International Mathematical Olympiad (IMO) Hall of Fame

Hi, guys

From today, I will be posting select problems from the IMO papers!

Whoever solves this and gives the official solution first will be recognised.

You can also tell me which IMO paper you want the next question to be from - I have a full library of UKMT and IMO past papers and solutions

For now, I haven't got individual IMO solutions so, for now, the IMO questions will come from the papers from $1970$ to $2019$ .

If anybody hasn't posted the official solution in $2$ days, I will post it (as a snapshot) and recognition will be lost (last submission will be $23:58$ pm on the day after submitting the problem.) (unless somebody has already posted a solution - I will check if it's the official solution - if it's not, the person's solution will be mentioned as an attempt (must have bits of official solution - minimum $1$ ). If it's the official solution, the person will be recognised as a true solver.

A full list will appear below in sections:

Algebra:

2019, Problem 4, Day 2 - Hamza Anushath - Attempt goes to Alak Bhattacharya for including one bit of the official solution.

2019, Problem 1, Day 1 - Lost - Attempt goes to Tom Englesman for including bits of official solution.

2018, Problem 2, Day 1 - Lost - Attempt goes to nobody

2018, Problem 3, Day 1 - Hamza Anushath - Attempt goes to nobody

2018, Problem 4, Day 2 - Lost - Attempt goes to nobody

2018, Problem 5, Day 2 - Lost - Attempt goes to nobody

2017, Problem 1, Day 1 - Lost - Attempt goes to Ved Pradhan for including one bit of the official solution.

2017, Problem 2, Day 1 - Lost - Attempt goes to nobody

2017, Problem 5, Day 2 - Lost - Attempt goes to nobody

2017, Problem 6, Day 2 - Lost - Attempt goes to nobody

Number Theory:

2019, Problem 3, Day 1 - Lost - Attempt goes to nobody

Geometry:

2017, Problem 3, Day 1 - Lost - Attempt goes to nobody

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# 4 spaces, and now they show
# up as a code block.

print "hello world"

Math

Appears as

Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

I'm not good enough for IMO :(

Adhiraj Dutta - 1 year ago

I'm not good enough for PRMO :(

Vinayak Srivastava - 1 year ago

I thought I was good enough for both...Reality set in after I attempted PRMO for the 1st time.

Sachetan Debray - 1 year ago

@Sachetan Debray – I might not be able to attempt again...although if I do, I think I can get till RMO

@Sachetan Debray – Or maybe that's just wishful thinking

@Sachetan Debray – When did you give PRMO, and what was your score?

Mahdi Raza - 1 year ago

@Mahdi Raza – I don't remember the score, but I know it was two marks below the cutoff

@Sachetan Debray – Ok, this year? And from which state

@Mahdi Raza – Yeah, this year. Maharashtra. What was your state?

@Sachetan Debray – The thing was-I focused too much on geometry, and ignored the number theory and algebra. Later I realised I should have done the opposite. I did manage to solve a few questions, but took too much time for them. My friend though-he wrote the INMO in 2020, same as you did. I didn't ask him his score as our Pre-Boards were going on, and then there was Boards. But he got a good score in RMO- 40 or above.

@Sachetan Debray – Ohh, All the best for next year (or maybe for the next two months (if they allow (due to COVID)))

@Mahdi Raza – Thanks. All the best to you too (if you're giving it). Maybe you'll write IMO next year, or in 2022.

@Sachetan Debray – Thank you Sachetan! I hope that happens!

How can I submit my answer in the first problem? The answer must be an integer.

A Former Brilliant Member - 1 year ago

Take a look at the solutions.

What's your answer? @Páll Márton

k=1;n=1 and k=3;n=2

@A Former Brilliant Member – Answer is the number of pairs - $2$ in your case.

@A Former Brilliant Member – Yes.

@A Former Brilliant Member – LaTeX, please!

A Former Brilliant Member - 12 months ago

@A Former Brilliant Member – What? $\LaTeX$ ?

@A Former Brilliant Member – Yes!

Thanks once again @Yajat Shamji!

Well, the solution is like the official, so...

Also, I have a task for you: can you find IMO solutions from $1959$ to $1999$ ? (I have got solutions from $2000$ to $2019$ ).

Hahaha! I have solutions from 1959 to 2003, but not in English.

@A Former Brilliant Member – Can you find ones in English? And thank you! Also, I don't need solutions from $2000$ to $2003$ - I have already got them. @Páll Márton

@Yajat Shamji...

All the questions are in the link

Click here for all the IMO questions

This may not ordered, but it may have all the solutions for the IMO questions

Click here for all the IMO solutions

@A Former Brilliant Member – I need PDFs! But, @Páll Márton has reduced the search - I now only need solutions from $1959 - 1969$ .

Nice try, @Hamza Anushath, though!

@Yajat Shamji, please check my other comment on this comment thread

Is this good?

It's in English, yes?

Yes?

@A Former Brilliant Member – I need PDFs, sorry! But really good effort!

@A Former Brilliant Member – And this one?

@A Former Brilliant Member – I have already got this document - I now need IMO solutions from $1959$ to $1969$ !

@A Former Brilliant Member – I don't understand. You need solutions from 1959 to 1969. And in this pdf you can see the solutions from 1959 to 1969 and from 1969 to 2009.

@A Former Brilliant Member –

@A Former Brilliant Member – Thanks for shortening the search!

It is very difficult for me to understand these tasks in English. I think everyone can find these tasks on the internet in the language that the best for them, and not have to share them here.

You are right, @Páll Márton. But I want to post as much IMO as I can. Besides, most of my ideas are rubbish anyways...

Me too. I can create logic problems based on ambiguous words but not in English.

@A Former Brilliant Member – Take a look at my profile and look through the questions before I started the IMO series. Is there not one problem where I have not got negative criticism? $^{\infty}$

@A Former Brilliant Member – Also, I can only solve $28.19\%$ of all BRILLIANT problems.

And, when I give a solution, either I am forced to delete it or bear negative criticism...

Clearly, the platform of BRILLIANT has decided I am a bad mathematician who tinkers too much...

And, clearly, I have been branded as a insane mathematical outcast by the BRILLIANT community...

@A Former Brilliant Member – @Yajat Shamji, I regard you (and others might as well) to be a great person in mathematics. But only one question:

How did you get your wrong/right percentage? Did you calculate it (great work if you did, I never thought of that...) or is it shown somewhere @Yajat Shamji?

@A Former Brilliant Member – $\frac{Problems solved}{Problems attempted}$ $* 100$

Problems solved and attempted are in Stats.

@A Former Brilliant Member – Look most of the great scientists-and mathematicians-have branded outcasts at some point or the other.

So at least you're in good company. Don't take it that seriously.

Second, criticism is a very useful thing. if valuable, you can profit from it. If not, you can simply ignore it.

You feel like a bad mathematician now because yo are comparing yourself to genii like Ramanujan, Gauss, etc. But, dude, this is an infinite world, with infinite variety. Where would the fun be if all of us could do whatever we wanted to do in a millisecond, and no work required? how would it be called learning otherwise?

I suggest take some time off Math. Explore other interests, then when you feel ready, come back. There are lots of things you can do to learn (not involving brilliant).

And hone your skills to the utmost possible, then people will still start respecting you. And if some still don't-well, at least they would have become fewer, right?

People disrespect greats-Messi, Newton, Paul Erdos, etc. all the time. Do they take it seriously?

But take criticism-which is valid-sportingly, and use it to improve your skills. That way, you can profit immensely.

Just a note-Einstein did math very slowly. He didn't memorize anything. Yet he said it helped him because he could understand things better that way, their whys and not just their hows.

Not saying you should copy that blindly-you should never do that-but try to get how and why, think on that. Keep moving even if you fail, for failure is like friction-it helps us walk, or run. Do what is right(not in the sense of morality), not necessarily what most people do, or what you want to do now-because the latter changes continuously, the former always remains the same.

Hope you got what I'm trying to say.

Sachetan Debray - 12 months ago

@Sachetan Debray – No, I don't get it. Also, you're becoming peachy...

@A Former Brilliant Member – Preachy. Yeah, I meant to delete this comment. i can be kind of insensitive at times

@Sachetan Debray – No, peachy...

@A Former Brilliant Member – OK, I'm unfamiliar with its use in that way.

@Sachetan Debray – I'm trying to say, don't delete it:

Peachy (North American) means fine / very satisfactory...

@A Former Brilliant Member – that's all right then

@Alak Bhattacharya , @Mahdi Raza , @Richard Desper , @Gandoff Tan , @Hamza Anushath , @Adhiraj Dutta , @Alice Smith, @Isaac YIU Math Studio , @Chew-Seong Cheong, @Páll Márton , @Darsh Kedia , @Vinayak Srivastava , @Zakir Husain , @Pradeep Tripathi , @Aryan Sanghi , @Culver Kwan , @Pi Han Goh, @Aaghaz Mahajan, @Sahar Bano, @Karan Chatrath, @Sachetan Debray

I mean, it is annoying that you always tag us again and again. And for getting solutions, there are a lot of answers in AOPS (Art of Problem Solving) website.

Isaac YIU Math Studio - 12 months ago

What? All I want to do is to show people this. And why not tag. I understand your frustration, but, according to me, this is the best way to get people...

Seriously, @Vinayak Srivastava, @Adhiraj Dutta? I called you because I know you can do it. Believe in yourself. Besides, all the questions look hard but they only require up to A-Level knowledge...

I haven't even learnt the basics!

What, you can't attempt even the first question I have posted?...

@A Former Brilliant Member – I got it correct(guessed it though)!

@Vinayak Srivastava – Great! And answer to my previous comment...

@Hamza Anushath, look above...

@Hamza Anushath , look above in the IMO Hall of Fame...

Please?

(°U° )

Thnx a lot @Yajat Shamji

Well, I changed the date and after seeing what you did, I thought it would be fair to give you the recognition.

Also, check out the 2018 problems, quick!

@A Former Brilliant Member – On it sir!

@A Former Brilliant Member – No need to call me sir, @Hamza Anushath. Call me Yaj (my new nickname for friends...).

@A Former Brilliant Member – Ooh...lovely nicknames for the lovely couple..@NSCS 747 @Frisk Dreemurr

evil chuckling in the distance

evil chuckling growing to an evil laugh

MUAHAHAHAHAAHAHAHA

A Former Brilliant Member - 7 months, 2 weeks ago

@A Former Brilliant Member – oh shit, oh god, oh fu-

deep inhale

oh fuck

Frisk Dreemurr - 7 months, 2 weeks ago

@Frisk Dreemurr – I said it, I said it, I said it

"day after day, we stray further from god"

@Frisk Dreemurr – Not really...I've said that multiple times, but Dad doesn't seem to stray away from me :P

@A Former Brilliant Member – fuck that how are you not angry she leaked the fucking nuke

NSCS 747 - 7 months, 2 weeks ago

@Frisk Dreemurr – See, now you are expressing your desires like how you want to...do the frick with...him... lmfao

@A Former Brilliant Member – lol

@Frisk Dreemurr – frisk fucking delete the abyss trick in your big brain time note you fucking idiot the public is not ment to know and i thught of all people you would know this was ment to be a fucking secret and now lam le knows and if he has actually made a fucking million line abyss then brilliant will be kicking all of our asses

@Nscs 747 – It is deleted now, all removed

@Nscs 747 – Did you actually check the note now, not a trace to be seen

Give a sec, I have another idea

Nobody has solved $2018$ , Problem $4$ , Day $2$ yet...

Refresh the page! Maybe I write a solution, but I finished the school today, and I must go to the school.

I was doing school as well online. I go to physical school on Friday...

@A Former Brilliant Member – I must do everything online too. In our school we had to photograph the copybooks.

@A Former Brilliant Member – The size of the pictures

@A Former Brilliant Member – No way! Check out this:

But, before, it was over $5$ GB!

Solved, no solution...

Does anybody want me to post any Geometry questions or Number Theory questions from the $2016$ paper? If so, ask now. @Hamza Anushath , @Zakir Husain , @Mahdi Raza , @Alak Bhattacharya

@Yajat Shamji - One of your problem is wrong see 2017, Problem 1, Day 1 see the reports

Sahar Bano - 12 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$