competition-math

[dapper magnet]

Post it in latex i cant read that

[fresh zenith]

@dapper magnet
Posted

[amber thunder]

Does anyone know a good resource for learning projective geometry?(Book, website, video)

[tall lance]

Google

[pearl holly]

What's a nice fact about Telescoping series and products?

Yeah, im asking stupid stuff but I wanna know if anyone is knowledgeable about telescoping

cuz its super fun :DDD

[sleek ivy]

where

[fresh zenith]

@sleek ivy
#latex-help

[sleek ivy]

yea m8 that aint helping you just put it in the exact same format

[gilded halo]

HahalolXD

[sleek ivy]

maybe start by finding f(x), it looks like a very simple integral

[fresh zenith]

Yeah
CONTINUE then

[sleek ivy]

f(x)=1/4 ln(x^4+1)

find the inverse

differentiate it

plug in pi/8

[misty torrent]

you don't need to differentiate the inverse function

[sleek ivy]

why not

[misty torrent]

plus FTC

tells us we can compute the derivative of f^-1 directly from what we have already

[sleek ivy]

oh yeaa

thats derived from the chain rule

[fresh zenith]

Yup you can Compute

[burnt trail]

can i get some help?

[misty torrent]

that image explains it pretty well

what part of it dont you get

[burnt trail]

oh i think i get it now

like the second circle when the radius is maximus

[misty torrent]

minimum

but yes

[burnt trail]

idk

[burnt trail]

like, if the radius of the second circle is x^2 = (10sqrt2 - 5)^2 what happens

[misty torrent]

that's the answer

well almost the answer

[burnt trail]

don't get it

[misty torrent]

what is (x+5)^2 + (y+5)^2, geometrically?

[burnt trail]

the minimum distance between (x,y) and (-5,-5) after the power of two

[misty torrent]

no, not exactly

yes, that

[misty torrent]

oh, you edited it

that's correct

[burnt trail]

what happens

[misty torrent]

that is the answer

[burnt trail]

idk, i don't get it

[burnt trail]

why do they give the first circle

[misty torrent]

what do you mean

what's your question

[burnt trail]

no i totally get it now, it was simple

[burnt trail]

is best to think about the second expression as the power of 2 of a distance of (x,y) and (-5,-5)

[misty torrent]

it's just the square of the distance

I don't know why you're saying it like that

[burnt trail]

that

my English sucks

also, if we find the minimum distance between (5,5) and (-5,-5) and we subtract the radius of the first circle we get 10sqrt2-5, which is the minimum distance between (-5,-5) and the first circle, then if we think as the second expression as the minimum distance squared between (x,y) and (-5,-5), we would need to square 10sqrt2-5 to get the smallest value of the second expression

[burnt trail]

they give the first circle because the minimum distance from (x,y) to (-5,-5) cannot be 0 because then (x,y)=(-5,-5), we need (x,y) to lie in the first circle , so basically it's asking for the minimum distance from a point on this circle to (-5,-5)

anyways, simple but cool problem bro

[dapper magnet]

huh

i got pi/8 + 512/pi^3

Set $y = f^{-1}(x)$, then $x = f(y) = \int_0^y \frac{t^3}{t^4+1} , \mathrm{d}t$

[gilded halo]

impract1cal

[dapper magnet]

If $y$ is invertible, then $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{\frac{\mathrm{d}x}{\mathrm{d}y}}$

[gilded halo]

impract1cal

[dapper magnet]

A fairly straightforward computation shows that y is invertible

now, $\frac{\mathrm{d}x}{\mathrm{d}y} = \frac{\mathrm{d}}{\mathrm{d}y} \int_0^y \frac{t^3}{t^4+1} , \mathrm{d}t$

[gilded halo]

impract1cal

[dapper magnet]

which is just $\frac{y^3}{y^4 + 1}$

[gilded halo]

impract1cal

[dapper magnet]

wait.

oh nvm yeah

[sleek ivy]

nah his answer was right

[fresh zenith]

Can I get the hardest Problem to solve yet

[acoustic nova]

why?

[fresh zenith]

It's fun to solve

Do u have any ??

[acoustic nova]

u probably aren’t at that level

[fresh zenith]

How could you say ??
Explain that

[acoustic nova]

One sec

[fresh zenith]

Yeah go on

[dry quartz]

r u sure

[dry quartz]

don't complain now

[acoustic nova]

Ok. Prove or disprove: Do there exist real numbers $a_0, a_1, …, a_{2018}$ with $a_0 \neq 0$ such that the roots of the polynomial $P(x) = x^{2019} + a_{2018} x^{2018} + … + a_1 x + a 0$ are $a_0, a_1, …, a{2018}$?

[dry quartz]

oh hn not number theory

[gilded halo]

hockeydude85

[fresh zenith]

I get your point
But I would try Solution Tommorow
Making an Availability for it

[fresh zenith]

I got your Solution

Texit is Doing it I mean its converting it

[rare bluff]

man you guys should take a look on this kid

[pallid tundra]

<@&268886789983436800> very off topic

[lament mist]

@rare bluff please don't post off-topic images like these in math channels

[rare bluff]

Wait the image is a 9 years old kid that solve integral

what "off-topic" images r you guys talking about?

[soft badger]

nah bro there doesnt exist any numbers a0.......a2018 such that they are the roots of that polynomial

[soft badger]

the product of its root is always equal to the the term with x^o divided by the coefficient of first term

[soft badger]

here if we multiply all the roots that should be equal to a0

now if a0 x a1 x ....... x a2018 = a0 here this is only possible when a0 =0

but in the eqn it is given that a0 is notequal to 0

hence there doesnt exist any roots such a0......a2018

[misty torrent]

why can't you have something like 1, -1, 1, -1, 1, -1, etc that multiply to 1?

then a0 * 1 = a0

[soft badger]

but they all are distinct

[misty torrent]

sure, if you want distinct then let's do 1/2, 2/3, 3/4, 4/5. ... etc. and then the final one can be the one that makes the product 1

[soft badger]

then it will equal to 1 not 1/2

[misty torrent]

we want it to be equal to 1

[soft badger]

no you take a0 1/2 thats why it should be equal to 1\2

[misty torrent]

try it with just a0 and a1, and see what happens

[soft badger]

??

[misty torrent]

(x-a0)(x-a1) = x^2 + a1x + a0

[scenic sun]

Where is this problem from? The answer is ||no|| since ||there doesn’t exist a real polynomial with degree 5 or higher that satisfies the property that the coefficients are it’s roots||. You can have a look at the first answer of the following link: https://math.stackexchange.com/questions/2689332/monic-polynomials-whose-roots-are-their-remaining-coefficients, which finds polynomials that work for degree 4 or less (note that there exists only one 4th degree polynomial that works which is nontrivial). As mentioned in the answer of this link, for the proof of the uniqueness of this 4th degree polynomial and the || non-existence of any polynomial with degree 5 or more ||, head over to this link: https://www.jstor.org/stable/2315341?origin=crossref, which should proof these things. However though you will need to log in through your institution there, which is why I cannot access the article

[acoustic nova]

Its from the CMC mock USAMO

this is their proof (he asked for something hard)

[sleek ivy]

trivial inequality 😭

[acoustic nova]

what?

[scenic sun]

From which year?

[scenic sun]

Okay, it’s very surprising because I understand the entirety of the proof, but thought that the solution would be actually harder than this. Indeed every step that they did is correct, and it’s a very nice proof. It’s just that I would’ve not thought about doing all these steps and using inequalities along the way, because it seems like it needs a lot of time. But again, wonderful proof, and if you are unsure about any part of the proof, I am happy to help

[near burrow]

lmao imagine this situation

i thought i was gonna have till friday to study for a stupid competition

starting today

turns out the test is tomorrow

im dying

[acoustic nova]

yeah u completely bs'ed this no offence

[alpine steeple]

does anyone have an olympiad math formula sheet /notes. I'm sitting an open book exam soon and the only thing that I really needs is circle geo ( like circumradius =abc/4A) notes and inequality notes

[soft badger]

ANYONE PREPARING FOR IMO

[pallid tundra]

NO

RECOMMEND NOT MESSAGING IN ALL CAPS

IT MAKES YOU SOUND LIKE YOU’RE SHOUTING WHEN YOU DON’T NEED TO BE

[acoustic nova]

why are u asking these questions? U didn’t solve my question

[soft badger]

sorry i will not do such things from now on

[soft badger]

i didn't understand it

can you elaborate it a little bit

[acoustic nova]

Ok I’m not trying to be mean I don’t rlly understand the solution either

[pearl holly]

Hi!
How do I deal with Telescoping Equations?

Because I think its just the same as Telescoping Series

https://www.youtube.com/watch?v=4BwL9ye4_4E&t=1256s
Referring here atm

[scenic sun]

The solution you provided just before?

[dry quartz]

🤨

[glacial jolt]

Can you give a example for a telescoping equations?

[dry quartz]

sum r = 1 to n 1/r - 1/(r+1)

[glacial jolt]

Not telescopic sum but telescoping equations he is talkin about

[pallid tundra]

if you actually read what they were asking about you'd see that they're two different names for the same thing

[glacial jolt]

👍 😂

[glacial jolt]

I will say post your exact question for help!

[pallid tundra]

i've never heard anyone call them "telescoping equations" but "telescoping" in the context of computational contests can only really refer to one class of series problems

where almost everything cancels

[glacial jolt]

How are you @pallid tundra ? long time no see

[glacial jolt]

I see

[pallid tundra]

the most common lazy way to do it is partial fraction decompositions like the classic 1/n(n+1)=1/n-1/(n+1)

[pallid tundra]

endless pain and suffering

[glacial jolt]

Is there any other effective way to do that?

[pallid tundra]

pfd is an extremely standard technique though for some reason US schools usually delay actually teaching it until calc2

basically it's common denominators in reverse

https://en.wikipedia.org/wiki/Partial_fraction_decomposition#Procedure see the "illustration" for an example

how does this help us do telescoping sums? if the factors in the numerator are all linear polynomials then potentially you can get lots of cancellations to happen

[glacial jolt]

yeah I see

[glacial jolt]

But I am asking that, Is there any other effective method to do telescopic sum as you say it's a common lazy way?

[pallid tundra]

partial fractions is the most common method i've seen

but there are other ways to make telescoping sums

lemme find another example

https://en.m.wikipedia.org/wiki/Telescoping_series

op the Wikipedia page has a few good ones

it also mentions the fundamental theorem of calculus as an extension of that telescoping idea

[near hill]

Are you asking how to invent a problem where there’s a sum that telescopes?

[glacial jolt]

No no I am asking him for some different approach as he says pfd is a common lazy method.

[near hill]

Huh. Perhaps he's saying that if the problem author is lazy and want a sum that turns out to telescope, partial fractions are a common principle?

[pallid tundra]

yea that's what i was getting at

[glacial jolt]

I see

[harsh apex]

from imc 2024

[high goblet]

are you asking for advice on how to do it?

||partial summation 1log1 + 2log2 + ... + nlogn||

[harsh apex]

thanks

[harsh apex]

guys try this

[glacial jolt]

😭 (for pfp)

[sleek ravine]

bro u def didnt think u were the only one with that pfp

[harsh apex]

lol

[harsh apex]

i love luffy so i search in google luffy and its give me this in the first one

[pearl holly]

How do I express the denominator?

My idea was something like n(n+1)/2 + 1.... idk why I had my intuition set to that

Update on this, nevermind

Had to take a break for a while and realized its (n+1)(n+2)/k

[calm raptor]

lol

[calm raptor]

you could also add +1 and -1 in the numerator and sperate it intro two terms

[soft badger]

option D

[soft badger]

yeah i did also like that

[soft badger]

every term will cancel out and we left with 6\210

which is 1\35

[soft badger]

can you elaborate a little bit

[pearl holly]

correct!

[vernal axle]

nope, the correct one is 1/7

it is 3/5 * 5/7 * 7/9 * ... * 19/21=3/21=1/7

so, it is (c)

[scenic sun]

You need to be bit careful when reading the problem. That would’ve been right if the numerator and denominator each fraction were increased by one number from one fraction to the next, in which you can cancel like that, but the numerator and denominator keep increasing by TWO numbers each time you move on to the next fraction. For example, numerator in first fraction is 1+2+3 and the numerator in the second fraction is 1+2+3+4+5 (an additional 4+5, not 4). Same thing applies to the denominators. Use algebra to find that each fraction can be simplified to n/(n+2), only then you can cancel across and simplify

[soft badger]

sorry i messed up

[knotty cobalt]

how do i qual to aime?

[scenic sun]

all good

[pallid ginkgo]

top 2.5% in amc10 or top 5% in amc12

[untold thunder]

that is around 100 in amc10 and 90 in amc12

[snow elm]

How to do this? I’m stuck

[soft vigil]

Draw AF

And it becomes much easier

[snow elm]

That didn’t work

[soft vigil]

You sure?

Also

Do you know menelaus or mass points

[snow elm]

Nope

[soft vigil]

Because either of those trivialize the problem

[soft vigil]

Then youre cooked

Go learn mass points

Its quite easy once you get the hang of it tbh

[untold thunder]

you don't need mass point

consider [ADF]/[AFB]

[snow elm]

I don’t know if that helps or not

[untold thunder]

well first do you know how to find [DFC]?

[snow elm]

Use ratios

[untold thunder]

do it rq

[snow elm]

32/3?

[untold thunder]

well the denominators right but not the numerator

how'd you get it

WAIIITI

wait

nvm

How'd you get that

[snow elm]

This

[untold thunder]

I think I see what's happening there but I think it would only work if you had a diagram like this

Let me show you how you would find the area

[snow elm]

Ok

I have the answer

[untold thunder]

Given that BH is the height of ABC and BCD what is the area of ABC and BCD in terms of h

[snow elm]

Yeah

[untold thunder]

you know this?

[snow elm]

Have u figured out the answer?

[untold thunder]

ye

[snow elm]

What is it

[untold thunder]

I didn't actually derive it so hollup

72/5?

[snow elm]

Nope the correct answer is 40/3

Idk how to get that

[untold thunder]

well here's my work I do believe it's correct

[snow elm]

So far I get is the total area is 200/3

[snow elm]

But the answer is 40/3 though.

[untold thunder]

I made a small mistake

[snow elm]

Bro are u sure that will works?💀

[untold thunder]

But see if you know what's happening here

[snow elm]

Why times 8

And why use 20/12

[untold thunder]

Well [CDF]=8

[snow elm]

But the area is not 8

[untold thunder]

You use 20/12= [AFB]/[ADF]

[snow elm]

The length is 8

[untold thunder]

The problem is structured so that it is

You get [CDF] = (DC/AD) * [ADF]

That general two

When two triangles share that same height

The ratio of their areas = ratio of their bases

The reason why your method doesn't work is because ADF and CDF don't have the same height as CBA

does that make sense or should I show you why

[soft vigil]

Yes

Ive olayed these games before

[snow elm]

American maths competition is crazy geez

[snow elm]

Why u use 20/12

Not smth like 8/20

[snow elm]

Could u show me how to do that using mass points ?

I want to see multiple solutions for a question

[scenic sun]

Let us call a random triangle ABC for example. Draw a line segment from B onto any point on AC and let this new point be called point D. Let us say that this divides AC into a ratio of AD:DC = x:y. Then what is the ratio of areas ABD and CBD?

[snow elm]

Do u mind if I ask u to show me a full solution? It’s like 0am now my brain aren’t working, I will probably understand ur move in the morning

[snow elm]

Okay

[scenic sun]

If you need a hint for the question I asked, let me know

[untold thunder]

I think you should just following adin

He'll probably walk you through it better than I can

[snow elm]

Okay

[snow elm]

9;4?

[scenic sun]

Don’t use the numbers or the original problem. I created a sub problem just so that you can understand the idea behind what we’re doing.

[snow elm]

Oh.

[scenic sun]

Also this is correct

[snow elm]

X^2:y^2

Ik im just trying to understand

[scenic sun]

Not really

[scenic sun]

Yes, that’s good

[snow elm]

Then idk

You don’t need to square ur scale factor?

[scenic sun]

No

[snow elm]

Then idk

It’s different from applied maths ig💀

[scenic sun]

I’ll give a hint. So we know that the area of any triangle is it’s base * it’s perpendicular height. Draw the perpendicular from B onto AC and let’s call this meet point E. What’s the perpendicular height of triangle ABD and CBD from AD and CD respectively same as?

[scenic sun]

You do applied maths?

[snow elm]

Yeah

Canadian applied maths

Not American

[scenic sun]

Is that in high school or a uni thing?

[snow elm]

I skipped 3 grades so that I can take applied maths💀

At grade 12

My school offers that

[scenic sun]

Ah, I don’t really know the system in Canada, but skipping 3 grades is bit risky lol. But then that means that you’re capable of taking applied maths

[snow elm]

Yeah exactly.

[scenic sun]

May I ask what are the other type of maths that they offer there?

[snow elm]

I didn’t do a lot of competition stuffs

[snow elm]

Essential, applied and calculus

[scenic sun]

Oh, I did some competitions, so I have an idea on how to solve these problems most of the time

[snow elm]

And there is a new section ig this year

Group theory ig

[scenic sun]

What’s the difference between taking applied and taking calculus? Sorry if I’m acting stupid

[scenic sun]

You get to take group theory at the end of high school?

[snow elm]

Applied is like for solving real life problems

[scenic sun]

Ohhh ok

[snow elm]

Nonnonono

I will failed

I hate that thing

[scenic sun]

Group theory sounds interesting, but I thought it’s only usually offered in uni though

[snow elm]

I will faint if I see that

Yeah but a uni teacher came to my school

And she starts teaching that

[scenic sun]

That’s really lucky. For us we have to wait until uni to start group theory

[snow elm]

MY SCHOOL PAID MORE THEN THE UNI PAID HER

That is all OUR MONEY NOT SCHOOLS

50k-70k per year bruh

[scenic sun]

It’s honestly unfair. No wonder why they moved. Why have I heard a lot of the time that unis are underpaying their teachers/professors (that’s actually really scary cause I plan to be one)

[dapper magnet]

Who pinged me

[scenic sun]

Wow that’s a lot

[scenic sun]

Ahh okay. Wait, is your school private?

[snow elm]

Yeah.

[scenic sun]

Ok makes sense now

[snow elm]

I’d take calculus and applied maths and physics at the same time

They connect to each other

It’s like ok for me

[scenic sun]

Hmmm. And btw how do you find applied math? I’m just wondering

[snow elm]

No pressure on that

[snow elm]

Combination of calculus, physics and some competition maths

[scenic sun]

Probs a lot of pressure

[snow elm]

Mainly similar to physics

[snow elm]

Depends on the teacher and topics

💀

[scenic sun]

Wait what. All of those things are in applied math? That’s interesting

[snow elm]

Yeah weird stuffs

I don’t even know I can use calculus in physics

[scenic sun]

Since when is competition math part of the school curriculum? Id wish it were the same over here

[snow elm]

And applied maths too

[snow elm]

Yeah

Mandatory.

[scenic sun]

I’ve not really even seen calculus in physics yet. I’m waiting to though

[snow elm]

Only Canadian competition thou

[scenic sun]

That’s lucky. Competition math should be mandatory everywhere (jk)

[snow elm]

lol

There are like different level maths classes

[scenic sun]

I’ve seen some Canadian math comps, they look good to me

[snow elm]

If u are in the highest level class then it’s mandatory

[scenic sun]

Oh ok

[snow elm]

I can show u some

[scenic sun]

Maybe in dms. That would be great

[scenic sun]

Uh did you try the hint from the below message from the one that I’m replying to?

[snow elm]

Idk

[scenic sun]

Did you first draw the triangle and the points?

[snow elm]

Yep

[scenic sun]

So you drew triangle ABC, points D and E on AC and drew AD and AE given the definitions I gave previously? Now what do you notice about the perpendicular height of the triangles?

[scenic sun]

okay I’m going to bring up this diagram for a new reference. What is the height of triangle ACB and DCB here?

[pure yarrow]

Did any one here participated in the IMO or passed it?

If there is please how was your study schedule Iean is there any daily recommended amount of time to do it

[acoustic nova]

14 hours a day on weekdays, 16 hours on weekends and 21 hours on holidays

[pure yarrow]

Hahaha that's super funny

[soft badger]

yes pls share what study materials should we follow

[pearl holly]

NOT AN IMO PARTICIPANT
Usually, what you want to do, is to just stop asking questions, and start grinding.
Books for competition math, starting the IMO journey, is to start with really awesome books like AoPs and MathDash!

These materials help you prepare for like AMCs, USAMO, AIME, etc. Internationally, this would also imply to other math competitions.

IMO GRINDSS
Read loads of textbooks, solve imo problems, learn how to prove, and uhh learn super advanced topics that a typical hardcore math professor would be

okay, TL;DR Just start grinding

[soft badger]

can you send pdf of books??

[pearl holly]

https://tinyurl.com/ContestGuideIntlGDrive

loads of contest and books there

[soft badger]

thank you so much

[pearl holly]

CL to E2 are your skill levels
CL being the classroom level -- standard highschool curriculum math
A1 - E2 being the starting competition maths to IMO level

[trim vortex]

Should I take notes when reading comp books or do I grind problems and those are the notes

[acoustic nova]

Preparing for the International Mathematical Olympiad (IMO) is a significant and rewarding challenge that requires deep understanding, problem-solving skills, and consistent practice. Below is a detailed study plan, broken down by phases, topics, and weekly routines, adaptable over 6-18 months, depending on your current level.

🔍 Phase 1: Foundation Building (Months 1–3)

🎯 Goals:
Solidify core mathematical concepts.
Develop mathematical thinking and proof-writing skills.
📚 Topics:
Algebra: Equations, inequalities, polynomials, functional equations.
Number Theory: Divisibility, congruences, modular arithmetic, primes.
Geometry: Euclidean geometry, similarity, circles, angle chasing.
Combinatorics: Basic counting, Pigeonhole Principle, inclusion-exclusion.
🗓 Weekly Routine (10–15 hours/week):
Day Task
Mon Topic Lecture (e.g., Algebra) + 2 Easy Problems
Tue Solve 3 Problems from previous topic
Wed Topic Lecture (e.g., Number Theory) + 2 Easy Problems
Thu Solve 3 Problems + Review solutions
Fri Rest or light reading (e.g., problem-solving strategies)
Sat Mock test (3 problems) + Discussion of solutions
Sun Review week’s work + Fill knowledge gaps
🚀 Phase 2: Intermediate Problem Solving (Months 4–8)

🎯 Goals:
Begin solving intermediate-level olympiad problems.
Refine techniques and learn multiple approaches to problems.
📚 Topics:
Deepen understanding in all four main areas:

Algebra: Inequalities (AM-GM, Cauchy), symmetric polynomials.
Number Theory: Diophantine equations, Euler’s theorem, orders.
Geometry: Inversion, transformations, angle bisectors, Miquel Point.
Combinatorics: Graph theory basics, invariants, recursion.
🗓 Weekly Routine (15–20 hours/week):
Day Task
Mon Topic Study (1–2 hours) + 2 Problems
Tue Problem-Solving Session (2 hours, timed)
Wed Topic Study (1–2 hours) + 2 Problems
Thu Mock test (2 problems) + Self-review

[sleek ivy]

is this chatgpt

[mystic shale]

Fr reads like it but i didnt wanna say in case it might offend them

The emojis are overkill

Especially the first sentence i dont ever see myself saying that line

[glacial jolt]

99.99% confirmed!

[harsh apex]

there is a competition math site for coding ?

[hushed charm]

Maybe https://projecteuler.net/

[harsh apex]

yea i allready find codeforces

is it good for math ?

[hushed charm]

These aren't great for competitive math, but certainly are for competitive programming

[harsh apex]

there is math here ?

[hushed charm]

Where?

[harsh apex]

in codeforce?

[hushed charm]

Of course, a lot of math

Competitive programming has a lot of math

[harsh apex]

so why is not good

[hushed charm]

Because competitive programming involves programming, algorithms and computer science, things that doesn't appear in competitive math

[harsh apex]

yea i want comp prog

[hushed charm]

There indeed is math in competitive programming, but if you want to study for math olympiads, competitive programming aren't the best resources

[hushed charm]

This discord server ain't really focused in competitive programming, there are certainly more focused servers

[harsh apex]

can you send me?

[hushed charm]

Don't know any at all, but with some searches you can find some certainly

[untold thunder]

For the problem "How many triples of three-digit palindromes have a sum that is also a three-digit palindromes?" would you use PIE to account for overcounting?

[soft vigil]

how would you even overcount

[gloomy sentinel]

anyone planning for imo?

[acoustic nova]

did u make imo?

or are u likely to make it?

[gloomy sentinel]

no @acoustic nova it is a competition.

you don't know about it?

[acoustic nova]

u mean the international math Olympiad?

[gloomy sentinel]

yeah

[acoustic nova]

^

if not this is getting ridiculous. (Of course) I haven’t made it but there are way too many questions about this then

[gloomy sentinel]

6 people get selected from each country

[untold thunder]

If two palindromes are the same you could have P, P, Q, P, Q, P, or Q, P P

should I say unordered to clarify that

[soft vigil]

Can you not just casework them

Its not thwt bad

[untold thunder]

I can but I'd like to know if PIE is applicable

Partially because I made the problem and I don't want a messy and fallible solution

[pure yarrow]

I study maths in french 😭, I am really struggling with materials mentioned by you

I have a question

Is mathtraining website good

I mean I started learning and I was able to solve a national level problem on angles and triangles

It also teached me how to think like do first of all angles chasing than start to break down the problem

[gloomy sentinel]

mathraining is a good website, I have seen its questions and theory, I personally think it is a good website, but it is your choice. ("mathraining est un bon site web, j'ai vu ses questions et sa théorie, je pense personnellement que c'est un bon site Web, mais c'est votre choix." in french if you understand french more.)

Hope this helped you!

[hushed charm]

Answer:

I need help to understand why ∠EBM = ∠FDB. I haven't read the entire solution yet, just read the beginning to try to discover the other informations. But I don't understand why ∠EBM=∠FDB

[vernal axle]

It is a standard property of the angle between a tangent and a chord to the point of tangency.
It is called alternate segment theorem
https://thirdspacelearning.com/gcse-maths/geometry-and-measure/alternate-segment/

[hushed charm]

Dang it

I didn't about this theorem, thanks a lot

[hushed charm]

Why is MA = MD? As it said in the end

[vernal axle]

MD is a median in the right triangle ADC

[ashen jacinth]

cana nyone help me with 2021 putnam B1 ||

I drew this and got x(theta) = (1 + cos theta - sin theta)/(2 cos theta)

Then integrated the square of that expression by 0 to pi/4 and finished by multiplying by 8/pi but im getting the wrong answer, it seems that instead they just integrate the square of

(1 + cos theta - sin theta)/2

Why am i missing random cos theta factor?||

https://kskedlaya.org/putnam-archive/2021.pdf

[soft vigil]

theres an amc problem that looks like ts

[trim bramble]

it was like last year right?

[soft vigil]

yeah yeah

with like multiple squares

[trim bramble]

very similar

[soft vigil]

there was another one

[trim bramble]

don’t remember it

[near hill]

The diagram looks similar, but the problem it accompanied is completely diffetent ...

[trim bramble]

yea i know

[ornate blade]

solution spoiler

nice problem btw

[restive onyx]

hi

solve this all for me

[ornate blade]

why bother with comp maths then

comp maths is meant for training your brain

[ornate blade]

1. you're in the wrong channel
2. you should show what you tried if you want other people to help

3. follow the instructions in:

!help

[scarlet root]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[azure sedge]

what’s the method to prep for amc 12

[pure yarrow]

Hello, is study around 3 hours maths per day, is it enough to be good in competitive mathatics

Mathematics*

[twilit patio]

What are u competing in?

(Out of curiosity)

[radiant jasper]

imagine 2 squares side to side, now draw a random line which has to go through the 2 squares, now, what is the probability of the ratio between the areas of one of the squares split in 2 by the line, to be the same as the other?

I came up with this problem myself.

So if this is terrible you know why.

[pure yarrow]

FFJM and three days ago I decided to start a journey hoping to qualify to the national Olympiad that makes me qualify to the IMO, I am from Tunisia by the way

[near hill]

This happens only is the line is horizontal or passes exactly through the midpoint of the side the two squares share.
You don't say which probability distribution you're choosing your "random" line with, but if it's a reasonable, continuous distribution, the probability of "horizontal" and "passes through the midpoint" will both be 0.

[hushed charm]

Depends a lot on a lot of things: how long have u been studying, how much time u have, how do u study..... But it isn't really possible to say if 3h are going to be enough. Focus more on studying correctly, if u really like math, eventually u will want to study more and need to study more.

[empty cairn]

Anyone wanna give me an integral

Challenging one

[hushed charm]

https://www.google.com/search?q=challenging+intrgrals&oq=challenging+intrgrals&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIJCAEQABgNGIAEMgkIAhAAGA0YgAQyCggDEAAYBRgNGB4yCggEEAAYCBgNGB4yCggFEAAYCBgNGB4yDQgGEAAYhgMYgAQYigUyDQgHEAAYhgMYgAQYigUyDQgIEAAYhgMYgAQYigUyBwgJEAAY7wXSAQkyMzM1NmowajmoAg6wAgHxBWrfiUqFH4Om&client=ms-android-motorola-rvo3&sourceid=chrome-mobile&ie=UTF-8

[empty cairn]

This is too easy

[azure sedge]

show me how to integrate non elementary integrals my goat

[empty cairn]

Which

[azure sedge]

idk i have never done any

only gotten to calc ii

[empty cairn]

alr dm me if u need help

I'll have fun too

[azure sedge]

when i get home

are you pre-uni

[empty cairn]

Yeah

I'm not in college

[sleek ravine]

college is uni

pre means before

so the answer was yes

[empty cairn]

What

[sleek ravine]

😂

[empty cairn]

who's gonna know

[vast hound]

you're pre ?

[sleek ravine]

pre birth

[hushed charm]

Don't know how to start

[near hill]

To start with, even n are impossible, because the sum of all the numbers is 0 (mod n), but for even n, the sum of the specified column sums is n/2 (mod n).

[radiant jasper]

When you have long ahh math problem and the answer is literally just 0...

[trim vortex]

can someone help me w this problem

ik its a d=rt problem but i cannot figure out how to interpret anything

[near hill]

I think ||all odd n ought to be possible||, though.

[hushed charm]

I don't really understand why, even though the total sum is 0 mod n, the sum of the numbers inside a line aren't necessarily 0 mod n, right? What did I miss

[drowsy leaf]

it's possible to arrange the numbers to make mod for both row's and columns 0, but arranging for Distinct seems not possible

like for n=5,

[hushed charm]

I tried with n = 4 and indeed it seems to be impossible, but i dont understand the relation between the sum of numers inside a line and the total sum

[near hill]

The row sums are all required to be different, so they are exactly all the residue classes mod n. For odd n they all cancel out against their negatives, but for even n, n/2 is its own negative so doesn't cancel.

[drowsy leaf]

1, 2, 3, 4, 5
5, 1, 2, 3, 4
4, 5, 1, 2, 3
3, 4, 5, 1, 2
2, 3, 4, 5, 1

this arrangement will give all mods as 0

[hushed charm]

Sorry, i don't understand

[near hill]

The row and column sums are all equal there. They were required to be different modulo n.

[hushed charm]

What do you mean they cancel out

[near hill]

a + (-a) = 0

[drowsy leaf]

exactly, it is possible to make the sum equal, but impossible to make it unequal

[hushed charm]

Right, but the numbers inside the board are all from 1 to n, so how is it possible to be a negative number

[near hill]

I have a family of solution with distinct row/column sums.

[drowsy leaf]

would like it if you could share it

[near hill]

It's negatives in modular arithmetics where multiples of n don't matter.
So if n=15, for example -6 = 9.

[near hill]

For example, for n=7: ||```
7 6 5 4 3 2 1
6 2 3 4 5 6 7
5 3 4 5 6 7 1
4 4 5 6 7 1 2
3 5 6 7 1 2 3
2 6 7 1 2 3 4
1 7 1 2 3 4 5

Or, perhaps nicer looking: ||```
6 2 3 4 5 6 7
2 4 4 5 6 7 1
3 4 2 6 7 1 2
4 5 6 7 1 2 3
5 6 7 1 5 3 4
6 7 1 2 3 3 5
7 1 2 3 4 5 1

[near hill]

You can either write down a lot of equations with a lot of unknowns, or cut it down to a simpler fact: going 80 miles at the initial speed is 1 hour quicker than going the same 80 miles at the reduced speed.
Then there's just one unknown to solve for.

[drowsy leaf]

I'll have to do a check later on

[drowsy leaf]

@near hill in the second case is the accident occurrence considered exactly after 1 hour? (Sorry, English isn't my first language)

[near hill]

I understand it as: in the second case the speeds are the same, but the accident happens whenever the train reached 80 miles past the point where it broke down in the first scenario. Those 80 miles do not necessarily take an hour to drive.

[drowsy leaf]

got it

[near hill]

So if the track looks like
Aytown ----------- C -----80mi----- D ------- Beetown
and the accident happens either at C or D, the train spends:
Either one hour A-C then 30 minutes stopped, then C-D at reduced speed, then D-B at reduced speed.
Or one hour A-C, then C-D at full speed, then 30 minutes stopped, then D-B at reduced speed.
The one hour, 30 minutes, and D-B segment are the same in both cases, so the only thing that makes a difference for the arrival time is whether the 80 miles from C to D were run on full or reduced speed.

[drowsy leaf]

you are very good at explaining

[near hill]

Thank you.

(if my mental arithmetic is right, the train's full speed is ||20 mi/h||, which sounds pretty pitiful even by 1955 standards...)

[trim vortex]

i have the first case as 2 + (d/r) = (r/r) + 0.5 + (d-r)/[(4/5)r] and second case as 1 + (d/r) = (d + 80)/r + 0.5 + (d-r-80)/[(4/5)r] according to ur logic above

[near hill]

Sure. Now if you subtract those equations from each other, many of the terms disappear.

In the second equation, I think you mean (r + 80)/r rather than (d + 80)/r.

[azure sedge]

thats frickin awesome

planning to do any amc?

i need to prep for amc 12 but feel so overwhelmed

idk where to start

have been learning number theory for a few days

[trim vortex]

I got 20mph tysm

[pearl holly]

Any tips in getting better at problem solving?

I am lowk loosing my mind

[radiant jasper]

Why is my train moving at negative mach 17

[radiant jasper]

imagine a cube of cubes made up of 1000x1000x1000 cubes, and you are on top of it right in the middle, now shoot a beam right below, it will go through 1000 cubes to reach the bottom, now, if you hold the beam at an angle with respect to the initial position, it will go through more cubes, now, find a general equation on how many cubes the beam will go through, and how that amount changes as you change the angle on x and z axis.

[sharp sandal]

it will go through 4000 cubes cuz in middle means you be standing and shooting in the middle of 2x2 square

[radiant jasper]

bro wait no

you are in the middle of a square

[sharp sandal]

try to imagine yourself standing at top in the middle of a 2x2x2 cube

[radiant jasper]

i will rotate it so the plane projected above it, the middle will line up with- you know what, who cares, there are 1000 cubes anyway, not 2, it's close enough.

i mean on each axis

1000x1000x1000

And no don't make the engineering joke

[sharp sandal]

change it to 1001x1001x1001

that will be cringe lol

[radiant jasper]

anyways just solve the question

if you can that is, this is impossible question.

[mystic shale]

i think you've to think more along the lines of the edges of the cubes than the cubes themselves

since if it hits within one cube it is guaranteed to hit all cubes in the diagonal

hollup lemme make an illustration

[radiant jasper]

don't forgot about the other axis.

you not only have to account for x but also z.

[sharp sandal]

i was just thinking, you can rewrite it as, imagine a 1x1x1 cube, with a laser being shot from the above, vertically inside the cube. If the sum of reflections it made from above and below face = 1001, the box breaks. If the sum of reflections it made from any side face and its opposite side face = 501, the box breaks. How many reflections would it make before the box breaks?
Also find an equation for how many reflections will it make before the box breaks when shot at an angle.

[mystic shale]

same logic for the z-axis, but idk how to proceed with the fact i just explained

[radiant jasper]

it it's 2 other cubes you didn't draw

[mystic shale]

i don't think a reflection mechanism is mentioned.

[sharp sandal]

i mean both questions are equivalent, not same but the answer to both questions is same

[mystic shale]

? i think those are sufficient to show my point, no?

[radiant jasper]

i thought about this problem myself randomly idk if it's somewhere else but it sounds like a math comp question.

But i am WAY too dumb to solve it myself.

[mystic shale]

oops just realised i shot the ss in fullscreen

better

[mystic shale]

idk what u mean by this btw

[radiant jasper]

what if we try to find how many faces it will intersect? is that possible? if so we can convert it to how many cubes.

[mystic shale]

i'm pretty sure the question you've formulated is wrong in the sense it should be 1001*1001*1001

since there is no "middle" in the current case

[drowsy leaf]

you get better by solving problems, simple 😂

jkjkjk, anyway, i would recommend solving riddles, puzzles, you could find some here in ted ed https://youtube.com/playlist?list=PLJicmE8fK0EiFRt1Hm5a_7SJFaikIFW30&feature=shared

you can also learn concepts from
https://brilliant.org/

these help improve your imagination

[mystic shale]

that said, the number of possibilities are (1001)^2. Idk how you can derive an equation in theta and xyz for the current problem since even for different values of theta or x,y,z you can have the same case happening.

[glacial jolt]

Are you by any chance Indie?

[drowsy leaf]

ye

you too?

[glacial jolt]

Are you by any chance preping in online allen?

for JEE

[drowsy leaf]

no, i simply love math, so i joined this community

I'm a CS graduate

[glacial jolt]

Oh my 💀

pg?

[drowsy leaf]

I am preparing for GATE, and doing some courses

[glacial jolt]

I see

Are you by any chance tamil?(If no nvm)

[drowsy leaf]

why the skull?

[glacial jolt]

Can't detect anyone's level lol

maybe mathematical level

[drowsy leaf]

i am not tamil !! 😂 curious why you thought that tho

[glacial jolt]

Obviously your name lol

[drowsy leaf]

my name is of bengali origin

[glacial jolt]

I see

[drowsy leaf]

so, are you tamil?

[glacial jolt]

prolly, ye

but not a grad lmao

[drowsy leaf]

ahan

so in 12th?

[glacial jolt]

Ye howdya know btw???????????????????????????????

💀

[drowsy leaf]

you asked about JEE so...

[glacial jolt]

I see

I know someone with this name preping for JEE in my batch

that's why I asked

[drowsy leaf]

ahan

not you?

preparing for JEE i mean

[glacial jolt]

I too

in my batch lol

[drowsy leaf]

GL then

[glacial jolt]

Thank you!

Have a good night!(actually I wanna say day but it isn't sadly)

[drowsy leaf]

you too^^

[tired depot]

thank god im off this

[glacial jolt]

What the hell with your banner? lmao

[tired depot]

lol

[glacial jolt]

I have a bad mind lol

[tired depot]

oh lmaoo

[glacial jolt]

sorry if it is not something I thought

[tired depot]

its not any hentai dw

[glacial jolt]

💀

[glacial jolt]

What are you off at?

btw

[tired depot]

The jee thing lol

i look back now

[glacial jolt]

You've cracked it?

[tired depot]

shii was traumatic

[glacial jolt]

that was?

[tired depot]

Dunno

what do u define

by cracking

[glacial jolt]

wrote this year?

[tired depot]

lastt

[glacial jolt]

I mean got your desired rank

?

[tired depot]

im satisfied yee

i asked a lot of questionss here

[glacial jolt]

Are you a IIT or IISC student now?

or even NIT

[tired depot]

had 6k in adv

[glacial jolt]

lmao idk cause I am not here in those days

[glacial jolt]

fr, GREAT!

[tired depot]

nahh

i shat

after mains

don't do tht

Had .66 in mains

Could've gotten better

But slacked

[glacial jolt]

shat?

wdym

[tired depot]

likee

how do o say

many people after mains

Go chill

I ws one of it

don't do that

[glacial jolt]

Oh I see

You got 66 in mains but 6k in adv

?

[tired depot]

99.66

my one friend had .63 he got 2k

[glacial jolt]

oooooooooooooooooooooooooooooooooohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyygggggggggggggggggggggggggggggggggggggggoooooooooooooooooooooooooooooooooooooooodddddddddddddddddddddddddddddddddd

[tired depot]

uh yea

don't slack after mains

Even after it g good

[glacial jolt]

Sure!(I always hold words of my seniors)

wbu now?

[tired depot]

i don't

Study now

[glacial jolt]

Working at an industry?

or stuck in korea?

or lost in discord?

@tired depot

[pure yarrow]

Hello everyone I am from Tunisia and most of my time I ama struggling because I study from random websites I don't't even have a single maths book that has problems within for competitive maths, I usually find problems on random websites and try to solve them

This is a one

Let a and b be distinct natural numbers. Show that there exist infinitely many natural numbers s such that a + s and b + s are relatively prime.

Can someone rate the difficulty of this problem

I hope also my English sounds good cause most of it I learned through listening to streamers

Or reading novels

[pure yarrow]

Anyone please rate the difficulty of this problem

[glacial jolt]

How are you going to prove this goofy thing?

[pure yarrow]

Did you do competitive maths before

@glacial jolt

[glacial jolt]

Nah but going to

[pure yarrow]

What are you going for?

Do you having any studying sheets or books or anything

[glacial jolt]

something called JEE

[glacial jolt]

ye

[pure yarrow]

Like waht

The books?

I mean the titles of books

Or the resources

I really lack them a lot

[glacial jolt]

It can't be bought anywhere sorry

[pure yarrow]

even if it is I can't right now

[glacial jolt]

'cause they are my Institutional books

[pure yarrow]

I understand

[glacial jolt]

What exams are you preping for?

exam*

[pure yarrow]

There are no exams I just wanna reach level of competitors in maths so I can be at the same level, I wanna by anyway improve my life and escape from my country there is nothing good here and it is very hard to find a teacher

They really ask for huge amounts of money so they teach you for 4 or 8 sessions

The only exam I am taking is kinda of mix of games of maths and logic

[glacial jolt]

I see

[pure yarrow]

FFJM

I study maths in french by the way

[glacial jolt]

What is your math level or grade?

[pure yarrow]

Because Tunisia is francophone country

I am at the second year of secondary education

But you know

[glacial jolt]

What abt your school teachers?

[pure yarrow]

Hhhh there only 4 maths teachers

I told you they offer very expensive private lessons

[glacial jolt]

I see

[pure yarrow]

And at school is usually get full marks or 90s without even putting some effort

[glacial jolt]

Is it that ez for you?

[pure yarrow]

Is there anyone here that did the IMO by anychance

[glacial jolt]

Idk anyone rn

sorry

[pure yarrow]

Not that much but kinda of

because our country selection test will be the by the begining of 2026 it will be such a great achievement to do well without a teacher that guides me

Wish you all the best in JES

JEE*

[glacial jolt]

You may talk to gfauxpas @pure yarrow

in dm

[glacial jolt]

Thank you so much!

[mystic shale]

why you giving them permission on behalf of someone else lmao

This is exactly what got you into trouble yesterday

[glacial jolt]

I don't get any trouble lmao

what is it?

[mystic shale]

When you pinged tropo

[glacial jolt]

I ain't

[mystic shale]

Or shubham did idr

[glacial jolt]

This isn't trouble at all lmao

I am iron man lmao

I like that opencry

I feel sorry to myself for that reaction

[summer roost]

That is not competition math though

[glacial jolt]

are you doing limits?

[summer roost]

Nope

I will do that next year

[mystic shale]

I see you came back to dc

[summer roost]

i never left

although my phone usage is basically 0 hours

[summer roost]

i am not sure if this can be counted as a proof

but we can say that there are infinitely many primes so infinitely many numbers of this form

is that correct ???

[vernal axle]

I think it's easy

just take s=p-a, where p is any prime greater than max(b-a, a) (in case b>a)

[pure yarrow]

Tha ks

I want a daily schedule recommendation

Like is 2/3 hours daily goos

good*

[summer roost]

it doesnt really depend on the time as long as your problem solving improves

initially 2-3 hours is quite good

[pure yarrow]

Ok

[formal trout]

Hello guys

I have this problem i’ve trynna solve

I know the answer and it’s quite obvious as we are driven by intuition to find the answer the question remains how to prove it without supposing elements in the sets

Here’s the problem i’d like you to gimee sum hints i haven’t gave up yet

Don’t use complex concepts tho

[near hill]

What exactly is N* there?

[formal trout]

Non zero postive integers

Well if you want answer i can say it

[near hill]

How about ||A=3N+1, B=3N+2, C=3N||?

[formal trout]

Exactly

The question remains how to prove it

[near hill]

And it doesn't just want one solution, but all solutions.
The one I showed isn't the only one; at least we can swap A and B.

[formal trout]

Swap A and C , B is stable

Otherwise you don’t have the a+c thing

[near hill]

No -- C is distinguished by being the numbers you can add to an a or b and not get out of A or B, respectively.

[formal trout]

Yeah exactly

[formal trout]

That’s the only two solutions btw

||(A,B,C)={(3N + 1,3N+2,3N*),(3N+2,3N+1,3N*)}||

Do you have any hints on how can i proceed to make a clean proof?

[near hill]

When you say

prove it without supposing elements in the sets
do you mean we can't start by saying "let c0 be the smallest element in C", for example?

[formal trout]

Oh no no it’s okay

I meant like we can’t say

Suppose 1 in A

[near hill]

I would say something like:
Let c0 be the smallest element in C.
Then 1, 2, 3, ..., c0-1 must be divided between A and B. And because we can add c0 to anything from A or B without leaving that set, this settles the fate for any number that is not a multiple of c0.

[formal trout]

Mmm

It seems clean but i’ll have to work it out

[near hill]

Assume without loss of generality that 1 is in A.
Then clearly the smallest number that can be in B is c0-1; otherwise the two smallest numbers in A and B would add up to something smaller than c0.

But that means (once we have excluded c0=1 or c0=2, which is easy) that c0-2 is in A, so (c0-2)+(c0-1) = 2c0-3 must be in C.
We've already seen the only numbers that can be in C are multiples of c0, so that means 3 must be a multiple of c0, which means c0=3.

And every multiple of 3 must be in C, because they can all be made as 1+(2+3+3+....+3).

[formal trout]

Thanks man i’ll use this smallest number thing

[acoustic nova]

broo i already sent u my perfect guide. every imo participant has followed it. hear it is again good sir

Preparing for the International Mathematical Olympiad (IMO) is a significant and rewarding challenge that requires deep understanding, problem-solving skills, and consistent practice. Below is a detailed study plan, broken down by phases, topics, and weekly routines, adaptable over 6-18 months, depending on your current level.

🔍 Phase 1: Foundation Building (Months 1–3)
🎯 Goals:
Solidify core mathematical concepts.
Develop mathematical thinking and proof-writing skills.
📚 Topics:
Algebra: Equations, inequalities, polynomials, functional equations.
Number Theory: Divisibility, congruences, modular arithmetic, primes.
Geometry: Euclidean geometry, similarity, circles, angle chasing.
Combinatorics: Basic counting, Pigeonhole Principle, inclusion-exclusion.
🗓 Weekly Routine (10–15 hours/week):
Day Task
Mon Topic Lecture (e.g., Algebra) + 2 Easy Problems
Tue Solve 3 Problems from previous topic
Wed Topic Lecture (e.g., Number Theory) + 2 Easy Problems
Thu Solve 3 Problems + Review solutions
Fri Rest or light reading (e.g., problem-solving strategies)
Sat Mock test (3 problems) + Discussion of solutions
Sun Review week’s work + Fill knowledge gaps
🚀 Phase 2: Intermediate Problem Solving (Months 4–8)
🎯 Goals:
Begin solving intermediate-level olympiad problems.
Refine techniques and learn multiple approaches to problems.
📚 Topics:
Deepen understanding in all four main areas:

Algebra: Inequalities (AM-GM, Cauchy), symmetric polynomials.
Number Theory: Diophantine equations, Euler’s theorem, orders.
Geometry: Inversion, transformations, angle bisectors, Miquel Point.
Combinatorics: Graph theory basics, invariants, recursion.
🗓 Weekly Routine (15–20 hours/week):
Day Task
Mon Topic Study (1–2 hours) + 2 Problems
Tue Problem-Solving Session (2 hours, timed)
Wed Topic Study (1–2 hours) + 2 Problems

[acoustic nova]

yeah this is nice cause b cant be a multiple of a + s = p by the setup

[acoustic nova]

like actual limits or just random computational rules?

[soft vigil]

what is this chatgpt ahh guide

highkey

you cannot do a routine for math

[acoustic nova]

yeah. thats the point ||it is chatgpt (obv)||

[fast wing]

what do you mean by that. how we supposed to then

[near hill]

Could you not?

[mystic shale]

Fr

Chatgpt just assumes peak excellence from everyone and gives you a guide that no one can follow.

[glacial jolt]

limits! anyways wdym by random computational rules?

[harsh apex]

what site i need for competitive math

how do i start comp math

[soft vigil]

Like this is the same for competitive programming

If you are trying to do a routine it wont work

Because you often fall behind with problrms that have bugs

[harsh apex]

where can i find problems

[ornate blade]

hackerrank

codeforces

[formal trout]

Can i use induction ?

[near hill]

That would be the natural choice for several of the subproofs here, yes.

[formal trout]

Okay thanks

[harsh apex]

i mean for comp math

[hushed charm]

Probably this is the biggest collection of competitive math problems you can find https://artofproblemsolving.com/community/c13_contest_collections

The olympiads from your country must have some sites either, where you can find past problems with solutions

[drowsy leaf]

anyone free?

[scarlet root]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[soft badger]

yes i am send question

[glacial jolt]

Just talk what you want, sis!

cause these kind of questions are not liked by this server lmao

@pure yarrow You may look at schoolhouse of KA but it for precalculus

anyway check it out!

[drowsy leaf]

i needed to interview someone, but it's settled now

[leaden plaza]

Hello, tomorrow I have a make-up exam for the entire math course. It includes Real Nouns, Fractions, Proportionality, Scales, Statistics and Probability, Algebraic Language, Grade 1 Equations, Tales, and Pythagoras. Could someone help me with this? Regards.

[glacial jolt]

Interview? lmao

[ornate blade]

practice on Khan Academy

the relevant sections will be in Algebra 1 and Geometry

oh wait a lot of is Prealgebra as well

[glacial jolt]

South, How many hours are you active on discord?

Like how many hours got you very active role

[ornate blade]

I have no idea

but you'll get *very active soon I bet

[glacial jolt]

lol

[ornate blade]

you're pretty active here

if you keep it up you'll become a loser like all of us

[glacial jolt]

Are you a graduate?

or

studying

[ornate blade]

undergrad but not maths

[glacial jolt]

You studying math yourself?

[ornate blade]

nah

I just like this server

not actively studying maths

[glacial jolt]

You're just helping with your knowledge of math you have lol

What is your major, if you don't mind?

[ornate blade]

sociology!

[glacial jolt]

I thought you are a mathy person

nvm me

lmao

[ornate blade]

there's no contradiction lol

[glacial jolt]

I see

[ornate blade]

okay the story is I was doing a maths degree but switched out

there you go

[glacial jolt]

What a sad story in my pov!

,, \prod_{k=2}^{\infty} \left(1- \frac{1}{k^2} \right)=\frac 12 ?

[gilded halo]

Monkey•D•Luffy

[soft vigil]

do you need very active role?

[glacial jolt]

not badly If I can, I wanna

suggest me, come on!

boboblakis

toni

@soft vigil

Howdya got emeritus?

[soft vigil]

just talked

i didnt even need to get active or very active for it

[ashen jacinth]

yes

[acoustic nova]

why

[indigo ice]

the math to sociology pipeline gotta be rare

[ornate blade]

Didn't enjoy having to grind STEM

[acoustic nova]

why?

but math in particular

[soft badger]

DONE should i send solution??

[hollow otter]

Hello?

[radiant jasper]

is there a channel dedicated to putnam

[hollow otter]

@radiant jasper

Man could you help with some maa putnam pyqs

[radiant jasper]

i think the prerequisite is olympiad

[radiant jasper]

r u on it

[glacial jolt]

I want to let you know that sending a solution to a question to others is against this server's policy.Also I am asking that is that infinite product correct!But it is fine now(Thank yor for your consideration ❤️)

[hollow otter]

Yes

[soft badger]

bro i was just asking if i should send the sol or not

[radiant jasper]

okay i never did prepare for olympiad i want to solve real analysis of putnam

[glacial jolt]

I see.I appreciate your consideration! But I have understood it already!

[azure temple]

you can set this equal to something, log it, then write the argument of the log as one quotient, apply log rule, factorise, apply log rule again, and i think it will telescope

[limber vault]

help pls

im genuinley cooked

[near hill]

A good start would be to find the measure of the visible angles not involving the short line between square and nonagon.

Also hint: draw this line. Notice anything in particular about the long thin triangle?

[gilded halo]

samuel

[hushed charm]

I haven't found any unseful information yet, needing a hint to start

[foggy mountain]

Is it 85

NAHHHHH you're a genius or I'm just dumb how did you make it that easy

[soft vigil]

oftentimes geo problems are solved by drawing something extra

[foggy mountain]

Yeah but it was just one line away

[soft vigil]

yeah

i dont think you even needed the line here

[foggy mountain]

Nah you did

[soft vigil]

hmm

yeah

[foggy mountain]

I drew a shit ton of lines and then realised all the lines are equal

Which means equal angles

[soft vigil]

well

you want AJ to be altitude

[foggy mountain]

Where is J

[soft vigil]

so what if show that the altitude intersecting withTI

be the point

J'

and show that J'D is parallel to FI

and then you are done

[abstract osprey]

Hi?

[quick harbor]

can you clarify the solution?

[near hill]

The two triangles on each side of the red line are ||both iscosceles||.

[quick harbor]

ah

why though? how do we know for sure?

[near hill]

All chords that span 3 corners of the nonagon have the same length, and all sides of the square have the same length too.

[quick harbor]

oh duh

[pearl holly]

Hi chat!
How do you guys learn stuff intuitively by not like applying theorem, rules, etc and random stuff?

[pallid tundra]

how do you ask a non vacuous question?

without throwing around buzzwords that show you don’t know what you’re talking about?

“intuitive” “concept” “rigorous”

when you’re reading a math text don’t do so passively

have pencil and paper to write stuff down and work the examples and end-of-chapter problems

ask yourself “why is this true” for anything that doesn’t seem immediately obvious

it’s a slow process but rewarding

that is how you deeply build your understanding of a topic

re intuition:

having good examples to fall back on is especially important once you get into more advanced topics if you want to hone your intuition

[grand iron]

hey guys quick question is it correct that there are 90 four digit palindromes?

[near hill]

Sounds right, if you don't allow leading zeroes.

Then the first two digits can be anything from 10 to 99, and those two digits then determine the last two digits.

[grand iron]

k ty 🙏

[grand iron]

yep that's what I did

[chilly elm]

One message removed from a suspended account.

[cyan rain]

no anwer?

[vernal axle]

It's obviously 1
😆

bc it is B(n+1,p+1)/B(p+1,n+1)

[glacial jolt]

Is it bernoulli number?

[vernal axle]

nope, it's Beta function

[glacial jolt]

Is this one of the definitions of beta function?

@vernal axle ?

[vernal axle]

The numerator and denominator are just integrals of x^p (1-x)^n and x^n(1-x)^p over [0,1] (which is a definition of beta-function)
You may not even know about beta-function. Just change variables t=1-x in one of them to see that they are equal

[glacial jolt]

wdym by changing variables?

[vernal axle]

change of variables in integral

[glacial jolt]

this? @vernal axle

[vernal axle]

yep, but in fact, you don't need this to find k.

[grizzled timber]

I need some help on my mathematical conjecture

[misty torrent]

#1021175428326633542

[deep field]

might be too specific but anyone know about the amc?

iykyk it's coming up soon

australian math competition

[crystal rock]

I know I'm like 2 days late, but to be sure, you can prove that TI is perpendicular to AD, implying that J is the orthocenter of triangle ATD.

[pure yarrow]

Hello

I wanna know who participated before in the match competition made by FFJM

[hushed charm]

Indeed, I found that either, but now I have to prove that TI is tangent to (AMN). Any idea?

[crystal rock]

I have a solution that works, but it's kinda.. weird.

Let (I) touch BC at a point, AD intersect (ABC) at another point
Those 2 points and F are actually collinear.

We can use that fact to find the angle TID more easily

[limber vault]

help pls ;-;

[near hill]

Forget for a moment that the area of ABCDEF is supposed to be 1 and just concentrate on finding the ratio between the side lengths of the two hexagon.

(For this purpose it may help to pick a different scale such that the side length of the green hexagon is 1).

[limber vault]

bro i got

√3/3

and then some horribly complicated number that i dont want to type

but √3/3 isnt correct

[near hill]

Exactly what is √3/3 supposed to be? The ratio I suggested you start by finding?

[limber vault]

no the answer

[near hill]

That's not the answer I get either.

[limber vault]

ope

aaaaaa

hold on lemme try the ratio thing

i got √3/3 before i asked this

ok first of all the side length of the big abcdef is √(2√3/9) right

sqrt{2sqrt{3}/9}

a

how dy type latex in this

[near hill]

Just surround it by dollar signs.

[limber vault]

oh

$sqrt{2sqrt{3}/9}$

[gilded halo]

no stop

[limber vault]

uh

ah whatever

[near hill]

You still need to type the same backslashes as you would in actual LaTeX.

[limber vault]

k

anyways back to the point is that the correct side length of abcdef

[near hill]

Anyway, it looks like you don't like my suggestion -- which is your right -- so I'll just wish you good luck.

[limber vault]

wait i wanna use ur suggestion

tryna f ind the smaller hexagon's side length

i got the larger one but idk if its right

[near hill]

My suggestion was to set the side length of the smaller hexagon to 1.

[limber vault]

oh

then the larger one would be √3 right

[hushed charm]

$\frac{\sqrt{2} \sqrt{3}}{9}$

[near hill]

Indeed. And that means that the ratio between the areas of the two hexagons is ...

[gilded halo]

samuel

[limber vault]

1/3 then?

[near hill]

Yes.

[limber vault]

tysm!

thanks!