competition-math

[pallid tundra]

it'd have to be a parallelogram for that to be true

oh that might lead somewhere ?

construct a parallelogram and see what happens?

[tight gazelle]

i was wondering if i could i could combine the tri afb and edc to be kite but im not sure where it leads haha

[vernal axle]

Hint: ||rotate CDE around C by 120 deg. counter clockwise (D->B, E->E'). Then triangles CFE' and CFE are equal, and the areas of AFB and E'BF are equal.||

[pallid tundra]

odamn that's hella nice

and here i was thinking i was gonna need to trig bash it 😭

[tight gazelle]

wait sorry i cant visualize

[pallid tundra]

i drew it out hold on

[tight gazelle]

am i understanding it correctly

oh wait cc

[pallid tundra]

FBE' and BAF congruent by SAS, therefore same area

CDE and CBE' congruent bc we're just rotating one to get the other

CE'F area 60 bc rotating by 120 deg forces another 60 deg angle to appear

[tight gazelle]

i got the first two statements

lemme process tha 3rd one

[tight gazelle]

thanks so much for your help everyone! will process everything first :)

[pallid tundra]

npnp

i miss when i had the time to do lots of contest problems 😔

[lime storm]

Hey, I want to know how I can get better intuition for solving Olympiad math problems. How do you usually approach these kinds of problems, and what books or resources would you recommend

[pallid tundra]

do lots of problems

that’s literally it.

[lime storm]

guessed so thanks

[lucid depot]

are there any good sources of problems and solutions?

[mental rose]

mathdash?

[mental rose]

do ultra dash

math competitions I think

[lucid depot]

not sponsored?

[lucid depot]

is it free?

[frank hornet]

Yeah.

[mental rose]

unluckily no..

it was actually a project for some MIT students i think

[dense tendon]

hi

[abstract wyvern]

Hello guys
This is a very beautiful arithmetic problem
I found two proofs of it
Text me if you have solved the problem

[pallid tundra]

don't spam the same message across multiple channels

<@&268886789983436800>

[stark swallow]

guys here pattern is clear that odd number repeats the odd times itself like 2k-1 repeats 2k-1 times, but help me converting some idea to mathematics

[pallid tundra]

do we know a formula for the sum of the first n odd integers

[sharp sandal]

ab=c²
let c²=p1²p2²p3²....
ab=p1²p2²p3²...
we see in the prime factorization of ab, each prime number repeats twice. This could have been that one occurrence of p1 is in a and the other is in b but that would contradict gcd(a,b)=1 so both occurrences of p1 are either in a or either b. Similarly for p2,p3... hence each of a,b have two occurrences of some combination of pi so they are perfect squares.
||maybe this isn't proper proof ||

[stark swallow]

yes it is n^2

or k^2

[pallid tundra]

yep

and how can we use that here

to find what the 2016th term should be

||what perfect squares is 2016 between||

[stark swallow]

why did you think of perfect square? i want to learn this thinking

because i couldn't think that

[pallid tundra]

the terms with index from 1 plus the kth perfect square to the (k+1)th perfect square inclusive are all 2k+1, the (k+1)th odd positive integer

2nd 3rd and 4th terms are all 2(1)+1=3 for example

5th to 9th are 2(2)+1=5

etc

so if we can find what perfect squares 2016 is between

then we have our answer

[stark swallow]

im thinking gimme 1 min

[pallid tundra]

in this case ||44^2=1936<2016<2025=45^2||

[stark swallow]

yes

[pallid tundra]

so the answer would be ||45th odd positive integer, 2(45)+1=91||

[stark swallow]

why did you take upper bound (45)

@pallid tundra i am not able to create these logics, does it mean there is lack of practice beacuse i just couldn't think that perfect square thing

[pallid tundra]

yea it takes practice

in this case my thought process was "each term appears an odd number of times, first 1 time, then 3 times, then 5, etc" -> "sum of first n odds is n^2" -> "use this to bound 2016 by its closest perfect squares to figure out what the 2016th term should be"

the more problems you've done the larger a knowledge base of past experience you have to draw on

[stark swallow]

you're correct

how summation of all the odd is related to a single Term(2016) ?

[pallid tundra]

$a_k=2n+1$ where $n$ is the unique integer satisfying $n^2<k\le (n+1)^2$

[gilded halo]

elrichardo1337

[stark swallow]

ok thanks

gonna practice now

[pallid tundra]

np

[stark swallow]

hey

in this problem, will the thought process be that perfect squares has even powers in its prime factorization?

10^4(2) + 10^3(a)10 + 10^2(9) + 10(b)10 + 1 = p^2(let)

but this is expansion of the number not prime factorization

[pallid tundra]

id start by bounding again

find the smallest perfect square >20000

then look at the units digits: what units digits would give you a units digit of 1 upon squaring?

use that kinda reasoning to narrow your search

also for finding b you may find the following fact helpful: perfect squares are 0 or 1 mod 4; specifically odd squares are 1 mod 4

[stark swallow]

150^2

[stark swallow]

it has 0 as unit digit

[pallid tundra]

?

0^2 != 1 mod 10

id check ||151^2, 159^2, 161^2, 169^2, etc||

[pallid tundra]

you want smth with units digit 1 or 9 before squaring

[stark swallow]

151^2, 159^2, 161^2 , 169^2 , 171^2 , 179^2

for unit digit to be 9: 153^2, 163^2, 173^2

[pallid tundra]

we don’t want a units digit of 9 after squaring lmao

i was saying we look at units digits of 1 or 9 before squaring

since both of those would give you a units digit of 1 after squaring

[azure veldt]

Please don't spam messages across multiple channels. One is really truly enough. Please keep this in mind for the future

[abstract wyvern]

@pallid tundra @sharp sandal
Text me i'll send you the proofs
I can't do it here

[compact roost]

this image looks suspiciously like the output of chatgpt

chatgpt math getting spammed in the channels is kinda hilarious

[rancid horizon]

Could anyone help me out here?

[radiant jasper]

any further math student. A'level

[rancid horizon]

I think I pretty much solved it but I want to see how other people do it and maybe use that

[radiant jasper]

can you solve this question

anyone

[pallid tundra]

!noans

[scarlet root]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[pallid tundra]

also this question might be better suited for the physics server, see #old-network for an invite link

[rancid horizon]

You talking to me or? 🥲

[pallid tundra]

nah lmao

[exotic badger]

this is very interesting

[exotic badger]

I am confused about this problem because if f(x) = x then f(f(x)) should be equal to f(x) consideringn that f: S -> S

maybe im just dumb lowkey

[rancid horizon]

Yeah same that’s why I am confused

[exotic badger]

yeah the second one checks out

[rancid horizon]

But I decided to take a different approach and say that f(f(x)) does not equal to f(x)

And go from there

[exotic badger]

by contradiction?

[rancid horizon]

Yeah

Maybe that will work

[exotic badger]

yeah makes sense okay hmmm i feel like im missing something here

[rancid horizon]

So there is kind of a sequence thing:

[gilded halo]

Σmilia

[exotic badger]

?

[rancid horizon]

Where no term is equal to the term preceding it

[exotic badger]

yeah

[rancid horizon]

Idk maybe I can somehow use that

OH wait

[exotic badger]

?

[rancid horizon]

Because S is finite, there should eventually be a repeating value, right?

[exotic badger]

hmmm i dont think thats what the question is asking

i was thinking that

[rancid horizon]

Well yeah, but maybe that can be used

[exotic badger]

how would you go by using it may i ask?

[rancid horizon]

Well it shows that the function must eventually repeat values (because S is finite). And we can use it to derive a contradiction based on the behavior of f, maybe with how the function increases or averages values. And then we can conclude that the assumption “f(x) is not equal to x” must be false

Wait I think I kind of got it 🥲

[exotic badger]

yes this may work

it just seems to me that there might be a better way but my brain is incapable of thinking right now

[rancid horizon]

Yeah probably

[sour perch]

yo

[tight gazelle]

how do i approach answering this

[rich cloak]

Hello

Can someone give me a quick ru down of catalan numbers

[exotic badger]

why do you want to learn about catalan numbers

[rich cloak]

Ugh I was doing few questions and in ones soln it said we should find C4

[exotic badger]

bruhh

[rich cloak]

Why

[slow veldt]

do both properties hold true simultaneously?

[tight gazelle]

why do i have a ping

[hollow cobalt]

i wrote the wrong answer to you

[tight gazelle]

other qn

[hollow cobalt]

so observing from middle the height of this shape is
(21 +21 + 15)
and the width is (21 + 21+ 15) = 57
Now add four A5 sheets to the corner to complete the square
Find the area of sqaure and then subtract the area of the 4 A5 sheets

[tight gazelle]

cant i do it like this

[hollow cobalt]

you can , but i thought lets do it without find its width 6 cm

[latent mango]

628x-y=x^2

Find y

[wide tendon]

Are there any restrictions?

like x,y intengers or unique solution

[latent mango]

nope just pure algebra 1 + 2

[wide tendon]

but how you're gonna find y so

is it in function of x?

[outer mural]

there are infinitely many solutions

it's a parabola

[latent mango]

yep

[wide tendon]

so what's the point lol

[quick edge]

in this question why can't we do it directly by taking 4c25c26c2 after this 1 more q left to pic from 9 q so multiply by 9c1 at the end

why is it imp to take cases

[outer mural]

wouldn't that double count? for example you can pick
1,2 from A
1,2 from B
1,2 from C
then 3 from A at the end.

but you can get the same result by picking:
1,3 from A
1,2 from B
1,2 from C
then 2 from A at the end

[quick edge]

woah that makes sense thanks

[severe eagle]

just wanted to share this trivial fe

[wide tendon]

really nice

functional equastions are my hope to get at an olympiad i'm gonna do

almost no content and pratically impossible to get 0

[severe eagle]

indeed

[rich cloak]

im im not wrong this is a otis question right?

[severe eagle]

I don't know about that

I found it

[tight gazelle]

idk how to approach this help pls

[ornate blade]

your idea works though; similar triangles

[exotic badger]

how do you do this?

[radiant jasper]

do a bunch of subs

[copper crypt]

If anyone can help me with this question!!! Pleaseeee

[ivory ember]

Consider the product of the roots

[copper crypt]

Ohk I'll try

[ornate blade]

also this isn't competition maths

[severe eagle]

sub

what have you tried

[prisma python]

is the answer ||only f(x)=x? thats the only thing i can think of||

[severe eagle]

No.

There's another one

[prisma python]

||f(x)=-x?||

[severe eagle]

Ok nvm i dont have paper rn and i aint gonna type ts out

||https://artofproblemsolving.com/community/c6t298f6h3643206_fe_on_real||

This is the original thread @prisma python @rich cloak @wide tendon

@exotic badger

[radiant jasper]

"original thread" > first post in the thread: "old problem"

i got the same sol as pco

even tho I had ||cauchy||

because im dumb i forgot about ||2002 usamo p4 trick||

[severe eagle]

mb

[torn gate]

You have two roots, so the polynomial can be represented as a(x - 2)(x - 1/2)

ax^2 = px^2, so a=p

And so on

[torn gate]

pco is the definition of functional equations

Bro solved these problems since 2007

I was born in 2009

[radiant jasper]

admits young

[vestal pond]

amc10 tips plsss

[golden oak]

I’ll assume your pretty good at AMC8 so based on that level and the time now before the AMC10 tests.
Go through pass papers from the previous years
Time yourself for mock exams yet pace yourself carefully
Refresh the key concept on the AMC10 using AoPS books, or other. Like algebra, number theory, geometry, combinatorics.
Practice your most high-impacted area, or areas your struggling with
Focus on the harder questions, especially the ones at the very end of the AMC10 test.

[exotic badger]

ooh i love art of problem solving

[civic trellis]

https://tenor.com/view/mad-face-baby-gif-23920184

[neon moss]

im self learning all the books, but should i take the AOPS AMC 10 problem series, just for a better understanding and more efficiency?

[golden oak]

If your taking the AMC10, then yes, it’ll definitely boost your confidence and capabilities overall, however, it is really close to the test dates for it atp, so starting now would be a bit late, but if you e already mastered the basics, then briefly scanning over important concepts in the book would be helpful!

[severe eagle]

112.5 for amc 12 papers twice in a row wtf

i am actually deproving

eh i do have like 5 more years to get usamo lmao

do yall have advice to do short answer combi questions quickly without bashing too many cases and wasting time

[long bobcat]

here's what i got

[vernal axle]

Right, 3 is less than 8/3. Just a little chatgpt moment 🙂

[vernal axle]

that's not true even for n=2.

[long bobcat]

i didn't double check it
crap

now the entire thing falls apart

now that you mention it, it's supposed to be the other way around, (2n-1)(2n-3)...(3)(1) should be > n(2^n/(n+1))

i feel stupider now

[sleek helm]

Did you try applying logarithm and moving everything to the right to check if it’s positive ?

[old yarrow]

what the f is this😔

[stark swallow]

Guys how ioqm went?

score

[outer mural]

This screenshot is cropped so don't even bother

It looks like there's a factorial cut off. Who knows what else was cut off

[radiant jasper]

17/100
im in Assam and in class 8 so I might make th cutoff

[stark swallow]

Very good for 8th grader

I scored btw 16-21 from Rajasthan

and second time, and not going to clear cut off 🤮

[radiant jasper]

is the paper out somwhere

ive seen some skull ioqm mocks and i wanna see if its actually skull

[wild solar]

i got 43/100 8th grader from telangana will i pass or not

[rancid horizon]

Any tips? I am planning on attending the BAMO (Bay Area Mathematical Olympiad), and then go onto harder olympiads, like the USAMO or even the IMO

Currently, I am just doing a ton of past papers from the BAMO to prep. Does that work? Or do I maybe need to time myself or do practice elsewhere as well?

I need textbook/workbook recommendations for proof-based questions. BAMO problems are graded on the clarity and correctness of the full mathematical argument, and almost all the five questions that will be presented to me there are proof-based

[novel patio]

43 as an 8th grader is genuinely crazy. its likely youll qualify, if not youll deffo do next year and for other attempts. do you have any prior experience in maths?

[rancid horizon]

That’s very impressive to get that score 👏

[blazing ore]

even I got 43/100 (but 9th grader) in the IOQM, but from karnataka

[blazing ore]

btw which version of the paper did you get?

like I think there were 4 versions or somethign

[pallid tundra]

just for kicks i asked chatgpt a problem i wrote for a math contest

its procedure was fine but then it screwed up the final computation

so uh yea it's just as unreliable as ever

[civic trellis]

L

[pallid tundra]

true

[civic trellis]

hey elrichardo

i got a question

i scored 237 on the NWEA mapp testing is that good

also we just got in 9th grade

[pallid tundra]

idk what that is

[civic trellis]

do u live in the US

[pallid tundra]

yes

and even then ive never heard of that

[civic trellis]

oh it basically measures ur ability on different subjects

like math for example

and if u score good u can get placed in honors

[pallid tundra]

hmm

[civic trellis]

did u graduate

highschool

[pallid tundra]

im in my last year of undergrad 😭

where i went to HS they didnt use this

[ornate blade]

standardised testing more often measures if your parents were wealthy enough to read to you as a kid, and enrol you in various extracurriculars

so like, that score would mean something very different for someone who 'beat the odds' of poverty, versus if you were born with a silver spoon in your mouth

[warped folio]

Sof(IMO) tips anyone?

[radiant jasper]

Different versions but all the versions had the same questions

Jst the numbering was switched

[blazing ore]

ohh

[pure hull]

wot

[spice lynx]

nah i deleted it

[pure hull]

o

[orchid raptor]

Hi guys, I heard abt AMC10 for like one month ago, so I have only two months and a half to prepare, do you guys think i can qualify?

[gilded halo]

Civil Service Pigeon

[pallid tundra]

depends on your baseline level

[novel patio]

its the same paper just mixed up question order like how it is in nse's

[silk silo]

Is there anyone here who has previous experience in math olympiads? I'm looking forward to participate this year and would like to receive advice from someone with some experience

[silk silo]

If so, please DM me

[pure yarrow]

I am just in your case yet I study maths in french because I am from Tunisia

Anyone who has advice please help

[civic trellis]

i got a question

why do people say maths

and not math

[pure yarrow]

Idk really

[novel karma]

Maths sounds smarter

[rancid horizon]

Because it’s mathematicS

[weak swan]

is the only way of getting good in calculus is genuinely doing calculus every where?

[weak swan]

yo same name habibi W

[outer mural]

"maths" is british english

[pallid tundra]

same way you do well in any other math class, practice

also wrong channel

#calculus

[exotic badger]

Is anyone doing the AIMO soon?

[tight gazelle]

thanks for this! the ans is correct although idr understand how the relationships work. what postulates/thm supports from line 2 onwards? thanks!

[tight gazelle]

this one too D:

i can see some vertical angles and angles on transversal but i dont get how u got the ratio

[ornate blade]

Do you get that the angles alpha and beta are equal?

[prisma python]

do you mean the asia international math olympiad?

[wild solar]

no lol i just wrote it i did like a week of prep

[wild solar]

version D

[blazing ore]

nice

were you able to solve that product question

like where you had to split the 2n terms into pairs

to get a perfect square

[wild solar]

what

nah i got 9 lol

i got the poly question the complex one

and teh sum of radii

and that 49

and teh red marble blue marble shit

[wild solar]

i did some dumb stuff and i got 9 lol

[blazing ore]

lol

I somehow managed to get that correct

[wild solar]

dang

[blazing ore]

what were the 5 markers you got?

[radiant jasper]

💀

[wild solar]

teh polynomial one liek R(3) question and sum of radii of 2circles. and teh consectutive square, liek m^2=49 and red marble blue marble asnwer 66

[radiant jasper]

omg math

[wild solar]

i got the strictly increasing strictly decreasing question too but i put 11 instead of 10 bubbling mistake

[radiant jasper]

I'm sad someone give me a nice problem 😭

[wild solar]

do all IOQM 2025 5 markers lol

[radiant jasper]

Send

[wild solar]

its online

[radiant jasper]

send link

too lazy

[wild solar]

sure one sec

ill send screen shot

still 8 more one sec

yeah done

[blazing ore]

were you able to do this one?

oh also were you able to the function one

where it was f(mn+1) = something something

[wild solar]

oh that

i did silly mistake

i took 0=1

[wild solar]

yes easily

[blazing ore]

howw

I guessed 7 and completely failed

[wild solar]

i just split 2x^2 and got roots easy remainder theorem

[blazing ore]

no I meant q20

the n^n mod 7 one

[wild solar]

brooooooooo i put 7

everyone in my class put 7 too

[blazing ore]

same

it was ||42|| right?

[wild solar]

yeah

[unique solar]

On a 9x9 chessboard, several rooks are placed in such a way that each rook is attacked by at most one other rook.

What is the maximum number of rooks that can be placed on the board?

In how many rows must there be exactly one rook? Does anyone know how to solve this?

[radiant jasper]

21
||Q(x)=(x²+1)(x²+x+1) | x¹²-1, so P(x)==x⁹ mod Q(x).
(x⁴-1)(x³-1)=x⁷-x³-x⁴+1==0, so x⁹==x⁶+x⁵-x²
x⁶+x⁵==-2x⁴-x³-x² so P(x)==-2x⁴-x³-2x²==2(x³+2x²+x+1)-x³-2x²=x³+2x²+2x+2 mod Q||

22
||CM bisects <DCB so BC=MC/√2=CD/√2||

[novel patio]

thats kinda crazy lol for an 8th grader

[radiant jasper]

I feel so inferior 😭😭😭

I scored 17 as an 8th grader

Praying for a low cutoff in my region rn

[wild solar]

i htought that was normal

[wild solar]

wht about remainder theorem

liek get root sform g(x)=0 as plus or minus i omega omega squre

[radiant jasper]

Bro that’s not normal😭😭😭

One of the smartest eight graders that I know couldn’t score 14😭😭

Well

Ig I’ll have to study harder

23
||n=1 fails. If n is even just pair i with 2n+1-i. If n is odd then prove that you can do it for n≥3. If n=3 pair 6 with 3 and the rest with a similar logic to the even case. If n>3 do the construction for n=6 then pair the remaining 2n-6==0 mod 4 as in the even case||

[radiant jasper]

wdym

[wild solar]

like, by remainder theorem equate divisor to 0 get roots and use dividen= divisorxquotient+remainder

[novel patio]

yeah no it isnt

[wild solar]

? wdym

[novel patio]

43 in 8th grade is an exceptional score

[radiant jasper]

i dont get what you want to do

[novel patio]

the x^2025 question?

[wild solar]

yeah

[wild solar]

bruh

[novel patio]

yeah its remainder theorem right?

[wild solar]

yeahj

[novel patio]

u can take omega and iota

[wild solar]

bulkolv didnt undestand

@radiant jasper uk want remainder theorem is right

[wild solar]

yeah

use omega cube 1

ez pz

[radiant jasper]

I know what it is but idk what it is

[wild solar]

lol

np

bte answers are in 2 digit ranging from 0 to 99 includded'

[radiant jasper]

yeah but who cares about the actual answer

[wild solar]

lol

[novel patio]

a polynomial p(x) if divided by another q(x) results in:

p(x) = q(x)x some other polynomial + r(x) where r(x) is remainder. if we substitute a root of q(x) well get p(root) = r(root) + 0

q(x) has roots i, i^2, omega, omega^2

when we substitute and compare real and imaginary parts after assuming r(x) general form we'll get the r(x) polynomial

[radiant jasper]

oh you were talking about that

[novel patio]

yes

[radiant jasper]

how do you find r(x) with those values

i mean i know you can do it but is there a very fast way

[novel patio]

this is the fastest way iirc

you only need to substitute iota and omega

the other two dont really matter

[radiant jasper]

wait you mean you solve the system

[novel patio]

theyll give you the same equations

[novel patio]

yes you can assume coefficients

and youll get r(x)

[radiant jasper]

letting r(x)=ax³+bx²+cx+d?

that's boring

my method is just as fast

[novel patio]

honestly yeah it is

[radiant jasper]

24
||This is not the sol I'm too lazy to do it 🤡 but it looks trivial||

25
||n² \in Q, (n+1)² \in Q -> n \in Q. Let n=p/q with (p,q)=1
(a+1)p²/q² +1 = a(p+q)²/q² -1
(a+1)p² +2q² = a(p+q)²
mod q: (a+1)p²=ap² so p²==0 which means q=1. So n=p \in Z
(a+1)n² +2 = a(n+1)²
n²-2an+2-a=0
If n=1 then we get 1-2a+2-a=0 so a=1 and m²=3. Now suppose n>1
n|a-2 so a-2≥n or a=2. We do a=2 later -> a≥n+2
So n²-2an+2-a ≤ n²-2n(n+2)-n<0 contradiction.
a=2 -> n²-4n=0. n=0 means m²=1. n=4 means the three values should be 3(4²)=48, 49, 2(4+1)²=50 ✓. So the highest is 49?||

[exotic badger]

no the Australian Intermediate Math Olympiad

[wild solar]

yeah correct

[summer roost]

if i remember correctly

you took part in this year's imo right

[radiant jasper]

yeah

[prisma python]

i'm not being sarcastic lol it's a real olympiad

[prisma python]

oh nvm then

[radiant jasper]

"Asia" and "International"

Maybe you were thinking of apmo

[prisma python]

https://globalolympiadsacademy.com/aimo-3-3/
yeah idk lol

[radiant jasper]

huh

clown name tbh

probably clown comp if I've never heard of it

or skibidi

[prisma python]

i had a friend who joined it for the past 2 years

but the questions aren't that hard

[subtle sundial]

are you the ceo of mathematics

[plucky panther]

A box contains 5 red balls and 7 black balls. A ball is drawn at random, its colour is noted, and then it is replaced along with two more balls of the same colour. This process is repeated three times in total (i.e., 3 draws with replacement + reinforcement).

Find the probability that:

1. All three balls drawn are red.

2. Exactly two balls are black.

3. The sequence of colours is red, black, red (in that order).

anyone?

[radiant jasper]

yeah

[radiant jasper]

oh

[bleak jasper]

oh i remember seeing this

sorry for ping

ye but i didnt see the solution

required sum combination of probabilities

[plucky panther]

Oh yes?

[plucky panther]

Solution?

[bleak jasper]

...

idk combinations of probs

and sorry for wasting ur time and some memory

[sharp sandal]

1. 5/52?

[outer mural]

i got || 5/11 ||

oh

now i got || 15/128 ||

|| 5/12 * 7/14 * 9/16 = 15/128 ||

[ivory ember]

can confirm ^

[barren frigate]

Hello can I get help with this one olympaid problem? Thank you!

[ivory ember]

Hint: Note that $$(n+1)!=(n+1) \cdot n!.$$

[gilded halo]

Civil Service Pigeon

[barren frigate]

yes but can I pls get some elaboration, like how I have to use the numbers around that sigma sign. And in a way I don't need a calculator too

[outer mural]

first you can cancel the fraction in a way that gets rid of the factorials

for the numbers around the sigma sign, you can do this

$\sum_{n=11}^{25}=\sum_{n=1}^{25}-\sum_{n=1}^{10}$

[gilded halo]

Axe

[sleek ivy]

It’s gonna be the sum of n(n+1) from 1 to 25 minus the sum from 1 to 10

[outer mural]

it's kind of funny, brute forcing it is only like twice as hard as applying the formulas

[radiant jasper]

it depends

[barren frigate]

I got it now - thank you all for your suggestions!!

[plain spruce]

australian intermediate 😢

i thought austrian international math olympiad

[sharp sandal]

I read it wrong : the ball drawn is replaced with 2 balls of same colour, so there were 12 balls initially you take one and replace it with 2 other balls so new total will be 13, but it meant to keep the one you picked and add 2 more balls to make total 14

[subtle sundial]

infeed

indeed

[umbral stone]

the sum is just the sum of (n+1)n from n=11 to 25 which is then the sum of (n^2 + n) fro n=11 to 25

use sum[n=1,m] n(n+1) = (m(m+1)(m+2))/3

go from there

not hard at all

[wide tendon]

3 Races of aliens G, P and R are going to hold a meeting. Each race is gonna send 5 representants and they're all going to seat on a round table wich 15 chais numbered from 1 to 15 in clockwise order. They've already decided that an Alien G is gonna seat on the chair 1 and an Alien P is gonna seat on the chair 15.

No Alien P can seat immediately to the left of an Alien G; No Alien G can seat immediately to the left of an Alien R; and no Alien R can seat immediately to the left of an Alien P

In how many ways can we organize the 15 aliens in the 15 chairs?

[plain coyote]

why is it that usually competition math are word problems

[pallid tundra]

??????????????????

where did you get that idea from

that is not even remotely close to being true

[cosmic yew]

Since the given G sits to the left of P, R can sit to the right of P(?)
After that you can make those 3 a sequence for all 15 seats and every combination(meaning every G alternating seats between one another, same with P and R) would give you the solution. And I'm pretty sure the one I said is not the only possible sequence

Depends on the view of left and right

If left means counterclock-wise then it probably would be different(?)

I was looking at it from their perspective and "their right"

[ornate blade]

what did you expect maths problems to be? a bunch of symbols?

maths is about communication so it uses words to ask questions

[wide tendon]

the usual one

just imagine that you are the one seated

but if I understand your answer, it's incomplete

I did that first too

You're not considereing cases where you have two aliens of the same race seated one right after the other

[cosmic yew]

Uh yeah it's incomplete, I'm currently at work so I haven't worked out all possibilities or the math at all

[cosmic yew]

True

[wide tendon]

fine

these are the alternatives

[stable fulcrum]

does anyone have any advice for getting a high mark in this test?
UKMT Senior Maths Challenge
i am planning on doing past papers but if anyone who has taken it has any advice on how they prepared for it id appreciate it

[rough prism]

I’ll also be doing this

Most past papers

I’ve got that on the 9th then TMUA on the 13th

[stable grotto]

hypothetically if I were able to get into JMO could I also get into AMO

[plain coyote]

I expected it to be much more straightforward like "prove that √3 is irrational" instead of asking "if Diddy has 67 mangos blah blah blah blah"

[snow thistle]

no

if u can get 12 on aime you can probably make amo

as long as you arent bad at amc

or just take usamts and if you get 12 on aime itll def make if you qual thru usamts

[stable grotto]

yeah if i get jmo with like 120/12 i should be able to make amo right

[snow thistle]

120 is kinda low

i mean if youre in 10th grade or below rn and you jmo with 12 on aime then youll probably make it by 11th

[stable grotto]

120

oh 130 mb

130 amc/ 12 aime should def be enough right

[snow thistle]

for jmo yeah

[stable grotto]

if i kept it up i could make usamo next year right

or even this year should be okay, right? since aime basically covers all amc12 topics

[snow thistle]

hmm

i mean if youre confident you can get 12 on aime then you can just take amc 12

but amc 10 and amc 12 are very ver ydifferent

if you havent made jmo before i would just go for jmo this year and then amo next year

if you get 12 on aime this year i wouldnt worry too much about amc 12

amc is not the biggest roadblock to usamo

so if you make jmo this year i would just start doing oly

[gilded halo]

TheSup_3912

Guys try solving 
\[
\int_{0}^{2} t^{x}\, dt = 3 \quad \text{. Find } x
\]

[pallid tundra]

no

#calculus

[copper dawn]

for that question u need to use ln

i think

[gilded halo]

TheSup_3912
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[earnest hawk]

hello everyone i want the fastest way to master number theory to enter IMB and i have read most of introduction to number theory published by AOPS so please help

[hushed topaz]

does this have a real solution?

[pure yarrow]

Hey guys, anyone who has an EMC copy, I'll be competing this year hopefully from tunisia

There is a kind of program and I will compete but I have no idea about past papers ( I couldn't find any online)

[radiant jasper]

aops

[pure yarrow]

Thanks

[tall heath]

Does anyone know how to get good at UKMT questions. I'm taking the Senior soon but I never know where to start when it comes to these types of questions

[arctic merlin]

hi im here to practice math

[green jetty]

Try solving
$$
a^{x}+bx+c=0
$$

[gilded halo]

TheSup_3912

[snow thistle]

what

[green jetty]

Its a Transcendental equation

When you want the answer, ping me

[snow thistle]

juist use lambert w

everyone knows this

what does it have to do with comp math 😭

[green jetty]

I thought it will be be a cool problem for problem solvers like the people of competition math

[snow thistle]

hmm

i mean something like this wont really show up in comp math

its not a diophantine

[green jetty]

Hmm ok

[fresh pine]

https://youtu.be/beHkSchC_9s?si=wEeGQPpQNPJfGGnY

[sterile helm]

Hi guys!

Do you need to sign up for AMC 10 through school?

[snow thistle]

not necessarily, if your school doesn't offer it you can sign up individually and you'll end up taking it a local testing site which will most likely just be a university in your area

[sterile helm]

oh ok thank you

do i sign up for a testing institute through MAA?

[snow thistle]

uhh actually im not sure about it because i always just take it through my school but im sure the individual sign up portal is on maa

[sterile helm]

ok thank u

[acoustic jetty]

@ionic flint you should be able to view this channel without any roles. There's no channels pre-uni can view that ug can't.

In general please refer any moderation issues to @quick aurora instead of DM'ing individual moderators

[ornate blade]

LANCE MODERATOR??

holy shit, congrats lancey

[hardy basin]

Guyz,
How can I prepare for maths olympiad? What are the grade I will have to study, what topics?

[pallid tundra]

you’re gonna have to be a lot more specific

1. decide which one you even want to do in the first place - is it a local, regional, national contest?
2. do lots of problems similar to what you’d see on the contest
3. the standard school curriculum is woefully insufficient to succeed on these contests

[fiery wolf]

Buddy of mine once tried solving
$$
x^{x}=x+1
$$

[gilded halo]

Mr_Mayonaise

[fiery wolf]

Not even lambert w can help here. Pretty sure you have to just use approximation methods or graphing

[bleak jasper]

even lambert is approximation isnt it?

/graphing

[fiery wolf]

I guess yeah

What I mean is you can’t plug in a single function like lambert w

You have to repeated iterate by newtons method or just use a graphing calculator to find the intersection

[bleak jasper]

ite

[mighty pine]

golden rule: plug in 0.5 and hope it works

[sleek ivy]

does any1 know any good youtube channels that cover competition style questions?

[snow thistle]

https://www.youtube.com/watch?v=f-ib2yw7rlY

joking

kinda

evan;s other videos are good but its oly

[astral warren]

i’m in hs trying to qual for usajmo i already qual for aime and am decent but is reading books like aops vol 2 worth it or is it better to just work through problems

[snow thistle]

if you already know everything in aops vol 2 don’t read it but generally it’s better to just do problems

maybe do mathwoot level 1

if u wanna qual jmo don’t forget to take usamts rn

for more chances

[honest loom]

Prime newtons

[candid fern]

Little fermat

[wide tendon]

Victor Teaches Math

[wide tendon]

10 years old boy solving competition problems

[radiant jasper]

🐐 🐐

[mighty pine]

let's think critically

[cerulean burrow]

https://youtu.be/pghP26lN5t0

[radiant jasper]

omg yes

Another goat

[lavish lily]

a chinese one, i assume

[radiant jasper]

?

[lavish lily]

now it is upto you what to comprehend

[radiant jasper]

that your brain malfunctioned

[lavish lily]

whatever you feel

i dont like geo uk

[radiant jasper]

it happened again

[lavish lily]

wtf man?

your goal is to insult me or what?

[radiant jasper]

yeah i finallly realised what my purpose in life is

you appeared in my dreams

[lavish lily]

yea

realise it

and leave this server

[radiant jasper]

im just trolling idk what you were saying tho

i dont get it

[lavish lily]

i never intended to say it you

it was the fact that chinese prolly know geo well

and appreciated that fact in my posts before

[radiant jasper]

huh

[orchid raptor]

Can I pass the AMC 10 with just two months of preparation🤡?

[sleek ivy]

you could qualify with 0 prep if youre good enough

[orchid raptor]

What does 'good enough' mean? How strong should my math be to qualify? 🐸

[sleek ivy]

take a practice test

see whatyou get

if you get over the qualification boundary for that year

youre good enough

[orchid raptor]

I did and I wasn't good🗿

[sleek ivy]

how much

[orchid raptor]

I solved the first 8 in about an hour

[sleek ivy]

youre going to have to about double that, but its a good starting point

[prisma python]

is it just me or is the audio on this video really bad

i couldnt hear what he said was the point L to XBYC

like at 26:36

[radiant jasper]

Miquel point

[radiant jasper]

yeah it's kinda bad

[prisma python]

thanks

[radiant jasper]

but I think his other videos are fine

[pallid tundra]

you don’t “qualify for the amc 10”, there is no prerequisite contest for it

[subtle sundial]

haha

[sleek ivy]

I think he meant qualify aime through amc10

[silk citrus]

so guys pls explain muirhead to me

anyone given ioqm this year

[candid fern]

I made a video about it

https://youtu.be/HcmkdwEs4zs?si=FPdGkwgcXsTHXBdg

[cloud panther]

[fresh pine]

https://www.youtube.com/watch?v=i1lv6Be_YHo

[pallid tundra]

#calculus

[mighty pine]

i ntegrate by parts

you can still do this given a limit implies you can do operations for a number that is in the neighborhood of an infinitely large number

[fresh pine]

or we can also show upper bound to be 1 and then show that the limit is not less than 1.

🙂

[mighty pine]

oh that's pretty neat ngl

[fresh pine]

i saw a collection of problems few months back (i forgot the source) where they've used the idea that you thought of in this comment

it was not integration by parts per se; rather they wrote the integral as sum of two integrals

[mighty pine]

yeah it's kind of the same idea as just doing this for those

factoring problems

you consider "approach"

[mighty pine]

no clue how this would work

[fresh pine]

ohh it was something like: break into two parts such that one of the parts is very small (using continuity etc.)

can't think off the top of my head the full argument right now.

😢

[mighty pine]

it's fine

👍🏼

[silk citrus]

little fermat bro have you qualified for IMO

[daring heart]

please help I dont understand, calculus ab

[subtle frost]

what is the amc?

[pallid tundra]

https://letmegooglethat.com/?q=amc+competition

“American mathematics competition”, contest for US middle and high school students

unless you were thinking of a different AMC

[soft vigil]

Ts was not needed

[pallid tundra]

is it really too much to ask to do some basic online research first before asking easily googleable questions like this

this just comes off as “I’m too lazy to look up basic information and now I’m making it everyone else’s problem”

[gilded halo]

TheSup_3912

[green jetty]

First time using DCT

[fresh pine]

This can also be solved using the mean value theorem.

🙂

[green jetty]

Yes, that's what the person in the video did....

[fresh pine]

https://youtube.com/shorts/Bv5NBh02FcU?si=SH02HLZs-TrXkgmm

[drifting cloud]

both zero ig

[bleak jasper]

m so cooked

[ancient gust]

hello

[steady coral]

hy

[pallid tundra]

high

[spice rapids]

1+1=2

2+2=4

4+4=8

8+8=??

10+9=??

[faint thorn]

is that a proof question?

[still skiff]

Ur gonna have to use wolfram alpha for that

[spice rapids]

Why

Because of i'm hard

[last raven]

@daring heart hi, could you tell what this website is

[drifting cloud]

21

[balmy lintel]

"There are m horizontal lines and n vertical lines drawn in the plane. Each point of
intersection between a pair of lines is coloured in one of 100 colours.
Find values of m and n such that, no matter how the colouring is performed, there
always exists a rectangle whose vertices are the same colour."

I was curious what are the most optimal bounds known? I asked chatgpt and he told me some bs with ramsey theory bounds but I found a better approximation.

[spice rapids]

Wrong, it's 19

[drifting cloud]

[prisma python]

is it useful to have an accurate sketch of the problem for geometry problems?

[vital summit]

Yes it is really useful to have an accurate sketching, especially regarding specific geometry problems. It can clarify the problem easier and prevent misinterpretation.

[faint thorn]

what about if the problem has no clear variables

like a BMO 2006 question has no specified variables

but u have to prove that NM is equal to smth idk

if u want i can bring up the question

i asked my professional msths teacher who has like won multiple IMO and like gold medals from olympiad (bc yk cram school) and he solved maybe half way through but i have no clue how anyone could solve it

[pale berry]

hey so im selected for math olympiads on the most important school on my city and i was supposed to start practicing a month ago
but
i didnt and now i got 7 days to prepare. any tips?
(10th grade)

[frank valve]

you're cooked bud sorry

all the math olympians be studying 8 hours a day out of evan chen books

[glass garnet]

LMAOOP

[wide quartz]

Time to larp

Who knows just do what your brains tells u

[chrome scaffold]

Lock in

[foggy python]

ok

[warped folio]

Hey can anyone give tips for vvm, ioqm 2026 and sof imo 2025

[agile gazelle]

A question for you all ( i need to know all your povs) if i got stuck in a math question for hours and then i solved it do i improve my problem solving skills or not?

[pallid tundra]

i need to know all your povs
impractical, no way to get literally everyone on this server to respond

but in all seriousness developing problem solving skills doesn’t stop at just solving the problem no matter how long it takes

you have to also reflect on how you solved it, compare to the “official” solution, identify key steps, use all this info to update your intuition

[civic flame]

I dont know if this will work for you but what I'd suggest is making a list of all the topics you need to study and assigning each of them to a day.
Break it down into smaller steps instead of overloading your brain with info on Day 1.

I.e.
=> Monday = study geometry or whatever topic you need most help in.

Obviously it will be really hard to catch up in 7 days so just really try your best! Don't burn yourself out and take breaks.

[agile gazelle]

Atleast tried

If u dont wanna respond you dont have to thats ur choice

[agile gazelle]

Yeah reviewing the original solution is important too

Thanks

[warped folio]

Anyone

[summer roost]

For ioqm you can check out the past papers i guess

That will give you an idea about the theory which you need to study

I don't think a lot of theory is necessary

[warped folio]

What about sof imo

[summer roost]

Not sure about that

[warped folio]

No problem thanks

[vital summit]

Alright sorry for the late reply. Even when a geometric problem does not provide variables, it helps a lot to introduce your own labels for points and angles. Test by starting with a neat and clean sketch and label every side with variables (A, B, C, D, E, etc.). Therefore, you could potentially apply synthetic geometry tools (like similarity or cyclic quadrilaterals) or switch to coordinates/vectors if needed.

[vital summit]

For BMO/IMO-style geometry, in my personal opinion, experiment on similarities first. If perhaps it is manageable to stall, pick coordinates (put a triangle on the plane or use the unit circle), which often converts the geometry into algebra you can solve through.

[faint thorn]

Ah thank you

[vital summit]

I'll provide over a list of suggestions on how to specifically answer your question. Thank you.

Experiment Using These Suggestions:

• Coordinates/Vectors (Place the needed figure on the correct coordinates (e.g. place a base on the x-axis or use the unit circle)

• Cyclic/Power Bash (Identify whether the specific points lie on a circle or whether power-of-a-point or equal tangents)

• Synthetic/Congruence Route (Practically like Congruence/Similarity that has SAS, AA, ASA, or angle chasing)

[faint thorn]

Bc I had some problem trying to find how to make it so that it aint confusing to look at but not assuming

Bc like if I assume a bunch of stuff I’m not providing anything

[vital summit]

Yeah i can potentially relate with that

[vital summit]

Try to experiment

and understand the concept

[faint thorn]

Thx man

[vital summit]

The more you experiment, the more you can know. Dont overthink it.

[faint thorn]

I’ll try find out about the answer sheet too

[vital summit]

No worries man

[faint thorn]

Yh

[faint thorn]

Thx

[vital summit]

Yep understood

[vital summit]

Your welcome once again

[vital summit]

**Start with Higher Level Maths (G10, G11, and G12) Topics. Usually for Olympiads, they would guarantee Higher Level Topics in G11 and G12, no matter if you are Grade 10. (Personally, I am a Grade 10 too)

So, I would suggest you study these topics:**

1. Algebra & Trigonometry – equation solving, inequalities, functional equations, and trigonometric identities (common in algebraic manipulations and geometry).

2. Derivatives – rate of change, slope of curves, optimization.

3. Integrals – area, accumulation, and summation techniques (useful for series and approximations).

4. Exponential & Logarithmic Functions – solving equations, growth/decay, and applying log properties in inequalities and series.

5. Series & Sequences – arithmetic, geometric, and more advanced expansions (Binomial, Taylor/Maclaurin for approximations).

6. Limits – important for calculus and for usual Olympiad limit problems.

7. Factorials & Binomial Coefficients – exceptionally crucial in combinatorics and series.

8. Number Theory basics (modular arithmetic, divisibility) – often tested in Olympiads.

[prisma python]

huh i don't think it's common to see calculus on a high school olympiad though

[vital summit]

Hahahah yeah. Usually Physics. Im not sure because I rarely compete in Maths one. I compete for Physics. However, maths are really logical and numerical, it has tricks behind it too.

[inland panther]

Can anyone help!

<@&286206848099549185>

[wanton ridge]

hi, first of all, please only ping after 15 minutes have passed and helpers still haven't seen your problem

second, what have you tried?

[inland panther]

I am deeply sorry I am new to the server and did not the protocols

[wanton ridge]

it's okay!

[wanton ridge]

^ can you maybe show a picture of your work?

or do you not know how to begin

[inland panther]

I tried it solving using co-ordinate system but that thing is getting hell lotta mess

[inland panther]

I tried using co-ordinate but ig there must be another quick way to solve as this is an Olympiad question

[wanton ridge]

try thinking abt what you need to get the radius

to get the radius, you need to get the diameter

[inland panther]

Hmm

[wanton ridge]

are there any lines here that look like they might be a good place to draw the diameter?

[inland panther]

The question is how to get that

[prisma python]

yeah theres mostly combinatorics in math olympiads

[wanton ridge]

give me a moment, let me draw a picture

do you agree that this line is the diameter?

(sorry there was a connection problem so took a bit long)

@inland panther

[inland panther]

Yes

So how will you compute the bottom part

[inland panther]

Np

[ornate blade]

you can let the side of the equilateral triangle be 1 unit instead

(then at the very last step, multiply everything by 2022)

[inland panther]

Ok

Lemme try that out

[wanton ridge]

sorry I was away for a while
that's a good point I still have another idea tho

let me draw another picture

[ornate blade]

they're trying it out so I won't say anything for now

no actually I will say: where is the centre?

[wanton ridge]

another hint if you need it ||EGD is equilateral||

[inland panther]

I'm getting close

I got R=2022

Using your idea of initially putting s=1u then ultimately scaling it up

Thankyou

@wanton ridge

!

[ornate blade]

(it was my idea but yeah)

no worries!

[inland panther]

Oh sorry

My badd

Did not see that it was you

😅

Anyways

...

Thankyou @ornate blade

[pale berry]

the thing is that i dont have a list of topics

[pale berry]

thank you so much, any tips for number theory since thats what im most lost on

[snow thistle]

is it like olympiad math or computational

the easiest way to get better at math is to just do problems

literally

if ur like just starting out then u have to learn some stuff

and if youre doing oly you have to learn advanced stuff

[snow thistle]

like imo geo is never like this

any olympiad geo

its rarely coordinates

for computationa lcoordinates is fine

but in oly the only geo solutions are like

synthetic, barycentric, projective, trig

complex is really common

but for like a lot of synthetic problems you have to know a lot of oly geo lemmas

[scarlet root]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[twin bane]

2

[scarlet root]

Show your work, and if possible, explain where you are stuck.

[grim prawn]

Can someone prove or disprove this:

If f is a polynomial such that f(f(x))-x has a root, then f(x)-x divides f(f(x))-x.

[surreal willow]

Just try a proof by contradiction

[outer mural]

oh

i think i found something, but i don't know why we need f(f(x))-x to have a root

let $p(x)=f(x)-x$. then $f(f(x))-x=p(p(x)+x)+p(x)$. It suffices to show $p(x)\mid p(p(x)+x)$, which actually seems to work out, if you expand all the terms

[gilded halo]

Axe

[ivory ember]

putnam 2024 A2??

[outer mural]

still, i must be missing something since i didn't use the fact that f(f(x))-x has a root

idk, is it?

[outer mural]

to show $p(x)\mid p(p(x)+x)$, let $p(x)=\sum_{n=0}^{\infty}a_n x^n$. Then
\begin{align*}
p(p(x)+x)&=\sum_{n=0}^{\infty}a_n (p(x)+x)^n \
&=\sum_{n=0}^{\infty}a_n(p(x)q_n(x)+x^n) \
&=p(x)\sum_{n=0}^{\infty}a_n q_n(x)+\sum_{n=0}^{\infty}a_n x^n \
&=p(x)q(x)+p(x)
\end{align*}
for some $q_n(x), q(x)$

[gilded halo]

Axe

[hexed oak]

I agree you don't need the f(f(x))-x has a root part, but a different solution would be saying

Let us say (x-a)^n divides f(x)-x, then modding by (x-a)^n we have
f(x) = x so f(f(x)) = x
So we have f(f(x)) is also divisible by (x-a)^n so we are done

[prisma python]

what are barycentric and projective? i tried searching them up but it's confusing

[vital summit]

Your welcome man. Number Theory? Hmmm i’ll do my best to try in explaining it easily since I’m only Grade 10. Number theory is basically the study of how whole numbers act, especially when you divide these ceritain Numbers, breaking them into specific factors, or look for any patterns.

In the concept of number theory, it doesn’t really have large and long calculations (complex), however you use more of logical tricks (like modular arithmetic or algebraic factorization) to find the solutions.

[vital summit]

Yeah but ive never tried IMO. Pretty saddening tbh.

[vital summit]

Lots of tricks behind the questions’ back to be honest.

[keen knot]

how effective is preparing for the UKMT SMC questions for the MAT? is the overlap significant?

[vapid stag]

Overlap between smc and?

[keen knot]

oh damn

MAT

idk why i didnt say that

😭

[vapid stag]

Well idk much abt mat but smc is more quick fire

There's not much beyond gcse level in the smc

[keen knot]

i was thinking especially with the new MAT format of 25 mcqs smc trains a lot of speed and quick fire thinking and pattern recognition

[vapid stag]

You sound well informed

You're prolly right

[keen knot]

😭 interesting

but i was also thinking that the mat syllabus expands into a lot of a level so the quick fire training from smc wont sustain into mat

[high goblet]

if you run out of MAT problems the SMC would be quite useful for the problem solving skills

also like one of my interview questions was somehow literally an intermediate maths challenge problem 💀

so anyway could be useful

[snow thistle]

barycentric is like describing points with masses

and projective is kinda like geometry with no concept of lengths and angle measure

its just points and lines

and theres a bunch of good properties

[prisma python]

oh wow that's cool, i'll check it out, thanks for explaining it

[glossy falcon]

Hm I thought smc was pretty different in my experience

[umbral elbow]

Guys help!

[weary vortex]

I don't think this is a competition problem?

[umbral elbow]

Its question of worlds 2nd hardest exam but i dont know its a competition problem or not

@weary vortex

[weary vortex]

I know JEE is hard af

[umbral elbow]

yep

[weary vortex]

but usually, these types of problems only test how much formulas/theorems can you remember. competition problems test whether you have a clever perspective on a certain problem

[umbral elbow]

thanks! btw

[weary vortex]

better ask it in Math Help, people usually don't expect exam problems in this channel

[pale berry]

got lost here, what is modular arithmetic?

[agile gazelle]

Im sorry to say this is easy

[slow spire]

Hello , I have a question how do you get started with IMO?

[agile gazelle]

Hello, i have the same question

[ashen hatch]

like, how do you qualify, or how do you prepare, or?

[vernal axle]

||This can be done using generating functions. We can write
g(x)=x+x^2-x^3+x^4+x^5-x^6+...=x/(1-x)-2/(1-x^3).
Then multiply by x^(k-1), differentiate and divide back by x^(k-1). This gives the g.f. for k+(k+1)x-(k+2)x^2+...
To obtain cumulative sums (which needs to be taken twice), multiply by 1/(1-x)^2.
Finally, summing over k=1,2.... produces the generating function for G_k which is in the picture. So, you get explicit formulas for G[3n], G[3n-1], G[3n-2] as polynomials in n of degree 4. The rest of the problem follows easily from these.||

[silent berry]

what is a good way to prepare for the amc competitions

been tryna do practice tests

[swift peak]

yeah thats the best way i think

[prisma python]

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

[vital summit]

Arithmetic operations that are mainly for integers.

[agile gazelle]

How to you prepare

[heady summit]

Oh that sure is tedious

[oak tartan]

I’m pretty new to competition math so how would I approach a question like this

[arctic narwhal]

how get imo plz

[ivory ember]

factor the left hand side with difference of squares to get ||(5x-3y)(5x+3y)=77^10||

considering ||the sum and difference of these factors|| makes it natural to work ||modulo 10|| and ||modulo 6||

[agile gazelle]

Use arithmetics

[ornate blade]

if you just want prestige, there are a million other kids who will have more motivation than you, cause they will have an actual reason for competing

really decide if you want to dedicate some of the most formative years on your life to something that 0.01% of students can achieve

or if there is something else that is more achievable and that would make you happy in life

[hearty obsidian]

this is something I need help with

anyone here?

[ivory ember]

Bash Newton's sums [https://artofproblemsolving.com/wiki/index.php/Newton's_Sums]

[ivory ember]

Also bash. [https://en.wikipedia.org/wiki/Golden_ratio]

[summer roost]

check out a few of your national competitions

and see if the problems are engaging or not

That will determine whether you should do comp math or not

[simple blaze]

How do i approach this problem

[sleek ivy]

what counts as an actual reason for competing?

[ornate blade]

I don't want to judge, but usually it's some variation on "I want to learn new things, cause learning is inherently fun" or "I enjoy participating in maths events with other people who also like maths"

try to stay as far away from a competitive mindset like "I need to succeed and be better than everyone else"

cause that just makes you miserable

[sleek ivy]

i feel like theres a lot more enjoyable ways to learn things than grind math comps

[arctic narwhal]

Why r u hating bro

[sleek ivy]

miserable people often succeed

[ornate blade]

I'm being completely honest with you

I want you to be happy and do well in whatever you choose to put your heart to

and for that to happen, you need to be able to make an informed decision about what this is actually like

[ornate blade]

exactly

[arctic narwhal]

I know what it was like

I was pretty close to USAJMO last year

[ornate blade]

okay then

[arctic narwhal]

But u don’t know if I’ll be able to push for usamo

[ornate blade]

then yeah, I should re-evaluate what I say based on that new info

[ornate blade]

okay that's much better once you started explaining

then it's easier for others to help

unfortunately I don't have experience of USAMO etc

[arctic narwhal]

Noob

[simple blaze]

Umm can anyone help me with this

[sleek ivy]

any advice for qualing AIME? Ive done all the relevent past papers for AMC12 (recent to 2015) scoring from 75-90 in most (90 more so in the old ones)

[ornate blade]

but if you genuinely want advice you could be more accommodating to those who want to help you

don't just call them random names yk

[arctic narwhal]

Noob

[ornate blade]

try asking in a help channel

[simple blaze]

I did got it

[ornate blade]

oh nvm you got it, I saw your channel lol

[simple blaze]

[ornate blade]

ok

[faint hollow]

huh

[radiant jasper]

solve anyone

[faint hollow]

what is P(x)

[sharp sandal]

is it 16

[radiant jasper]

show work

?

apparently it's 22

[sharp sandal]

lol nvm

Median divides triangle into two triangles of equal area. I used that here.

[radiant jasper]

oh you mean that question

[sharp sandal]

2

[radiant jasper]

i thought this one

yeah it's 2

A-B=2

[pure hull]

do you know what nilpotent of index 2 means

[simple blaze]

I got it someone helped me solve it

[pure hull]

🆗

[tiny eagle]

I’m kinda new to comp math too but I’d say do past tests of previous years specific to the competition to get a feel for the problem style

Then learn how to solve every single problem on the previous test(s) so that you really understand the problems

[pallid tundra]

fastest way to familiarize yourself with the kinds of questions they put on contests is to do a lot of them

[austere wedge]

should i read textbooks and shit

or just do problems

[crisp orchid]

get every aops textbook

and do every problem

and understand it

that’s how i qualified for jmo

[tiny eagle]

Wait can I get the aops textbooks for free

I don’t have monies

[soft vigil]

big news

usa(j)mo is now amc+20*aime

[novel karma]

Yo can I dm u

[crisp orchid]

ok

[crisp orchid]

you can find most of the actual textbooks online for free but you probably have to buy the sols manual

[crisp orchid]

where did u get this from

[soft vigil]

maa website

https://maa.org/student-programs/amc/maa-american-mathematics-competitions-policies/

[crisp orchid]

broooo

[lime osprey]

Do practice tests from previous years and figure out what you dont know and learn what you dont know

[vestal pond]

AMC10 predictions? like AIME score, average score, whether A or B will be more difficult, etc.?

[nova gate]

hello

i need help with math notes

[hot moss]

honestly i think it’s better because sillying even just one question in a more difficult test with longer time is harder than sillying 3 questions on the AMC

[proven magnet]

Can anybody tell me where to learn Algebra for olympiads after learning proving techniques?
Iam using richard hammock book of proof rn

I prefer a book with less computation, but more proof based

[worldly swift]

Larson's "Problem Solving Through Problems" and Paul Zeitz's "The Art and Craft of Problem-Solving" are both fine books, imo

But these are more so for later down the line in math contest preparation (e.g. AIME, USAMO and so on)

For the AMC, I would recommend AoPS Volumes 1 and 2

And just spending a lot of time on past AMC 10/12 problems

(assuming you're in the US, that is)

[summer roost]

Aops volume 1 and 2 are a bit outdated

I didn't find them that useful during my preparation

[sleek ivy]

what did you use then?

[summer roost]

Since I am not from the us

It was a book specifically made for my region math competition

I had heard about aops but it wasn't particularly useful in my case

Since aime is much harder now

[summer whale]

guys

i still dont get what is this for

[turbid cipher]

for nerds

[twin bane]

help on number 3

[ivory ember]

Reposted here: #help-33 message

[delicate meadow]

Can anyone tell me when we register for AMC 10-12?

[pallid tundra]

ask your teacher

registration apparently closes pretty soon so be prompt in asking

[analog snow]

is this waterloo

[subtle sundial]

for the olympiad kids

[frank hornet]

Yes, I remember doing it.

[cosmic pulsar]

wait is anyone joinign the AMC 8 2026

[radiant jasper]

hey y'all, I wanna be good at competition level trig ques. can anyone tell me how to approach such questions in which we have to prove RHS = LHS, I am good at it but in many question's I just can't figure out how to exactly start and have to try many trail methods to get closer to LHS/RHS :/ which takes reasonable time, it happens with some normal ques too, can anyone tell some tips to me.

[radiant jasper]

i think those questions really just require alot of practice

i used to suck at them and think they are impossible to be good at only to find myself

doing really well at after a while

of doing

you just pick up the common patterns only to be learnt with practice

[radiant jasper]

what questions you practiced? like any specific book or some online sites

[astral jacinth]

does anyone have any good anti-problems and/or a doc containing them?

[near hill]

Anti problems? As in we give the answer and you have to figure out what the question was?

[astral jacinth]

problems whose solutions are really "dumb"

[near hill]

Yes, at least if we assume both spaces are normal Hausdorff.

[astral jacinth]

like that one putnam question that asks whether every composite N can be written as xy+yz+zx+1, where x, y, and z are integral

and the answer is ||yes, z=1 -> N=(x+1)(y+1)||

[astral jacinth]

troll problems

[ornate blade]

https://arxiv.org/abs/1110.1556

[astral jacinth]

thx

[ornate blade]

there was a good YT video on these but I can't find it