competition-math

[ornate blade]

I was told that these problems were carefully designed to have elementary solutions (so that the Department could avoid scandals) that were nearly impossible to find. Any student who failed to answer could easily be rejected, so this system was an effective method of controlling admissions.

[astral jacinth]

yeah

oh i never checked yt

i should

ty

[sharp sandal]

If anyone from India, are these online classes from Unacademy, PW, etc. enough for Jee Mains if you study well from your side? I have no experience of it so I am just thinking if online or offline classes will be better.

[hexed thistle]

No too old

[ornate blade]

pray that the 13 year old who replies to this won't drive you insane

[scenic kestrel]

guess who??? 😜

[stable umbra]

Does anyone have any tips for taking the Putnam exam other than learning the material more and practicing questions

[willow bramble]

Does anyone know any free textbooks that could help me on the AMC10?

[stuck tartan]

i heard that like coffin problems are similar to this

they were created to prevent jewish students from entering universities or mshtg

[pale berry]

Last tuesday i experienced the unfairest experience i have ever had on olympiads, you see, i went to a very recognized school on my city to participate in olympiads , so, i go and get presented the next problem: On the sucession: 8,2,-4,-10... determine if 132 is part of the sucession. first thing i do is check if 132 is a 6 multiple , and turns out that it was, so i said yes and they said that was not the solution, so i try to do all the terms until 132, but no, the guy that was checking on the participants take my paper out of my hands and tells me that my solution needs to be checked by organizers, the thing is that i had 180 seconds to solve, by the time the paper was brought back to me i got 30 seconds and got to do until 112 and time finished. Note that this is supposed to be 10th grade (Colombian 9th grade) olympiads where i saw 8th grade problems. Opinions on this? What could i do to participate on TRUE experiences of olympiads?

[astral jacinth]

132 is not part of the sequence tho? The sequence is of numbers two more than a multiple of 6, right?

Anyways, the succession is going the wrong way so even if it were 12, 6, 0, -6, 132 wouldn't show up iirc

[pale berry]

Thats what i realized, so decided to write all the terms on the sucession, the thing is that even tho evaluator told me the thing was wrong he took my paper no reason at all

[astral jacinth]

Oh dang

I've never really done a math Olympiad before but that sounds infuriating

[pale berry]

yeah it was

[torn bane]

Can anyone coach me on competitive math problems?

[pallid tundra]

this is not the place to ask for that

[torn bane]

It's the competition math channel, no?

[ornate blade]

we don't offer tutoring on this server

if you have a specific comp maths problem you would like help with, you can just post it here

[torn bane]

oh ok, thanks for the clarification

[winged sluice]

What's 1÷0?

[near hill]

That doesn't produce a result.

Divisions with 0 in the denominator do not have a defined meaning.

[torn bane]

does IMO or AMO have varying tests for different grades?

[next coyote]

limit positive x-> 0 1/x is infinity

[near hill]

They didn't ask about a limit, though.

[winged sluice]

That's the mistake most people does

[winged sluice]

Yupp

[safe elk]

JMO is for people who qualified through amc 10

but no, IMO and AMO are the same for all grades

[digital quiver]

cuz we have TH=TD

so then we can just prove TH.TI = TE.TF = TD^2 = TH^2

but stuck here

[novel karma]

Bro why you sending ts here

[prisma python]

i think it was a bot lol

[novel karma]

lol

[hardy basin]

I see this channel dedicated for competetion maths so can can anyone tell me resources from here I can prepare for Maths olympiad?

[austere wedge]

i get the answer but like

how in gods name do you come up with it

[astral jacinth]

Is it 334?

What is it

The bottom equation is the first minus thrice the second plus thrice the third I think

[austere wedge]

yea

[austere wedge]

how does one just see this

[stoic tinsel]

you can find the difference between 1st and 2nd equation

then the same for 2nd and 3rd

you get 3x + 5x + 7x + 9x + 11x + 13x + 15x and 5x + 7x + 9x + 11x + 13x + 15x + 17x

the difference between them is 2x + 2x + 2x + 2x + 2x + 2x + 2x

adding that to 3rd gives final equation

[astral jacinth]

Note that (n+3)² is linearly dependent on (n+2)²,(n+1)²,n²

Also I hoped the three equations were linearly dependent and they were!

[stuck tartan]

basically finite differences on the sequence n^2 if ur familiar with it

[sleek helm]

You can row reduce the. Use the first 2 factors to determine the right linear combination

Do L2 <- L2 - 4 L1

L3 <- L3 - 9L1

etc.

[manic tulip]

My approach was trying to make 100 with plus or minus 49, 64 and 81. The other stuff just works out then.

[digital quiver]

no bot bro 😭

im out of idea for this problem ive been thinking it for like 2 days

[near hill]

They were not talking about you. Someone else whose post was deleted.

[prisma python]

yeah there was a scam that was deleted

[worthy fable]

There are better ways of thinking but if can’t see it then can always do the algebra until it gets clearer

[worthy fable]

or like this

[azure hull]

hello ow can i train for the IMO ?

im in 10th grade

[pallid tundra]

to be blunt: if you need to ask that question you’re not ready to do IMO level problems

start by learning about the qualification process from your country

what contests do you need to do to enter the qualification process?

study for those, do well enough to advance, repeat

[autumn linden]

is this happening to everyone?

[woeful orbit]

Hello

[keen mirage]

hello

are aops volumes 1 and 2 good for training competition math at a middle school level (like mathcounts, amc 8 and 10, MOAA, and other things like math kangaroo)?

[pallid tundra]

they’re very outdated compared to modern resources, supplement with actual recent contest problems

[keen mirage]

oh

is mathdash good?

[pallid tundra]

I have no idea what that is

[keen mirage]

https://mathdash.com/contests

[pallid tundra]

haven’t looked at middle school level stuff in at least 7 years

[keen mirage]

oh

mathdash is like a practice platform thing

[pallid tundra]

don’t restrict yourself just to one platform

as long as you’re practicing on challenging problems you’ll be improving your skills

[keen mirage]

yeah but im a lazy person

so

yeah

[stuck tartan]

It’s not as good as it used to be

there’s a decent amount of ai slop and the educative material is mid

If you want to do the contests feel free to do them but there’s better options for an educational experience

[thin geyser]

is there anyone who got a good score on the amc 10 or 12 who can help me study

[minor yarrow]

guys

how do you register amc 8

and mathcount

[keen mirage]

oh

[keen mirage]

is your school doing it?

or for mathcounts

[stoic tinsel]

they are good, but the best option is just to grind past year tests

[keen mirage]

oh

[violet lark]

Can someone help me for Thailand IMO Heat round?

Secondary 1

[rare sable]

Can help with questions and concepts

[sleek ivy]

how much have u gotten on practice tests

[thin geyser]

Umm last time I took it I got 76 ish

[simple drift]

I HAVE BEEN BEATING MY HEAD AGAINST THE FUCKING WALL, AT THESE GOD DAMN MOTHERFUCKING ALCUMUS PROBLEMS FOR 2 GOD DAMN HOURS! IT MAKES NO FUCKING SENSE! ITS ALL SO FUCKING STUPID GOD DAMN IT! WHAT THE FUCK DO THESE STUPID FUCKING ASSHOLE BITCHES WANT ME TO DO!!!!!!!!!

FUCKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

[compact wing]

💔

[simple drift]

I’m so fucked bro

It was casework counting

[novel karma]

Bro chill the fuck out

[pallid tundra]

secret achievement “ragequit”: leave alcumus for 12 hours after getting a problem wrong

[simple drift]

I didn’t get “ a question wrong” I got 80 questions wrong

[pallid tundra]

80 😭

[simple blaze]

uhh can anyone tell me about incho ? ive heard about it before as im preparing for JEE but have no idea on what it actually is

like whats the level of it

[simple drift]

im kinda fucked

can u help

[stuck tartan]

idt 76 is a possible score bro

[stuck tartan]

what defines a good score

DHR?

[lavish marsh]

Are there any tricks, or not-well known formulas for conic sections that anybody can slide my way? Im doing an Oral presentation contest for the North Suburban Math League in illinois and our topic is Conic sections from AoPs Intermediate Algebra Chapter 5

[soft vigil]

ima be real wit u

the most important part is solving problems and getting consistent (fewer sillies)

[soft vigil]

if u want i can add u to the IL math discord

[lavish marsh]

yes pls

[soft vigil]

check dms

[stuck tartan]

how to get gud at amc 12 fr 💔

[robust dune]

Practice

Js

[fallen shale]

Can anybody help me with gmat exam..i haven't started anything and didn't touch math for 2 yr

[rare sable]

What's the syllabus

[fallen shale]

Data Sufficiency

Data Analysis (graphs, charts, tables)

Multi-source reasoning

Two-part analysis (quant + verbal mix)

Statistics & probability applications
Arithmetic (percentages, ratios, fractions, averages, profit-loss, simple & compound interest, speed-distance-time, work-time, number properties, etc.)

Algebra (linear equations, quadratic equations, inequalities, functions)

Word problems

Geometry basics (lines, angles, triangles, circles, coordinate geometry)

Statistics basics (mean, median, mode, standard deviation, probability, permutations & combinations)

[rare sable]

I can help with doubt solving

Of syllabus later to statistics

[fallen shale]

Ok thanks ..can i ask doubt on personal chat?

[viscid plover]

I can help with algebra, geometry and some parts of statistics

[thin geyser]

can someone help me prepare for aime

i got a 76 on amc 10

[dusty pulsar]

hello!

so for the first time ever, I'm going onto my highschool's math team!!

[novel karma]

How

[thin geyser]

wdym

that is really bad

[stuck tartan]

It id physically impossible to get a 76 💀

[novel karma]

You didn’t get a 76 vro 💔

Bro give the actual score

6 x correct + 0 incorrect + 1.5 x skip

[thin geyser]

idk

it was 76 ish

i think

might of been 76.5

[glossy tinsel]

what do they mean by this what is it specifically

are they referring to method of differences for summations?

[green jetty]

Difference equations are like x_n+1 = x_n + a
Or something like x_n+1= x_n + ax_n
Or something similar
So basically it's a equation which relates one term of a sequence with another

[glossy tinsel]

is that not just a recurrence relation

[green jetty]

Yes

But yeah , they will ask you solve such an equation

[glossy tinsel]

ahh alright thank u

im so confused as to why they chose to put it that way

[green jetty]

Me too, I had to google it to be sure. I had forgotten that such a thing exists

[echo hatch]

esesd

Hello.

Can you hear me?

[rare sable]

Hellow

[echo hatch]

NIce to meet you

[rare sable]

yep

[echo hatch]

I'm sorry interrupt you.

[rare sable]

?

[echo hatch]

I am a university student, and I came here first.

can you help me?

I don't know about here, well

[rare sable]

With what topic

[rare sable]

Ok

[echo hatch]

anything about here

[rare sable]

See there are channel here

Where ppl post doubts

[echo hatch]

yep

[rare sable]

And some smartass ppl answer them

[echo hatch]

ya

[rare sable]

You can do discussions to

#math-discussion

[echo hatch]

!

[rare sable]

Related to maths

And general things in #chill

I guess u got it

[echo hatch]

in chill, what can I do?

hello?

[rare sable]

Talk to ppl

[echo hatch]

ppl? So sorry,What is it?

[rare sable]

People

[echo hatch]

oha. sorry.

[rare sable]

Bruhh.

[echo hatch]

hhh

and How can I call you?

[rare sable]

Got any doubts related to concepts in maths , question solving shoot!

[rare sable]

Don't call me, just ping me

[echo hatch]

sorry

[rare sable]

Using @ sign

@rare sable

See easy

[echo hatch]

LOKI?

it is your name?

[rare sable]

it's what my friends used to call me

Nickname

[echo hatch]

I see.

[rare sable]

Is happy smile ur name

[rare sable]

u can't see , u can read

[echo hatch]

It's too my nickname.

[rare sable]

Really

Bruh

I'll call u happy

Suits as a nickname atleast

[echo hatch]

Would you like to be friends?

hi?

LOKI?

?

[rare sable]

Ok

Happy

[echo hatch]

Where have you gone?

[rare sable]

Busy

[echo hatch]

why?

[rare sable]

organic chemistry

[echo hatch]

studying? now

[rare sable]

Yep

[echo hatch]

or testing

lecture?

[rare sable]

Studying

[echo hatch]

Ok.

[rare sable]

Self study

[echo hatch]

Good

[rare sable]

Byee

[echo hatch]

👍

[rare sable]

[echo hatch]

When can I see you?

[rare sable]

Chat in dm dude or in #discussion

[rare sable]

U can't see me

[echo hatch]

I don't know it

[rare sable]

Use #chill

[echo hatch]

right know,possible?

Hello?

anybody here?

[next swan]

Bot ahhh

[rare sable]

Bro I told you not to chat here

[radiant jasper]

Unfortunately I cant join the math competition in the college and im f-king upset AAAAAA

Cuz i finished all math class

But I have still 3 years of college left

[simple drift]

I think I got the tech , to get ready in time. I have very little studying done but if I do 2 AoPS chapters a day 17 alcumus sections a day starting from the very start I have a full 17 days I can spend fully on doing real past AMC 10 problems and watching old videos reviewing full past exams

Can I make it

[feral drift]

olympiad people, help me solve this

On line l, points A and B are placed, and on line S parallel to it, points C1, C2, ..., are placed in order. Find the total number of triangles formed inside the trapezoid by connecting these points in all possible ways.

[ivory ember]

Probably reposted? #help-3 message

[feral drift]

yep no one figured it out

[ivory ember]

in the future, please be considerate and don't repost in multiple channels

cause it can lead to helpers double answering, which is inconsiderate of their time

[feral drift]

Got it

[viscid plover]

Let's see who is able to solve this problem.

The price of a gem is proportional to the square of its weight. Prove that the maximum depreciation occurs if we split it in half.

[tiny eagle]

One fraction of the gem is x so the other part is 1-x

The price is proportional to (1-x)^2

This is minimized when x=1/2 by parabola

QED

Olympiad level proof trust

[stoic tinsel]

You could first connect all the C points to A

[stuck tartan]

I assume the trapezoid is the largest quadrilateral that can be formed using the points?

[stoic tinsel]

Then, when connecting C points to B, it creates a new triangle, and extra ones for each intersection

[stoic tinsel]

I would guess so

[stoic tinsel]

Each line to B intersects with one fewer line to A as you draw the lines, or something to that effect

Trying smaller cases is probably the easiest way

[manic tulip]

Has anyone here taken the octm and if so, what was the difficulty of the matrix probs on it

Dont say answees obviously, i just want to know how much i should focus on them

[honest pollen]

does anyone wanna join my server?

[manic tulip]

Whats it abt

[viscid plover]

This is not correct at any time you have justified how it can be that the price is proportional to the weight ^2. If the minimum price of the maximum were split in half

A hint, this is an optimization problem.

[viscid plover]

Problem to solve is this

[kind pulsar]

what does depreciation mean here?

[viscid plover]

The minimum price

[kind pulsar]

ohh

[zinc escarp]

Isn't this a simple calculus problem? We need to prove that the minimum of x^2 + (1-x)^2 is at the point x = 0.5, which can be simply found by taking the derivative and setting it to 0

[viscid plover]

Indeed!!

But x is not equal to 0.5, don't put that equal, it's false. They put 0.5 so you can verify that value.

And not even x = 0.5

So, solve it well

[near hill]

It's even simpler to notice that the depreciation will be a polynomial of degree at most 2 (you don't need to actually find the coefficients) with f(0)=f(1)=0 and f(½) =½>0, so it must be a parabola with a maximim at the apex. And the apex of the parabola is midway between its roots, which we already know are 0 and 1.

(Assuming, as we need to for the problem to make sense, that we're implicitly supposed to cut the gem into two pieces. If there can be more than two, the specified conclusion is not even true -- we can approach a depreciation of 100% by grinding the gem into dust...)

[wintry kiln]

I have about less than a month before like an invitational math contest, I have a bit of backgrounds working with comp math, should I just grind out the questions of past papers or is there something better to do

[prisma python]

<@&268886789983436800> spam bot

[kind pulsar]

Let number of points in line S = n

Case 1: Top vertex on line l
Number of triangles
= C(n,2) * 2
= n!/(2!(n-2)!) * 2
= n(n-1)/2 * 2
= n(n-1)
= n²-n

Case 2: Top vertex on line S
Number of triangles = n

Case 3: Intersecting lines
Fix the 2 points on line l
Pick 2 points on line S
Each results in 2 triangles
Number of triangles = C(n,2) * 2 = n²-n

Total number of triangles
= (n²-n) + n + (n²-n)
= 2n² - n
= n(2n - 1)

[rare sable]

Is it 4

number of ways of selecting 3 points out of 4

[kind pulsar]

@feral drift is this correct?

[tight trench]

which book is best for olympiad math?

challanges and thrills of precollege mathematics 4th editon book and mathematical Circles Russian editon?

[rugged saddle]

how to sign up for amc 8

[queen oriole]

Really depends on your level. Overall, I think no book is the best for all Olympiad math, but some are really good for certain topics. For example, the best geometry book will most likely not talk about ROUF, etc.. overall, start with aops, then go deeper into a certain subject

[wanton mauve]

look at basic olympiad notes introducing concepts and easy problems and work from there

[fallen adder]

don’t have my school

you do not want to be in the southeast

[scenic kestrel]

if your school offers it take it through there

otherwise if u live in a decently populated place there should be a local testing center

[cosmic fractal]

yo is the P(n) approximately 1/(4n *sqrt(3) *exp(pi (sqrt(2n/3))
real?

I found it off the movie

[cosmic current]

Honestly, both options are good, but most people I know prefer the challenges and thrills of pre-college math.

[cosmic current]

I have one piece of advice: If you choose the book "Pathfinder to Olympiad Mathematics, 1st Edition" by V. Seshan and Vikash, you won’t need to look for any other books. It’s my favorite! It contains a good number of solved examples and many useful tricks, along with hundreds of questions from real Olympiads.

[tight trench]

ok honestly CATOPM is the good one as it have many exercises over 1500+ smthing so!

Thanks, as also this is not the channel for book discussion so maybe u understand!

[agile gazelle]

Does it countain complex numbers problems or algebra

[agile gazelle]

Can any1 help in this putnam question

[rugged saddle]

how would i find it

[scenic kestrel]

heres a list. https://maa.org/wp-content/uploads/2025/09/2024-2025-Higher-Learning-and-Learning-Center-MAA-AMC-Sites.pdf

if u cant find it ask local colleges and universities

[heavy pagoda]

very natural way to solve such problems is to set them up on complex plane let the center of the circle, $O$, be the origin of the complex plane, so $O$ corresponds to the complex number $0$. Let the vertex $A_1$ lie on the positive real axis. Since it is on the circle of radius $R$, its coordinate is the real number $R$.
The vertices $A_1, A_2, \dots, A_n$ form a regular $n$-gon inscribed in this circle then they can be represented by the $n$-th roots of $R^n$. The complex number corresponding to vertex $A_k$ is therefore given by:
$$ a_k = R e^{i \frac{2\pi (k-1)}{n}} \quad \text{for } k = 1, 2, \dots, n $$
These $n$ values are precisely the roots of the polynomial equation $z^n - R^n = 0$.
The point $P$ lies on the line segment $OA_1$ extended beyond $A_1$. Since $O$ is the origin and $A_1$ is at $R$ on the real axis, $P$ must also lie on the positive real axis. Let its coordinate be the real number $p$. The condition "extended beyond $A_1$" means that the distance $OP$ is greater than the distance $OA_1$. Thus, we have $p > R$. the distance $OP$ is simply $|p| = p$

[gilded halo]

Yuxuan Wang (Trusted By Mods ®)

Yuxuan Wang (Trusted By Mods ®)

[heavy pagoda]

recognizing the product might be helpful here $\prod_{k=1}^{n} (p - a_k)$. since the complex numbers $a_1, a_2, \dots, an$ are the roots of the polynomial $z^n - R^n$, we can express this polynomial in its factored form:
$$ z^n - R^n = \prod{k=1}^{n} (z - ak) $$
This identity holds for any complex number $z$. maybe then we can therefore evaluate it at our specific point $z=p$:
$$ p^n - R^n = \prod{k=1}^{n} (p - a_k) $$ this much takes u very far in proving final thing u can move from here easily ig

many putnam problems r often repetitive in structure or ideas i have seen such problems like lot of times

[dusty pulsar]

I'm going into my highschool's math team!

[pallid tundra]

nice

when is y’all’s first competition

[novel karma]

What’s a fast way to solve 2011^2011

[pallid tundra]

1. don’t

[novel karma]

Im mostly trying to look for patterns but nothing seems to work

[pallid tundra]

what are you looking for

its actual value?

[novel karma]

Oh sorry

[pallid tundra]

its value mod some number?

[novel karma]

I meant hundreds digit lol

[pallid tundra]

oh these kinds of problems

uh

take it mod 1000 and see how the digits cycle?

[novel karma]

Yes

I did that but i see no patterns

[pallid tundra]

you could reduce the exponent a fair bit with Euler totient

and use similar tricks to try to reduce it to smth you can compute relatively easily

[novel karma]

Alr I’ll try again.

[crisp mica]

Hey guys, im a junior oding amc 12, and I took the amc 12 a 2025 just now and got 64.5. Is it possible for me to qualify for aime with one moneth left

[pallid tundra]

1. spelling
2. if you’re that far off cutoff when mocking it’s highly unlikely

[stuck tartan]

2011^2011 = 11^2011 = 11^11 = (10+1)^11 = 10^2 * 11c2 + 10^1*11c1 + 1 = 5500+110+1 = 611 (mod 1000)

using fact that 11^phi(1000) = 1 (mod 1000)

[faint thorn]

guys im cooked for SMC could someone pls help me

like helping me through past paper question and particularly logic

[reef condor]

Orz Mopper

[novel karma]

Would his be a “hard” question on amc 10

[stuck tartan]

Bro what

[stuck tartan]

Probably no because it uses standard topics without any other critical thinking

[ornate blade]

in fact, Euler's totient theorem is not even needed

[novel karma]

I didn’t even know what that was lol 😭

[ornate blade]

(10 + 1)^2011 = 1 + 10 * 2011 + 100 * 2011 * 2010/2 + 1000 * ....
= 1 + 10 * 11 + 100 * (units digit 5)
(mod 1000)

[novel karma]

But yeah binomial theorem is the best way right

Like there are no cycles

[ornate blade]

yeah, so the idea was that you use Euler's theorem

the only prime factors of 1000 are 2 and 5, so phi(1000) = 1000 * (1 - 1/2) * (1 - 1/5) = 400

[ornate blade]

don't even think about that

consider that there are 3 terms before you get multiplication by 10^3, 10^4 and so on

[novel karma]

That’s smart

[ornate blade]

yeah it is just the binomial theorem

of course there's some level of depth needed to answer it

[novel karma]

Lowkey binomial theorem is way better instead of finding patterns

Like hundreds or thousands digit

[ornate blade]

there's also Hensel's lifting lemma that can be used for other problems where 1000 etc is also composite

brilliant.org has a page on it

[reef condor]

Didn’t you mop

[stuck tartan]

no 💀

[unborn heart]

I dont understand when is a fraction

[near hill]

The fractions are just certain numbers between 0 and 1.

Those particular numbers have the nice property that the other trigonometric functions of the same angle will also be nice tidy rational numbers (which you can compute).

That way you'll have everything you need for plugging into the angle addition formulas.

[robust edge]

Yall what resources should I use to study this syllabus. The document recommends Art of Problem Solving, Volume 1, 7th ed and Problem-Solving Strategies by Arthur Engel. Any suggestions?

[heavy pagoda]

arthur engel was my first book of maths

i highly recommend it

great book

[robust edge]

Oh ok Ill try it

thanks for your recommendation

[heavy pagoda]

yea its more a general book to start out then u can maybe look at books on what u wanna learn

for example pham kim hung has great book on algebraic inequalities

titu andrescu has great book on combinatorics

and justin steevens for introductory number theory etc etc

[robust edge]

Ok I'll read them

I was really confused for where to get questions from

[sleek ivy]

What competition is this syllabus for?

[robust edge]

Harvard undergraduate science olympiad India

[lusty plinth]

did anyone do usamts this round? it ended yesterday

[queen oriole]

Yes

Not able to talk about it tho because of the extension

[deep needle]

I did

and @odd talon

[odd talon]

yes

i love usamts

[deep needle]

yip not until later tonight

or tomorrow

[proud dove]

yes, this round was my first!

[eternal arrow]

only had time for 1 problem sadly

cause i learned about it a few days ago

[eternal arrow]

me too

[radiant jasper]

a + b = 10
ab = -11d
c+d = 10a
cd = -11b

Integrate (a+b+c+d) dx when a,b,c,d ≠ 0 and are not equal also.

[No ai Allowed, just try]

[deep turret]

<@&268886789983436800> spam of the same thing across multiple channels

[acoustic jetty]

Replied to 'em in another channel, thanks for flagging!

[stray pumice]

hi!

I'm new to competitive math and i want to prepare for an entrance exam but I'm having a lot of trouble writing proofs... basically i'm am idiot pls help T-T

[novel karma]

wlog is used in this problem but i don't get why/how it works

like setting a = 1

[manic heron]

anyone done the UKMT SMC ?

[orchid latch]

yes

[manic heron]

how wasit

[orchid latch]

it was okyay

[ivory ember]

In the future, you should give all the context when asking your question (so in this case, that would involve actually showing the solution where it says "WLOG").

Anyway, I looked it up, so don't worry about it this time. The use of "without loss of generality" is abusive - they're moreso abusing uniqueness (using the fact that there must be a unique answer as per the question format, so they're picking a simpler case to work with). This is supported by the solution saying later on that "this time-saving trick works only because ... a^2 - b^2 + c^2 will always be a constant" - unless you proved that a^2 - b^2 + c^2 must be constant beforehand, you cannot say a = 1 without loss of generality.

[jaunty ginkgo]

Wait so they just pull out a^2-b^2+c^2 = constant from thin air in the sol because idk, it's being asked?

[ivory ember]

yes

[jaunty ginkgo]

That sounds hilarious

[novel karma]

So it’s not a “correct” solution
And basically using wlog in algebra almost never works right

I only use it in geometry problems

Where sides aren’t given

[near hill]

There's nothing wrong with saying "without loss of generality" when it's actually clear that no generality is lost.
The problem is more that there doesn't seem to be any reason (other than metagaming) to expect that picking a value for a won't lose generality.

It's fairly bad form to pose a problem that gets so much easier by metagaming it (or, conversely, so much harder if you're purist and refuse to look at the answer options).

[novel karma]

What’s meta gaming?

[near hill]

In this context, arguments that attempt to derive information from the fact that the question was asked at all.

It's not really a crisp technical term.

However, when we're done being disappointed with the problem setter, it's actually an interesting problem. The two linear equations we're given pick out a straight line in (a,b,c)-space, and it's really extraordinary that the quadratic expression a²-b²+c² would be constant along a line -- that's not something one would expect in the general case.
The solutions to a²-b²+c³ = D when D is a positive constant is a one-sheeted hyperbolid, one of the classical example of ruled surfaces.

[jaunty ginkgo]

I understand the line part that a,b,c satisfy are on a line but how one prove they're solutions of hyperbolid

[near hill]

That's where the problem is less than satisfying.

[jaunty ginkgo]

Are we doing algebra?

[near hill]

Well, I mean, ignoring the line, whenever you pick a D>0 and look at the equation x²-y²+z²=D, that gives you a one-sheeted hyperboloid.

But for proving that the line in the problem lines in one of those hyperboloids ... the algebra-bashing way would be to find a parametric equation for the line and plug that into a²-b²+c², then simplify and see that it becomes a constant after the dust settles. That's sounds rather cumbersome.

If you already know you're going to find a constant, it would suffice to find three distinct (but otherwise arbitrary) points on the line, evaluate a²-b²+c² at each of them and then see that those three values are equal. Then note that the only way a quadratic expression can have the same value at three different points on a line is if it is actually constant along the line.

[jaunty ginkgo]

Oh yeah, interesting but in fact we can do this w/o even touching WLOG, doesn't it just give the constant right away after doing so

math is weird

[high goblet]

btw i think there's an embargo on SMC rn so don't share too many details

[ornate blade]

LY it's been such a while

how are you?

[high goblet]

btw when the embargo's over u'll probs find more discussion of SMC in the UK section of mods

[high goblet]

i'm good! wbu?

[ornate blade]

wait this isn't hlounge

[high goblet]

lol i lurk here everyday i just don't msg every day

[radiant jasper]

Bruh is that you who was once making this computer inside a simulation using rust

Year or two ago

Making circuits

[white pier]

well @high goblet are you born on 27 ?

[high goblet]

no?

[high goblet]

no

[radiant jasper]

nvm

[pallid tundra]

shameless self-promotion time! https://engage.usc.edu/scmathcompetition/scmc-fall-2025/

[faint thorn]

Hi guys

Did anyone do the SMC

On Friday

[pliant swallow]

mee

[novel karma]

What do yall think about mathdash

Better than alcumus or nah

[faint thorn]

Did u get cooked or did u ace it

I’m a 15yr old doinf it

I only managed to do 21 of the questions

[remote island]

i use alcumus for problems specific to a certain topic and mathdash to test my knowledge

tbh, i use mathdash more often and just skim through alcumus problems

[pliant swallow]

did all 25 but internet crashed at the last minute

so i dont know whether all my answers saved

😭😭😭😭😭

[pliant swallow]

me2

[faint thorn]

Sweat

[pliant swallow]

no 😭😭

all my orher school friend only did like 15+

it was really hard ngl

[austere wedge]

Is there any list of like

recommended exercises for aops books

why do they have. So much.

[stoic tinsel]

Honestly js grind it out

It’s long but worth it

If u master everything in it ur set for a lot of comps

[manic heron]

Guys

How was the ukmt smc 2025

I just marked my paper

Do you think the grade boundaries for bmo will drop

Like prob 104???

[amber blade]

does anyone know how to answer this imocsea question

[lunar badge]

if you draw out the rest of the circles, it's easier to find the area of ABE as half of the intersection of two circles that go through each other's centers

then you can just take the area of each quarter circle and add them, subtracting ABE, and then subtract all that from the square to get DEC

[kind pulsar]

Area(DEC) = Area(Square)-Area(DAE)
-Area(CBE)-Area(AEB)
Area(DEC) = 2×2 = 4
Area(DAE) = Area(CBE) = (30°/360°)×pi×2²
= (1/12)×pi×4 = pi/3
Area(AEB) = ½×2×sqrt(3) = sqrt(3)
Area(DEC) = 4-(2pi/3)-sqrt(3)

[jaunty ginkgo]

5th grade math in china (jk)

[pallid tundra]

eh i dont think this would be unreasonable for a strong 5th grader

[amber blade]

THANK YOU

[amber blade]

China math built different lol

[modern tartan]

hlo

[ornate blade]

https://www.scribd.com/document/825240426/2022-Questions-AIMO-Open-With-English
this is 5th grade in Hong Kong

they already have these

the whole paper is lower secondary difficulty: these concepts are usually taught in 8th or 9th grade

but if kids go to competition maths tutoring, they learn them earlier

[jaunty ginkgo]

I can see my friend tripping over these problem

That's scary

[ornate blade]

I'm not saying these are hard, but most people don't know how to do these in 5th grade

just like most people can't do AMC8 problems in 5th grade

[near hill]

Wow, that's horrible notation in (11).

[quick verge]

crazy

[frigid sable]

Are there books based on such problems?

[ornate blade]

I know

[frigid sable]

@ornate blade do you know where I can find such problem sets for competition math?

Sub tenth grade level

[ornate blade]

https://artofproblemsolving.com/wiki/index.php/AMC_8_Problems_and_Solutions

there's also AMC10

[quick verge]

what are AMC

[ornate blade]

also if you register an account on AoPS you can get Alcumus problems

[jaunty ginkgo]

Now I take a closer look, do 5th graders here know a^2-b^2=(a-b)(a+b)

scary in anyway

[quick verge]

and a^2 +(-) 2ab + b^2

[jaunty ginkgo]

My 5th grade cousin asked about telescope sum once but it's in term of product not different of square like this bruh

[amber blade]

i wish i learned math in a way chinese kids learn it because its looks so easy for them while im struggling here lol

[ornate blade]

most Chinese kids also find it hard, especially in secondary

just cause the teacher is teaching at a million miles per hour doesn't mean the students are following

[jaunty ginkgo]

Nahh you dont want to study for 12hours/day 💀

[ornate blade]

also like contest maths is different from regular school maths

regular school maths is definitely not this advanced

[frigid sable]

I wish to do it

I find it hard to do it through pure willpower alone

[amber blade]

i already do that anyways 😔😔

7:30am to 7:30pm

[jaunty ginkgo]

ehhh I'm pretty sure they start thier day at 7am

But that's still kinda crazy

[ornate blade]

we got to school at 7:30am but class wouldn't start until 8

cause if the school buses left any later, we'd spend way more time in traffic

[amber blade]

Tbh i dont even think im gonna pass imocsea 😭😭 goodbye japan trip

[quick verge]

same for me at hs, bus gets there at 7:40 then class at 8

[delicate meadow]

When do we register for AMC this year?

I heard the deadline is on 14th

[wraith lagoon]

any volunteers?

[high goblet]

oof rip

i mean if it didn't save in the end and you think doing bmo1 would be beneficial you could always pay for a discretionary

[high goblet]

i did hear that this year's smc was found to be harder, but i've also heard otherwise

[ivory ember]

In the future, please show what you’ve done so far when asking for help - it gives us more context of where to help you (and saves our time from explaining things unnecessarily). \ \

By definition, we have
$$I=(A^{-1}+B^{-1})(A+B).$$

Now, consider expanding this.

[gilded halo]

Civil Service Pigeon

[ivory ember]

Further hint: ||Multiply this by A.|| On the same thread, ||multiply by B as well.||

[wraith lagoon]

no i already know the solution

i just was wondering how someone else would solve it

[shy raptor]

Well then, ideally you should mention how you've solved it, and if other people then have a different idea to yours (or otherwise aren't happy with how you've done it), they can then say that to you

[wraith lagoon]

oh okay

[near hill]

FWIW that seems to gets me nowhere.
Well, it does lead to a 2×2 counterexample with complex entries (||A=e^(2ipi/3)I, B=e^(4ipi/3)I||) , so the real case cannot just be an algebraic sleight-of-hand with determinant properties ...

[ivory ember]

$$I=2I+A^{-1}B+B^{-1}A \implies A^{-1}B+B^{-1}A+I=0$$

Multiplying this by $A$ and $B$
$$\begin{cases} B+AB^{-1}A+A=0 \ BA^{-1}B+A+B=0 \end{cases}$$

And so
$$AB^{-1} A=BA^{-1} B$$

Taking the determinant of both sides yields
$$|A|^3=|B|^3 \implies |A|=|B|.$$

[gilded halo]

Civil Service Pigeon

[near hill]

How did I miss that?

[forest grail]

help

[near hill]

First, "right triangle where the square of the length of the hypotenuse is 4 times the area of the triangle" lets you conclude something very specific about the angles/lengths in the triangle.

[forest grail]

bro can someoen helptho!

[near hill]

Fairly sure I'm not your brother, but I did post a hint.

[novel karma]

anyone else having this problem

i can't seem to get the aops website to show

[iron terrace]

is studying 1-2 hours a day enough to prepare me for my mathcounts chapter competition (in late feb)

if i qualify for state, i would prob start studying 3-4 hours

[heavy pagoda]

cool

[stuck tartan]

let a,b be the 2 legs. It is given that a^2 + b^2 = 2ab --> a^2-2ab+b^2=0

what can you conclude about a and b

[kind pulsar]

Let length of the 2 legs be a and b and length of hypotenuse be c
using Pythagoras we get:

a² + b² = c²
c² = a² + b²

Area = ½ab

therefore:

c² = 4 * ½ab
c² = 2ab
a² + b² = 2ab
a² + b² - 2ab = 0
(a - b)² = 0
a - b = 0
a = b

thus the right triangle is an isosceles right triangle
since it's a right triangle the circumcenter lies on the midpoint of the hypotenuse (Circle Theorem)
and one of it's angle bisector is also the height which connects the point of the righr angle to the circumcenter
thus it also bisects the hypotenuse since it's isosceles

hence option (A)

[chilly sluice]

hey can someone help me out here, i keep getting 9216 on this after a few tries but my answer sheet says 9210

[formal ice]

does anypne know what happened to aops? i literally can't find any webpages that are actually helpful

i wonder if it's my disable google ai extension?

or did its seo get fucked majorly

[pallid tundra]

everything's still on their website

[jaunty ginkgo]

Ehhhh it's because: when one of the boxes is empty
Take 1 way in case one for example:
B1 B2 B3
Now let's say B1 and B2 are supposed to have even numbered balls but B1 is empty
And take one way in case 2 :
B1 B2 B3
Let's say B1 and B3 are supposed to have odd numbered balls but B1 is empty

Even though the assumption for 2 case are different

It's basically the same, as B1 have no ball , B2 has all the even-numbered ball and B3 has all the odd nunbered balls

There are, I guess,6 cases like this

[chilly sluice]

I guess they mean that a box with zero isnt odd or even

Thank u mane

Wait it says a box can be empty

[chilly sluice]

But the weird thing is that if any box s empty then the other 2 boxes satisfy the conditions

Since its 11 odd 10 even

[jaunty ginkgo]

no

oh wait

yeah lol

[jaunty ginkgo]

ehh not sure wym here

[plush mist]

вфьт

[kind pulsar]

you are also counting cases where 1 box is empty

so you need to subract them then re-add the number of cases where 1 box is empty

in each of case 1 and case 2 there are 6 cases where there is 1 empty box

so total 6×2 = 12 cases

9216 - 12 = 9204

and there are an overall total of 6 cases where there's 1 empty box

so 9204 + 6 = 9210

thus the reason you get more than you should it's cuz you counted the cases where there's 1 empty box twice since they are the same case in case 1 and case 2

[rare sable]

Take cases where you place all odd numbered balls only(11 balls) , even balls (10 balls) only, 1 box odd and 2 even and finally 2 even 1 odd

Use formula (n+r-1)^ C (r-1)

n is the number of Balls to be distributed

And r is 3 (to be distributed among)

And -1 is for empty boxes allowed

Hope this hint helps you

[jaunty ginkgo]

why y'all still doing that problem it's already be resolved

[prisma python]

this is seamo right

i'm joining that olympiad too

[hollow lance]

nice

i have been attempting olympiads for past 3 years

[old sorrel]

Hey so I am taking amc 10 and 12 and I was wondering if any of yall know a comprehensive study guide over the topics covered since I'm having some difficulty finding good pages on the web

[pallid tundra]

make one yourself

[sleek ivy]

how?

[thick gale]

23C2

[jaunty ginkgo]

,w binom(23,2)

[gilded halo]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by fionna_fx

[jaunty ginkgo]

Ehhh the answer for that is 9210 if that's what you meant

[jaunty ginkgo]

And

[rare sable]

Dude

[rare sable]

Let others help if they want

Their solutions may be easier than yours

[jaunty ginkgo]

I gave no solution

They ask why their sol is wrong

And I answer

[rare sable]

I js mean let others answer if they want too!

[jaunty ginkgo]

You are not supposed to give out the sol here

[rare sable]

i know

[jaunty ginkgo]

Ehhh, yeah that might make this channel feel more alive ig

[rare sable]

but things ain't always according to Book

[rare sable]

now you got it correct

[rocky kraken]

hi guys

[agile gazelle]

Calculate |Z|^2

Its extremely hard compared to olympiad questions but its not a reason to not try

[ivory ember]

$\begin{cases} n, & n \text{ odd} \ 2n, & n \equiv 0 \pmod{4} \ 0, & n \equiv 2 \pmod{4} \end{cases}$?

[gilded halo]

Civil Service Pigeon

[ivory ember]

$$|Z|^2=\sum^{n-1}{k=0} \sum^{n-1}{j=0} \omega^{k^2-j^2}=\sum^{n-1}{k=0} \sum^{n-1}{j=0} \omega^{(k-j)(k+j)}$$
Now let $m=k-j \pmod{n}$. So,
$$|Z|^2=\sum^{n-1}{m=0} \omega^{m^2} \sum^{n-1}{j=0} \omega^{2mj}$$
and the rest should be trivial if I'm not an idiot

[gilded halo]

Civil Service Pigeon

[ivory ember]

i rlly need to sleep

[agile gazelle]

Ggs

[jaunty ginkgo]

I have this pretty interesting problem that I haven't been able to fully solve

Using 12 iron bars to create the frame of a rectangular box with dimensions 20, 30, and 60. When placed outdoors, the edges of the box cast shadows on a flat surface. Assume that all the light rays are parallel. Determine the minimum and maximum values for the total length of the shadows of the edges

This's the whole problem, if you're curious. It doesn't state how the box is placed

[jaunty ginkgo]

You can ask Carbo

[uneven obsidian]

well, we discussed it ourselves already

he doesnt know

i mean he showed me the question so

[jaunty ginkgo]

damn, must be tuff

[uneven obsidian]

yesh

[sweet pewter]

||Let AE intersect BC at G. Easy to see that GF^2 = GD^2 = GB.GC. Let H lie on line BC so that G is the midpoint of HD. We get C, B, D, H as a harmonic set of points and F lies on (HD) -> F lies on an Apollonius circle||

[uneven obsidian]

hm

[ornate blade]

that's fucking smart

[rare sable]

Is answer zero

[dim gulch]

HALO

I AM NEW GNG

[sleek ivy]

hard compared to olympiads 😭

[ivory ember]

In the future, please show what you’ve done so far when asking for help - it gives us more context of where to help you (and saves our time from explaining things unnecessarily). \ \

I'd do this by counting the complement. There are three cases to consider:
\begin{itemize}
\item All $6$ digits are the same.
\item One digit appears $5$ times and a different digit appears once
\item All the digits are distinct
\end{itemize}

[gilded halo]

Civil Service Pigeon

[pseudo venture]

what i did was consider total cases as 6^6
then subtract cases where nothing gets repeated thats 6!=720(so i get cases where alteast one gets repeated)
then subtract 2 more cases
not repeating 5 times that is 6x6x5
not repeating 6 times that is 6
so i got 46656-720-186
that is 45750

[formal ice]

yeah but its hard to search for resources

when i search amc12 i literally cant find aops unless i specifically google forit

[keen lake]

this is MODSMO?

[chrome ivy]

anyone got some grade 11 question for competitions and could help out with them?

[jaunty ginkgo]

what competition

[chrome ivy]

math

[jaunty ginkgo]

I meant which math comp

[chrome ivy]

wdym which

like my city's

grade 11-12

well technically 9-12

[jaunty ginkgo]

Well then I don't have any of those I don't know what your city is

[chrome ivy]

yeah no i get it but im just looking for some coaching

since every time its different problems

Ive found some that could be there

do i send it here or message you?

[jaunty ginkgo]

It would be better for one who knows or even have participated in that comp coaching

[chrome ivy]

Ive been there for 4 years so far

I found some similar ones if you could help

[jaunty ginkgo]

no, I don't think I can. I'm senior highschool

[deep needle]

Usamts delay 💔

Was supposed to drop yesterday

[gleaming crater]

$What fraction is to the n^{th} power?$

[gilded halo]

Average_X^2

[radiant jasper]

yes

[late flint]

is anyone here doing the carnegie mellon winter math comp?

[sonic bridge]

IS ANYONE DOING JEE MAINS OR JEE ADVANCED OR CMI OR ISI

[jaunty ginkgo]

YES

Not me but JEE takers here are numerous

Well not that many but we do have

I also know some

[sonic bridge]

WELL IS THERE WHO CAN HELP ME OUT

[jaunty ginkgo]

with what

a problem?

[sonic bridge]

A PROBLEM

[jaunty ginkgo]

just send it here lol

[sonic bridge]

OK

[sonic bridge]

CAN YOU MENTION SOME

[jaunty ginkgo]

sorry mate I can't ping them for no reason

[sonic bridge]

OKAY

[midnight valley]

yuri...

[deep needle]

W yuri!

[heavy pagoda]

competition math channel is so weird lol

[uneven obsidian]

wdym

[modern tartan]

OLYMPIADS BE LIKE

[rare sable]

Why is it so?

[heavy pagoda]

cuz i cant see any discussion which is remotely related competiton maths (talking about IMO/putnam etc)

i see homework problems mostly but nvm

[rare sable]

It's fine, atleast the channels are active a bit

[jaunty ginkgo]

You can't expect people who are grinding for comp to be active

They're in their 24 hours study session

[vapid crest]

That if you would say 2×4 and 2+4 are the same

[heavy pagoda]

what tf do u even mean by that lol

also i have done fair bit of math olympiads those exams doesnt mean u have no life lol

[jaunty ginkgo]

I just meant that they spent so much time grinding

[heavy pagoda]

i literally participated in maths olympiads

u dont "grind" all day

also anyways this server has many working mathematicians who have fairly more work to do in that sense then but i think just quality of this channel is poor thats it

[jaunty ginkgo]

[jaunty ginkgo]

Yeah could be

[heavy pagoda]

there r advanced channels below

[jaunty ginkgo]

Ngl I had like 6 hours back when I was studying for comp...

6 hours hw

For a day

After that I say no more for competition

[hollow narwhal]

just send it here lol

[pallid tundra]

false.

this is not r/mathmemes keep your unfunny completely inaccurate generalizations of olympiads out of this channel

[high goblet]

i think it's also bcus everyone who's seriously studying for maths olys will be discussing in MODS

(linked in channel description)

so mostly the ppl here will be those new

[silk citrus]

any good resources for combinatorics for math olympiads for begginers like for coloring invars monovars and stuff with problems

[odd talon]

who else eagerly waiting for usamts round 2

[snow elm]

Any suggestions for preparing CSMC?

[snow elm]

Go to Aops

[abstract bolt]

how hard is amc10 and amc12 compared to like calculus 1

[novel karma]

Way harder

[abstract bolt]

what is tested in amc10 and amc12

is it like sat

[strange hemlock]

Guys

Can I get a good stradegy for AMC 10

[strange hemlock]

No not really

[fierce bluff]

does anyone have suggestions for mathcounts? its my last year and i need to lock in on chapter sprint rounds i average 21/30 in 40 mins but thats not good enough for my schools team. i practice with rounds from 2019 and everything but i always struggle around the same point

i think im supposed to ask that here

[strange hemlock]

Hey there, turts, I did mathcounts as well with a lot of good people, I think I can help you out! So what I think would be best to do is go to aops, and find the art of problem solving books for competition math, if you haven't already. Also doing mock tests is pretty helpful. I hope you have great time at mathcoutns and do really well!

For the books try AMC 8 and MATHCOUNTS Level

There may be harder level problems but getting those right just means your even more prepared

[fierce bluff]

got it, thank you very much!

[strange hemlock]

No problem

[gritty eagle]

Hi I’m in 6th grade can u help with this math counts question The second round of the Major League Baseball play-offs is “best out of 5,” meaning that two teams will
play each other until one team wins three games. How many different ways could this play-off match-up

This is an AOPS question for my homework

[stoic tinsel]

the best way to solve this is most likely just to casework on the # of games played

They either play 3, 4, or 5 games

[fierce bluff]

btw, if youre under 13 you cant be on discord

[gritty eagle]

Oh it’s for my robotics team

Thx for helping me also

[hollow narwhal]

That if you would say 2×4 and 2+4 are the same

[thick gale]

Nahh

Wrong

It's 8 and 6

[ornate blade]

I feel 13 is the minimum age one could expect you to understand that companies mine your personal information online for profit

it's already a nebulous concept for a lot of adults

[vapid crest]

✨Why ✨do ✨you✨ care?✨

[azure torrent]

Is anyone here preparing for IMC( international mathematics competition) undergraduate or you know someone ?

[jaunty ginkgo]

uhhhh this channel is in category "pre-university"

so probably not

[azure torrent]

I see

[fierce bluff]

i care for other peoples safety

just making sure hes aware dam

[vapid crest]

Safety? Oh yeah, if statements like that are just keeping people safe then I'm freaking jezus

[fierce bluff]

“just making sure hes aware”

whats your problem

[radiant shoal]

how does comp math even work

[near hill]

What do you mean? Are you asking how competitions happen practically?

[radiant shoal]

yeah

[near hill]

It varies from competition to competition, but a typical format will work more or less like a written exam, since competitions tend to be organized by or in collaboration with school systems. The problem sets are designed to be so challenging that even very good participants will not have time to answer everything perfectly; this makes it possible to speak about who did best.

[delicate mesa]

hi i have a competition this afternoon, its 5 am rn lol

do u guys have any study guides on the theorems?

especially binomial theorem and stewarts theorem because i genuinely dont know

oh also chinese remainder theorem i need to study theorems

[near hill]

If you haven't slept already, doing that will help you more than any amount of last-minute studying will.

[queen oriole]

A man and his dad put a bomb in the sink

[delicate mesa]

i already slept

and im cooked for my exam thats why i woke up early

[delicate mesa]

man + dad = bmb + cnc?

is that stewarts?

[queen oriole]

Yeah

[whole jay]

Does you Binomial Expansion part include Combinations and Binomial Probability?

I don't know the context of your competition, but studying Pascal's triangle and the general expansion form of the Binomial is a good way to do it

[hollow narwhal]

Wrong

[pallid tundra]

pascal's triangle is like day 1 example to introduce binomial coeffs

[agile gazelle]

It goes deeper than that tbh

You can visualize every theorem with pascal’s triangle

[radiant jasper]

[pallid tundra]

ok then tell me how is fermat's last visualized with pascal's triangle

[silk citrus]

this is 334 right?

[hollow minnow]

hey im preparing for a math competetion next month its called georhr mhor and how would i study for a competetion its largely focused on geometric knowledge and combinatorics and some trigonemetry but mostly angles but i could use some help

[waxen frigate]

i think you should make a tree diagram

[kind plinth]

im trying to do the amc 12

[pliant swallow]

ooh how is it

heard the competition is soon

[agile gazelle]

Its so asian

[winged quail]

Got a problem at some idk what paper

Let F be a field and let f(x) = F[x] be
an irreducible polynomial of degree n.
Consider the field extension
K = F[x]/(f(x)).
Let a Є K be the image of x under the
canonical projection. Prove that:

1. K≈ F(a), the field generated by a
   over F.
2. Every element of K can be uniquely
   expressed as a linear combination
   ao + a₁α + . . . + an-10-1, where
   ai Є F.
3. If f(x) is separable, then K is a
   separable extension of F.

[pallid tundra]

#groups-rings-fields

[soft vigil]

is it bad that i remember this exact problem

[soft vigil]

theres actually a really nice way to do this

you can let the LHS be a second degree polynomial

cause x_1, x_2, etc are just coefficients of some terms of it

then you can set whatever

and its like f(1)=1, f(2)=12, f(3)=123 and you can find f, then answer is f(4)

[reef condor]

Bubo. Orz!!!

[stuck tartan]

orz

[civic trellis]

@soft vigil

check dms

nvm u have to add me first

[soft vigil]

??

[hollow minnow]

anybody got advice on youre first math competetion

[subtle sundial]

prepare months in advance

dont learn new topics the day before

just review if possible

[novel karma]

Ikr why is everyone Asian like specifically Chinese

Don’t mean to be racist

[pale berry]

what do i do if i got 2 days

[gaunt egret]

just relax ngl i went to a kangaroo math comp a while back and i fumbled so bad bro because i was so stressed i couldnt think straight

[jagged violet]

Just do a shit ton of practice problems and learn theory on the way tbh

You could use resources like amctrivial, aops, etc for problem sets to do

[rancid stratus]

i wrote the question in the top left where it says log2(x^2) + 2logx(8) = 392 / [log2(x^3) + 20logx(32)] given x > 0, can someone verify if i got my a-substitution calculations right

[ivory ember]

,w log_2 (x^2) + 2 log_x 8 = 392/(log_2 (x^3) + 20 log_x (32))

[gilded halo]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

Civil Service Pigeon

[rancid stratus]

oh ok thanks really needed that

[subtle sundial]

pray lol

its the nerves that get you during your first competition

[steel parcel]

Hello, Dhruv!
We have situations:
WWW
LWWW
WLWW
WWLW
LLWWW
LWLWW
LWWLW
WLLWW
WLWLW
Then this could be for either team's perspective. Therefore, 18?

I am not sure, however.

Hello, everyone!
What are some book recommendations for AMC10? I aim to make USAJMO this year but have my 8th grade (next year), my 9th grade, and my 10th grade years.
I use all books on the AOPS Book Store, handouts, AMC books, formula books, and other resources found on https://mathematics.gg/books.

[worldly swift]

I'm writing this year's Putnam. Not exactly the IMC, but I would be open to practicing those kinds of problems too

[low wind]

Is there anyone here that went to community college and participated in AMATYC?

[tired cobalt]

Everything in here lowk making me tweak

Do they cover this stuff in a levels

I thought this was meant to be pre uni 😭😭

[karmic copper]

fr tho! i'm here doing good (for my year/grade), then see this and start thinking i just have a dumb class 😭

[tired cobalt]

I even tried learning some of the content myself

To get ahead

And come here just to be humbled

[rare sable]

What's the matter dude?

[tired cobalt]

The maths got me confused bro

But I thought it was meant to be pre uni

[karmic copper]

i think this is the higher end of high school

so just before uni

or collage

[random rain]

um so im in 10th rn, im in imo rn, what other stuff shoulld i enroll for??

like maths related

or anything else

i signed up for imo il be writing it in like a couple weeks

[random rain]

or anything if im being honest, not specifically math

my extracurriculars are kinda ded

[quick haven]

chat

anyone here participated or will participate in International Youth Math Challenge?

[half arrow]

I did it last year

[quick haven]

any advices or what resources did u use

[prisma python]

you could do more olympiads, like smaller ones

depends on where you live and what olympiads are available, but there should be at least a few

[steady elbow]

Should I study for the Putnam exam while in high school?

Does it help my academic journey in college?

I really need an advice on this, I find the material in the exam interesting. Also I'm doing well in my senior year and I want to try smth out. Is putnam worth trying?

[random rain]

ya valid

here qualifying for the national olympiad tea,'s a big deal

i cant find anywhere to continue coursework tho

like the required coursework for the prep

like combinatorics which is extremely out of portion to the stuff we learn in school

[half arrow]

I qualified for the final round, but I didn’t pay for it because I thought it wasn’t worth it. I heard that the final round is very fast paced, maybe practice doing early AMC8/10/12 questions within 1 minute?

[half arrow]

I don’t know the difficulty of the problems in the final round, so the suggestion is quite off

[quick haven]

umm why not worth it ? so the whole competition is not necessary?

like is it a waste of time

[half arrow]

In my opinion, yes. It’s not necessary because I don’t think it is that prestigious. You can do it just for fun and get a certificate, I don’t think 10 quid for a certificate is a bad trade at all. I didn’t do it because I knew I’d get stressed about doing well on the final round and divert my attention away from things that I actually wanted to do

[quick haven]

Ok thank you so much

[pallid tundra]

from my experience almost no one actually studies seriously for Putnam

the MIT kids who dominate every time are coasting off their very strong HS Olympiad preparation

and you’ll be busy with more important things during your undergrad anyway

[steel parcel]

IMO? What country

[steel parcel]

Hello, pls help.

[snow elm]

how to do it

[gilded halo]

Poly(^///^)

[steady elbow]

||you can brute force this, 7^2 aren't that many combinations||

[orchid raptor]

Guys how many hours do u study for math competition per day/week?

I know it depends on the type of competition and many other factors, but in general?

[robust dune]

Usually 1h/day
Sometimes 3h/day

From what I remember

[orchid raptor]

Which competition were u preparing for?

[robust dune]

I don’t remember

It’s been like 8 years since I attended it

[random rain]

India

[stuck tartan]

i assume the IMO he's referring to is not the international math olympiad cuz u can't really sign up for itt

[junior mason]

U qualified INMO

And got selected in team?or is it some private olympiad

It must be some private olympiad
Because to get selected in imo team u need to clear many stages and only 6 students from a country are selected

[random rain]

yes

no i mean the school titles it as imo

i mean ur really just writing lke prep for the exam

qualifiers essentially

[random rain]

yup

ik

i rly dk y its titled as such

but that the name given to the exam

and ill write it soon

for th imo team i undertsand u have to write rmo

and a bunch other stuff

im rly not good enoughf or that stuff

soo if any of u have written the rmo in india

i was wondering if u guys had any tips for prep

balancing it with other prep like JEE stuff and what not

[junior mason]

This year i gave ioqm
Wont appear for rmo because im preparing for inpho and jee

My score was 48

[random rain]

is that good ?

mb i rly dont know

[random rain]

any suggestions

ill prolly write it after i finish boards

[junior mason]

U should have written it this year

Paper is tough

[random rain]

ic

what abt the syallbus

im too lazy to search it

send pwease

i genuinely have no idea of any kind of math outside 10th syllabus, but i've always wanted to learn

seems rly fun

is it ?

[random rain]

ru ICSE or CBSE btw ?

[junior mason]

11th
Dummy school

Cbse

10th i did with icse

[random rain]

ic

im in icse rn

10th

maths marks aint that bad

[junior mason]

In icse only history and geography is dangerous

[random rain]

oh i got fried inhista nd geo

*in hist

mid term

i rly dont wanna talk abt my marks rn

🙁

[junior mason]

R u in any foundation program?like i was also styding 11th with 10th

[random rain]

wdym

no

ill start next yr in cbse

allenor base

[junior mason]

Next year give the olynpiad of the subject in which u have interest

Like maths ioqm
Or physics

[random rain]

ic

k ill keep that in mind

ill focus on boards this yr

[junior mason]

*Dont
If ur syllabus is completed try to start the syllabus of class 11th

[random rain]

ic

portion is complete

soo well see

[terse canyon]

yo

has anybody here done the UKMT maths challenge

[foggy python]

take a look at this beautiful question

this one too

[ornate blade]

is the answer to this one 0?

[foggy python]

no

[ornate blade]

interesting

[foggy python]

its a fraction

[ornate blade]

ah, I made a mistake when considering the polynomial ||(sqrt(x^2 - 1)^20 + 1)^2 - (7 sqrt(x^2 - 1)^3)^2 = 0||, so yeah, I see how it's ||187/53|| now

[foggy python]

absolutely correct

[ornate blade]

they actually teach this method of root transformations in A level further maths

as for the first question, I have zero idea

[foggy python]

correct approach

this was in IOQM

[ornate blade]

really?

I'm actually surprised you understood my method based only on that

[foggy python]

when i see a question thats interesting

i try to see all the approaches to solve it

so yeah

[foggy python]

this is a monster tho

oh wait

cyclic expressions maybe

[ornate blade]

spoiler link for the 1st question: ||https://math.stackexchange.com/questions/3825746/find-the-value-of-the-sum-600-sum-a-1-infty-sum-b-1-infty-sum-c||

[foggy python]

I solved it

[odd imp]

where did u get this from????

[foggy python]

IOQM

[dusty fable]

anyone else qualify for BMO1?

[outer raven]

anyone else is argentinian and qualify for OMA national olimpics?

[stuck tartan]

This one Js pfd the denominator

1/2(1/r+i + 1/r-i)

And then use a polynomial root transfer to create polynomial with roots r+i

And another poly with roots r-I

And then viettas

[outer raven]

that's an international olimpiad?

anyone speaks spanish?

[patent kernel]

No

ioqm is the qualifier

and no that problem is not from IOQM

It's from a random jee channel called "JEE SIMPLIFIED SUBJECT"

[outer raven]

like, IOQM is just a qualifier instance

[patent kernel]

ioqm is a qualifier for the regionals

[outer raven]

from where?

[patent kernel]

and if you qualify regionals you go to nationals

[patent kernel]

what do you mean whete

where

[outer raven]

which nationals?

[patent kernel]

let me finish

then you can ask questions

[outer raven]

like, from which country

[patent kernel]

oh India