – Prince Loomba · 1 year, 3 months ago

I have added but image is small to be clearly visibleLog in to reply

My fifth question on chess.

Roomy Rooks – Lee Care Gene · 1 year, 3 months ago

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problem about lcm and gcd – Margaret Zheng · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Ah, that's a nice one!Log in to reply

Here is a problem for Limits of Functions – Hjalmar Orellana Soto · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

Fourth question on chess.

Queenly Queens – Lee Care Gene · 1 year, 3 months ago

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Third question on chess.

Kingly Kings – Lee Care Gene · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

This is nice!Log in to reply

– Lee Care Gene · 1 year, 3 months ago

Thanks! I will post more questions like this.Log in to reply

A more complicated one on Combinatorics-Conditional Probability: Date with a Psychic. – Worranat Pakornrat · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Ah, be careful of division by zero!Log in to reply

Here's the easy one on Combinatorics-Conditional Probability: Rain or Shine. – Worranat Pakornrat · 1 year, 3 months ago

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Second question on chess.

Fill It Up With Pawns – Lee Care Gene · 1 year, 3 months ago

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Here's my problem for GCD/LCM! – Pranshu Gaba · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

Short and sweet setup! Reshared!Log in to reply

Here is my different sequence – Akash Shukla · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

Hmmm, what chapter does this question falls into?Log in to reply

– Akash Shukla · 1 year, 3 months ago

At first its from number theory,then it comes from sequence.Log in to reply

– Pi Han Goh · 1 year, 3 months ago

Shouldn't this fall under Diophantine equations?Log in to reply

– Akash Shukla · 1 year, 3 months ago

I don't know about this. But if you say so, then it must be.Log in to reply

Hello! Here is my Chess problem: The new knight – Arul Kolla · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

– Pi Han Goh · 1 year, 3 months ago

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

– Seth-Riley Adams · 1 year, 3 months ago

Great problem!Log in to reply

Here is my twenty-third entry for GCD/LCM section. – Ashish Siva · 1 year, 3 months ago

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principle of inclusion and exclusion than GCD and LCM. – Pranshu Gaba · 1 year, 3 months ago

Nice problem, Ashish, although I think this is more suited forLog in to reply

– Ashish Siva · 1 year, 3 months ago

Hmm. Thanks :) :)Log in to reply

@Calvin Lin sir is arithmetic progressions, limits removed drom the problem writing party? – Ashish Siva · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

Here is my twenty second entry for AP section. – Ashish Siva · 1 year, 3 months ago

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Here is my twentieth entry for AP section. – Ashish Siva · 1 year, 3 months ago

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here is my another problem on limits, Limit of intercept – Prince Loomba · 1 year, 3 months ago

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My entries will be posted here.

Limits:

Pattern Recognition:

Arithmetic progessions:

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Here is a problem on limits... – Sparsh Sarode · 1 year, 3 months ago

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Here is a problem:

3 in 1 – Soumava Pal · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

Here is my nineteenth entry for AP section. – Ashish Siva · 1 year, 3 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 · 1 year, 3 months ago

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Another problem on limits: can u limit the floor? – Sparsh Sarode · 1 year, 3 months ago

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My entries:

AP & GP - Here, here and here – Hung Woei Neoh · 1 year, 3 months ago

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Here is a problem on limts – Sparsh Sarode · 1 year, 3 months ago

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It would be great if the solution was in Latex too :) – Calvin Lin Staff · 1 year, 3 months ago

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Here is my seventeenth entry for AP section. – Ashish Siva · 1 year, 3 months ago

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Can this one be useful for the problem writing party? – Alex Spagnoletti · 1 year, 3 months ago

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For starters, you can post some simple Euler's theorem questions that uses fermat's little theorem. – Pi Han Goh · 1 year, 3 months ago

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– Alex Spagnoletti · 1 year, 3 months ago

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

– Pi Han Goh · 1 year, 3 months ago

Sure thing!! =DLog in to reply

Here is my seventeenth submission for AP – Ashish Siva · 1 year, 3 months ago

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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 · 1 year, 3 months agoLog in to reply

– Ashish Siva · 1 year, 3 months ago

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

– Pi Han Goh · 1 year, 3 months ago

Unfortunately, your comment is not necessarily. Consider the case when the common difference is negative.Log in to reply

– Ashish Siva · 1 year, 3 months ago

I have indicated that it is a positive integer.Log in to reply

– Pi Han Goh · 1 year, 3 months ago

Oh right. My bad.Log in to reply

– Ashish Siva · 1 year, 3 months ago

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

– Pi Han Goh · 1 year, 3 months ago

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

– Ashish Siva · 1 year, 3 months ago

Thanks! I did that one.Log in to reply

Here is my sixteenth entry for AP – Ashish Siva · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

– Ashish Siva · 1 year, 3 months ago

Thank you very much. :) :)Log in to reply

Here is my fifteenth submission for AP section. – Ashish Siva · 1 year, 3 months ago

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– Sparsh Sarode · 1 year, 3 months ago

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

– Ashish Siva · 1 year, 3 months ago

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

i didnt understand can u plz explain?(abt thiz party) – Palepu Tarun Sathwik · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

a towering limit a moderate level problem on limits that i just created ! :) – Rohith M.Athreya · 1 year, 3 months ago

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I've converted your solution to LaTeX. Hope you liked it! – Pi Han Goh · 1 year, 3 months ago

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– Rohith M.Athreya · 1 year, 3 months ago

yeah its great!!thanks:)Log in to reply

Here is my fourteenth submission for arithmetic progressions, pattern recognition and to some extent logical reasoning. – Ashish Siva · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

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 · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

– Calvin Lin Staff · 1 year, 3 months ago

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

Here is my fourteenth submission both for pattern recognition and arithmetic progression. – Ashish Siva · 1 year, 3 months ago

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Avoid over-complicating a problem.

Also, a bonus is not a hint. – Calvin Lin Staff · 1 year, 3 months ago

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– Ashish Siva · 1 year, 3 months ago

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

Where will you add this question @Calvin Lin :P – Sambhrant Sachan · 1 year, 3 months ago

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– Pi Han Goh · 1 year, 3 months ago

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

– Sambhrant Sachan · 1 year, 3 months ago

I think you are right , I will split the questions . By the way , the limit exists . Hint : Sandwich theormLog in to reply

Here we go:

Arithematic progression 1

Arithematic progression 2

Arithematic progession 3 – Abhay Kumar · 1 year, 3 months ago

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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 · 1 year, 3 months ago

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– Abhay Kumar · 1 year, 3 months ago

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

– Calvin Lin Staff · 1 year, 3 months ago

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

Here is my twelfth one for AP – Ashish Siva · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

I've offered a much cleaner solution. Can you figure that out?Log in to reply

– Ashish Siva · 1 year, 3 months ago

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

A new one on LCM-GCD: GCD vs LCM – Worranat Pakornrat · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

– Worranat Pakornrat · 1 year, 3 months ago

Thanks. It's a basic fact that many may overlook.Log in to reply

Here is a question on arithmetic progression..algebra it – Sparsh Sarode · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

– Sparsh Sarode · 1 year, 3 months ago

Changed it.. Thank youLog in to reply

My question on GCD/LCM.

Cubic Cuboids (Updated) – Lee Care Gene · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

– Lee Care Gene · 1 year, 3 months ago

Really sorry. I carelessly got the answer messed up. Updated the question.Log in to reply

@Calvin Lin sir, question for AP and GP together:Just, AP – Rishabh Sood · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

Here goes my 11th one. – Ashish Siva · 1 year, 3 months ago

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Here's my problem Find It Without Plugging Values – Anuj Shikarkhane · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

– Anuj Shikarkhane · 1 year, 3 months ago

Thanks!Log in to reply

Here is my tenth submission for AP section. – Ashish Siva · 1 year, 3 months ago

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My problem on conditional probability-The Luck – Www Www · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

Here is my limit submission. – Geoff Pilling · 1 year, 3 months ago

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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 · 1 year, 3 months ago

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– Geoff Pilling · 1 year, 3 months ago

Ha ha ha... Thanks Pi! ;-)Log in to reply

Here and here are my conditional probability submissions... Enjoy! :^) – Geoff Pilling · 1 year, 3 months ago

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Here is my seventh submission for AP section – Ashish Siva · 1 year, 3 months ago

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This inspires me to post an arithmetic progression question of my own! – Pi Han Goh · 1 year, 3 months ago

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Here is my sixth submission for arithmetic progression section. – Ashish Siva · 1 year, 3 months ago

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heron's formula and brahmagupta's fomula! Do post more questions! =D – Pi Han Goh · 1 year, 3 months ago

Haha! This reminds me ofLog in to reply

– Ashish Siva · 1 year, 3 months ago

Herons formula! LOLLog in to reply

Second Floor – Rishabh Deep Singh · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

Here's my question on Combinatorics-Conditional Probability: Fighting Fish. – Worranat Pakornrat · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

That's a killer question!Log in to reply

– Worranat Pakornrat · 1 year, 3 months ago

Thanks. That's the way it is. ;)Log in to reply

Here is my fifth submission for arithmetic progression part. – Ashish Siva · 1 year, 3 months ago

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The question could be tidied up slightly by simply asking:

– Calvin Lin Staff · 1 year, 3 months agoLog in to reply

– Ashish Siva · 1 year, 3 months ago

Thanks, I have edited it accordingly.Log in to reply

Here is my fourth one on Arithmetic progression- – Ashish Siva · 1 year, 3 months ago

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Here is my third submission for pattern recognition part. – Ashish Siva · 1 year, 3 months ago

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It just so happened that I published a chess problem yesterday :) Here it is. – Brilliant Member · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Perfect timing :)Log in to reply

Here is a problem for Arithmetic Progressions – Hjalmar Orellana Soto · 1 year, 3 months ago

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Here is my twentyfirst entry for AP section. – Ashish Siva · 1 year, 3 months ago

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Here's my limits of functions entry! – Pi Han Goh · 1 year, 3 months ago

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And here's my entry for Euler's theorem! – Pi Han Goh · 1 year, 3 months ago

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Here's my entry for GCD/LCM! – Pi Han Goh · 1 year, 3 months ago

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– Geoff Pilling · 1 year, 3 months ago

Nice problem, Pi!Log in to reply

– Pi Han Goh · 1 year, 3 months ago

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

@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 · 1 year, 3 months ago

Two problems forLog in to reply

But great questions nonetheless! – Pi Han Goh · 1 year, 3 months ago

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– Geoff Pilling · 1 year, 3 months ago

Ah... Number theory... OK, lemme see what I can come up with.Log in to reply

Here's my entry for arithmetic progression. – Pi Han Goh · 1 year, 3 months ago

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method of differences with this "method of sums". – Calvin Lin Staff · 1 year, 3 months ago

Oh nice one. I wonder if we can relate theLog in to reply

Try this – Abhi Kumbale · 1 year, 3 months ago

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– Abhi Kumbale · 1 year, 3 months ago

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

Do post more though! – Pi Han Goh · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

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

Here is my ninth submission for lcm section. – Ashish Siva · 1 year, 3 months ago

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– Christopher Boo · 1 year, 3 months ago

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

@Christopher Boo you are absolutely correct , I have requested @Ashish Siva to edit the solution. – Rishabh Sood · 1 year, 3 months ago

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Here is one for Euler's theorem. – Aaron Tsai · 1 year, 3 months ago

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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 · 1 year, 3 months ago

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– Aaron Tsai · 1 year, 3 months ago

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

– Calvin Lin Staff · 1 year, 3 months ago

Hm, but your solution doesn't use Euler's Theorem ...Log in to reply

@Calvin Lin sir I think this question would be terrifically for the logic quiz: logic challenge 1 – Rishabh Sood · 1 year, 3 months ago

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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 · 1 year, 3 months ago

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– Rishabh Sood · 1 year, 3 months ago

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

– Christopher Boo · 1 year, 3 months ago

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

– Rishabh Sood · 1 year, 3 months ago

Thank you, :DLog in to reply

Expected value level 5 leave me please! – Akul Agrawal · 1 year, 3 months ago

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Problems that are engaging, clearly explained, and simplified are much more likely to appeal to the community. – Calvin Lin Staff · 1 year, 3 months ago

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good luck Calvin Lin .. I will do . – Mohamed Aboalamayem · 1 year, 3 months ago

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– Calvin Lin Staff · 1 year, 3 months ago

Thanks!Log in to reply

Here is my second submission for GCD section. – Ashish Siva · 1 year, 3 months ago

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– Christopher Boo · 1 year, 3 months ago

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

this one? – Ashish Siva · 1 year, 3 months ago

Hmmm it was intended to be simple. Or how aboutLog in to reply

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 · 1 year, 3 months ago

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– Alex Li · 1 year, 3 months ago

Not sure these are arithmetic progression problems...Log in to reply

@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 · 1 year, 3 months ago

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Josephus problem which is exactly the same as yours! The coincidence, haha. – Christopher Boo · 1 year, 3 months ago

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

– Rishabh Sood · 1 year, 3 months ago

Very well noticed 👍👍👍👍👍Log in to reply

– Calvin Lin Staff · 1 year, 3 months ago

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

– Rishabh Sood · 1 year, 3 months ago

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

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 · 1 year, 3 months ago

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– Rishabh Sood · 1 year, 3 months ago

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

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 · 1 year, 3 months ago

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– Rishabh Sood · 1 year, 3 months ago

Thank you sirLog in to reply

– Ashish Siva · 1 year, 3 months ago

Congrats!Log in to reply

– Rishabh Sood · 1 year, 3 months ago

ThankLog in to reply

– Rishabh Sood · 1 year, 3 months ago

You broLog in to reply

– Rishabh Sood · 1 year, 3 months ago

This is an example for 100 people in a circleLog in to reply

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 · 1 year, 3 months ago

These are not problems inLog in to reply

@Calvin Lin sir are these questions fine? Please at least see them once you never appreciate my questions – Rishabh Sood · 1 year, 3 months ago

UhLog in to reply

– Calvin Lin Staff · 1 year, 3 months ago

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

– Rishabh Sood · 1 year, 3 months ago

😂😂😂😂😂😂, sorry sir.Log in to reply

Just, AP Just, AP 2 – Rishabh Sood · 1 year, 3 months ago

More AP questions:Log in to reply

I do not understand what "Just AP 2" refers to. – Calvin Lin Staff · 1 year, 3 months ago

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– Rishabh Sood · 1 year, 3 months ago

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

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 · 1 year, 3 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 · 1 year, 3 months ago

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