competition-math

[soft vigil]

and practicing it

[dusky whale]

sounds good, thank you

[gray heart]

actually, ||f(r)= e^iθ * "r
where "r is the conjugate of r
and θ is arbitrary, since the |e^iθ|=1||

[jolly solstice]

isn't r real?

[gray heart]

not necessarily

[shrewd girder]

Last line is so real

[dense schooner]

If anyone's had a bad day

[radiant jasper]

Aww

[forest brook]

thank you

[high goblet]

ur missing a solution, f(x) = -xconjugate

so u've gone wrong somewhere

it's a bit cliche but just do practice

exhaust all the AMC12s available

if u've done that then try finding equivalent competitions for other countries

anyway my last piece of advice would be to not shy away from hard problems

i'm not american so i'm not sure what comes next, AIME?

anyway once ur nearing the point where you're almost consistently getting enough to get into AIME

is when you should start doing AIME past papers

the common trap to fall into is some ppl want to perfect their current competition before they move onto the next one

but if u do that, u'll find u stagnate

[crude prawn]

hello, can someone recommend me books for math olympiads?

[swift imp]

Yea in USA it’s

AMC 10 or 12 to AIME to USAMO to MOP to TSTST to TST to IMO something like that

[ornate blade]

https://artofproblemsolving.com/store

AoPS books in general

[gray heart]

in general any constant with magnitude 1

[gray heart]

i mean the coefficient, it's not only 1 and -1

[high goblet]

but any constant with magnitude 1 doesn't work

only +-1 works

[gray heart]

i just checked again,
since k^2|y|^2 = |y|^2 yeah ur right,
my bad

[high goblet]

so what's ur full solution?

[gray heart]

P(x,0) implies the involution
P(x,f(y)) = P(x,y) so
|f(y)| = |y|
then f(y) must be a rotation of y, or the conjugate of y
checking for f(y)=ky gives that Re(y)*Im(y)=0
if Im(y)=0 then it'll be just a specific case of the general solution and if Re(y)=0 it quickly contradicts
then checking for the conjugate leaves +-1 ,
still can be 1 for some y and -1 for the rest
setting a,b , with f(a) ,f(b) with different signs in P(a,b) leads to -|b|^2=|b|^2
that's pretty much it

[high goblet]

checking for f(y) = ky gives Re(y)*Im(y) = 0

how did u get this?

[dreamy dagger]

Noice

[gray heart]

(ky)^2 = |y|^2
well, tbh in that point we can just leave it like that since it refers to some specific y and y is a parameter

[high goblet]

how?

it's k*kbar, not k^2?

[gray heart]

f(y(f(y)) = f(ky^2) = (ky)^2
right?

[high goblet]

but why is f(ky^2) = k*ky^2?

we could have a different k

so like f(ky^2) = aky^2

[gray heart]

oh

oh shoot

[high goblet]

but yeah basically my suggestion yesterday was that we know

f(yf(y)) = |y|^2

we want to exploit the fact that f is injective

let's write y in modulus-argument form, so let's say

$y = r\exp(i\theta)$

[gilded halo]

LY

[high goblet]

plug that into here and use f is injective to see what u get

[gray heart]

so it's basically playing more with the fact that f(yf(y)) is real, to make a relation between the angles, then go to the actual value of f(yf(y))

im in class rn so ill go afk

[high goblet]

yh nw

[trim yoke]

Hey guys, this is my first math competition, I'm prepping for the AMC senior division. Can you guys give some useful tips and tricks

[wide dome]

The MCR is hosting a 1-hour rated math contest. You can join anytime until October 30. We hope this will be good prep for the AMC & other upcoming contests, and more importantly, that the experience is enjoyable for you :)
Discord server: https://discord.gg/xv6ZEnVJaR
Contest page: https://mathcontestrepository.pythonanywhere.com/contest/ntt1

[soft vigil]

dont forget usajmo

also i think everyone at mop gets invited to tstst

[swift imp]

Yea

[modern prawn]

mop isnt a part its just a program i thoguht

[swift imp]

well it requires a good score in usamo/usajmo

so its like the next part

[modern prawn]

after usajmo is straight to imo i thought, i thought mop wasnt required

[soft vigil]

no it is required

after usa(j)mo

you get invited to the irl camp

MOP

[modern prawn]

Damn what if you dont want to

[soft vigil]

then there you end up taking TSTST

[modern prawn]

what is tstst

[soft vigil]

then you cant make imo team

[soft vigil]

team selection test selection test

[modern prawn]

bruh if u fail you can never become part of it?

can you take it multiple times

[soft vigil]

then whoever does good on that

makes tst

[soft vigil]

?

u can always take tstst the next year

[modern prawn]

how do u take mop twice

wait so mop is basically a camp for all potential mop team

they train them like crazy

then tstst

[swift imp]

no its really hard to get team usa for imo

[swift imp]

yea theres like a bunch of groups of mop but after mop is done, they take the tstst and like the top scorers in that take the tst later in the year and thats how team usa is made

[deft wraith]

i think a few things like rmm also count for selection i'm pretty sure it's not just tst

[spring prawn]

hi guys, can you all explain some physics knowledge to me please?

[novel spire]

Maybe a stupid question, but isnt this wrong? Wouldnt it be 2^2000-(all combinations with only one number). Since it has to be a sum of at least two numbers?

Oop never mind I mis-interpreted total subsets as total possible answers

[royal estuary]

Aks

[sleek ivy]

What a nice name

[soft vigil]

In two different years

[high goblet]

how about instead of calling USAMO the USAMO, how about we instead call it the TSTSTST

[pallid tundra]

T(ST)^3 😱

[swift imp]

yes

hrk.

[deft wraith]

halliday resnick krane is really good yep

then if you're a bit more olympiad inclined you can work through handouts (i.e knzhou, kalda) and lots of problems otherwise work through textbooks i.e purcell e&m, griffiths quantum, k&k mechanics and also lots of problems

[radiant jasper]

https://dontasktoask.com/

[deft wraith]

https://doasktoask.com/

[radiant jasper]

ty I'll take a look

[swift imp]

Bro I asked someone to give help in em one time and they linked me Griffith electrodynamics 😭

[deft wraith]

i mean griffiths is a good book for e&m and it's fairly self contained (at least more so than purcell from what i remember) i know several people use it as an advanced text in the pho scene.

probably not suitable for a complete beginner though

could've been worse, they could've reccomended you zangwill or jackson (the latter of which is quite infamous for it's difficulty while the former is one of my favourite physics textbooks)

[swift imp]

I am a beginner

😭

[deft wraith]

yeah -- maybe not the best advice then

[glad zinc]

this video is so good

anyone who did the SMC this year, how did you find it

[deft wraith]

It was slightly easier than usual

The grade boundaries were quite high

[glad zinc]

ong, i cooked this year, got full

[glad zinc]

yeah 110 for bmo is crazy

[high goblet]

nice gg!

yeah i think i got full in Y11, and then my score was just a strictly decreasing function after that lol

[glad zinc]

I did the triangle question in the goofiest way possible

[ornate blade]

hi Cam dude

[high goblet]

i heard, i'll probs try the paper at some point when i'm free

[high goblet]

hi!

[glad zinc]

Honestly you'll probably get full, the only potentially difficult ones are the two geometry questions and even they aren't that difficult. And there were a couple good questions but they could easily be solved from just plugging in the answer choices so it ruined it

[ornate blade]

hmm so FJ:JK:KG = 1:2:3 may be useful

[glad zinc]

I did it in such a weird way, using coordinate geometry and gauss's area formula

[high goblet]

i mean last year we as the 1st year trinmos did the SMC drinking game lol

start on Q25, work backwards to Q1

2mins/q for 25-21, 1min/q for 20-1

i did not cook lol

[ornate blade]

bruh

[glad zinc]

2 mins for 25-21 is rough

[high goblet]

(1/2 shot of vodka/q you get wrong btw)

the year above us did a BMO1 drinking game 2 years ago, although i heard that ended being more drinking and less mathsing

[glad zinc]

cambridge students be looking for any excuse to drink as much as possible

[high goblet]

if u've never done a scuffed solution to a problem have u really ever done an olympiad problem?

[deft wraith]

most lively party with mathematicians

[ornate blade]

ah so is it just 32 divided into the ratio (1+2):3 or 16 and 16
so FKH = 16 and hence IKH = 4?

[glad zinc]

true true

[glad zinc]

i think 4 was the answer yes

[deft wraith]

yes it was 4

[ornate blade]

YES found the sol, it is 4

yeah like it's a nice question

but nowhere near AMC 12 difficulty where getting to the algebra is half the battle

and without a calculator even the algebra is tedious

but it was nice, doable if you just be patient

[deft wraith]

i think some amc12 questions can be bmo1 p1s i saw a diophantine which you could do with SFFT and i've definitely seen a similar difficulty diophantine in the primer

[ornate blade]

oh wow had no idea

[glad zinc]

I feel like, comparing the difficulties of the AMC 12 and SMC, british kids are worse at math than the us kids, or maybe the best US kids are just better than the best UK kids

[ornate blade]

yeah it's the 2nd

you can't make population-level comparisons considering a tiny minority of people do contest maths in any country

but I think the best US kids are definitely very bright, and there's a lot of support in that area

like all of the summer camps are in the US I feel, not too many in the UK

[ornate blade]

IMO results for instance

[ornate blade]

by any chance have you watched the movie X + Y

[glad zinc]

true but Im pretty sure alot of kids in the UK do the SMC and other competitions, so maybe thats why too

[ornate blade]

autistic British guy goes to Taiwan for IMO camp, falls in love with Chinese girl

[glad zinc]

so alot of average/below average kids do it

[ornate blade]

competes in IMO in Cambridge

stars Asa Butterfield

[ornate blade]

yeah low barrier to entry

[high goblet]

no i haven't

[ornate blade]

it's a joke cause all of us found the AMC 12 pretty scuffed at my high school

even AMC 10 was challenging

and then we looked at the SMC and lmaoo

[high goblet]

i've heard it doesn't represent the UK selection process very well tho lol

[glad zinc]

im literally farming awards with ukmt comps its crazy

[ornate blade]

my secondary did all sorts, so we also did the CEMC, the written one where you need to justify your answers in a written response

also like you could go overseas

[glad zinc]

if i did amc i do not have a chance

[ornate blade]

we did the American monthly one which is 35 mins on 7 questions

was like SMC but shorter and a bit easier

[ornate blade]

sotrue

[glad zinc]

bmo1 in 25 days i have not started studying i may be cooked

[high goblet]

who doesn't love having a large collection of UKMT certificates

[glad zinc]

how should I study bmo1, I'm gonna do past papers but I know that I don't know alot of tricks and content so I have to learn that first

[normal lodge]

yo guys

I need a good question

[deft wraith]

i like the soundtrack

[ornate blade]

oh interesting

yeah that movie was my first exposure to Asa Butterfield as an actor

[deft wraith]

also i think it's loosely based on daniel lightwing who has a documentary of youtube which was a recording of the 2006 imo + ukmt process leading up to it i believe

not sure how accurate it is nowadays

[ornate blade]

the same guy appearing in say, Sex Education, just blows my mind away

[ornate blade]

thanks for the context

yeah that guy's name sounds familiar

[high goblet]

yeah they made a documentary based on the UK team that year

[ornate blade]

wow

[high goblet]

haven't watched it, although i've heard the UK team that year was a bit...quirky

[glad zinc]

"co-founder of the London-based Internet/gambling business Castella Research, which uses high-frequency trading inspired methods to place bets on sports exchanges." Damn thats kinda sick

[high goblet]

which might've given the impression that all UK imo team members are like weird nerds lol

[glad zinc]

We all are a little quirky, thats why we do maths 💀

[high goblet]

don't, it's like you could learn a lot of tricks then find problems to practice those tricks on

[ornate blade]

oh yeah that's unfortunate

[high goblet]

but like it's much better to just do problems

[ornate blade]

motherfucking why do so many maths guys go into trading or poker

[high goblet]

you might come up with a clever trick

and then like it'll stick

[glad zinc]

lol thats exactly what i wanna do

wanna become quant PM

[high goblet]

(you'll also understand why that trick was useful)

[ornate blade]

there's a movie based on an MIT team that won big in Vegas with poker

[glad zinc]

fair enough ill just spam past papers then

[high goblet]

anyway i'm gonna go back to watching my galois lecture recording

[deft wraith]

it is definitely quirky

[glad zinc]

have fun

[stiff zealot]

brother i cant even read that

[royal estuary]

Uh

Wait

That looks legible

[royal estuary]

<@&286206848099549185>

[shy meteor]

Hi

Is anyone doing AMC

[radiant jasper]

Me

[jolly solstice]

I was able to grind it down by replacing x with 2x, y with 2y, z with 2y and then dividing out, reducing mod, and working through cases. Pretty tedious and not really that interesting, but maybe there's a better way

[radiant jasper]

note that the circumcenter is equidistant from all 3 points of the triangle

what did the problem writers have in mind when they said that DE is parallel to AC?

[swift imp]

yes

[vague temple]

Hey everyone, what’s the recommended order of study for AMC 12 based on the quantity of problems based on each topic? For instance, from the book: “Mastering AMC 10/12”: Combinatorics, Algebra, Number Theory, Geometry, Advanced Topics?

[vague temple]

I keep parsing “SFFT” as Sliding Fast Fourier Transform

[swift imp]

there is no step by step way to study for any contest math

as in - you decide what is best for you

and you into whichever hole u want

[vague temple]

Are there some topics that appear more than others?

Is what I am asking

[swift imp]

it will always be

algebra, number theory, geometry, combinatorics

These 4 will always be there

[vague temple]

In that order?

[swift imp]

no

all of them will be there

some might not show up, some might show up in easier questions, some might show up in harder questions, but those 4 topics will be usually in any math contests broadly

[vague temple]

But I should do trig, complex numbers, logarithms last, right?

[swift imp]

just pick what you want to do

theres no set path on what to do

just find what interests you

thats what math contests are for - not to win, but to solve interesting problems

[vague temple]

I counted, it seems like Algebra and Geometry appear the most frequently, so I’ll focus on those first

Combinatorics and probability is third from what I saw

[vague temple]

Yes, my goal this year is to win the honor rolls because I never scored well in AMC before

[radiant jasper]

GLLLLLL

[shy meteor]

What is the textbook you’d recommend for amc 10?

[swift imp]

Uh when I started studying I used a pdf my friend gave

Add me

[royal estuary]

Cmon evryone knows that

[wintry kiln]

Anyone have suggestions on how to study for comp math in about 5 days

[royal estuary]

Ur cooked lil bro

Do previous year questions

[wintry kiln]

Ive only done advanced math

My parents forced me to do the open math comp

[royal estuary]

What does it cover

Calc

[wintry kiln]

Calc 1, doing calc 2

A bit of real analysis

[royal estuary]

Oh ok

But that's not useful in comp math

[wintry kiln]

yeah...

my point

[royal estuary]

You know geometry ?

[wintry kiln]

What is a "geometry"

[royal estuary]

Huh

[wintry kiln]

geometry dash reference?

[royal estuary]

Geometry

[wintry kiln]

Sure

[royal estuary]

Shapes

[wintry kiln]

but what type

[royal estuary]

Euclidean geometry

[wintry kiln]

angles, areas

yes

[royal estuary]

Almost everything

[wintry kiln]

i suck at comp math geometry but sure

[royal estuary]

Mostly angles,lengths,and areas

[wintry kiln]

(I suck at everything Comp math but sure)

[wintry kiln]

Ye

i did a bit of it when i was younger

[royal estuary]

5 days is way too less

[royal estuary]

How old r u

[wintry kiln]

Freshman

😀

[royal estuary]

College

[wintry kiln]

Of hs

[royal estuary]

Oh

[shy meteor]

What are you taking in school? Like math wise

[wintry kiln]

Fucking fractions and algebra

[shy meteor]

1 or 2

[wintry kiln]

Wdym

[shy meteor]

Algebra 1 or algebra 2

[wintry kiln]

Were solving equations like 5x=10 what is x

(Algebra 1)

[shy meteor]

Ohh

Okay

[wintry kiln]

Yup 😃

I love school

[royal estuary]

But u said you know calc

[wintry kiln]

Ye

self taught

[royal estuary]

So you can do quadratics and stuff

[wintry kiln]

a bit, not too much on integration

[wintry kiln]

I may yes

[royal estuary]

Functional equations ?

[wintry kiln]

Functions?

[royal estuary]

Yea

[wintry kiln]

ye

[wintry kiln]

log, trig funcs,

[royal estuary]

Smth like this

[wintry kiln]

Series = bad

[royal estuary]

Ah ok

[wintry kiln]

Ye i do know 😃

idk i just wanna know a bit of what else more i could do in terms of stusying for the contest

[royal estuary]

Amc ?

[wintry kiln]

i am doing previous years tests

[wintry kiln]

Comc

canada

[royal estuary]

Oh

Alr

Just skim out some previous year questions

Idk what's the weightage tho topic wise

[wintry kiln]

Well what do you think is more "helpful" here

So theres 3 sections

a,b and c

a being the Easiest and c being the hardest

do you think i should skip a and some of b and do perhapes harder/more complex questions or should i do the test as a whole

[royal estuary]

Obv the easy ones

Try doing what you can do

Don't focus on sections

[wintry kiln]

I see i see

i was forced into this and i only knew like 2 or 3 weeks ago

[royal estuary]

Yeah nw

Just focus on what you like

[wintry kiln]

But wouldnt it be more applausible to challenge myself to some harder questions as it could perhapes show up on the contest in different forms?

[royal estuary]

Yeah but

It's mostly geometry

[shy meteor]

When does amc start? Like the competition

AMC 10

[royal estuary]

And equations

[wintry kiln]

Hm

[royal estuary]

November 6

Ig

[shy meteor]

Is it only once a year?

Thanks

[wintry kiln]

Imagine comc starts on November 6th 😭😭

[royal estuary]

No twice

One on 12

And the other on 6th

[wintry kiln]

But if i was to do it next year @royal estuary

what would you recommend me to do?

[royal estuary]

Go through number theory

Geometry

[shy meteor]

What does that mean? Like in November 6th and 12th?

[wintry kiln]

(Im kind of cooked this year)

[royal estuary]

Yeah

[wintry kiln]

Interesting, is there somewhere i could by chance find what youre talkikg about?

[royal estuary]

Do amc 8 questions

Then amc10

[wintry kiln]

But im doing comc

Are they related??

[royal estuary]

Yeah

[wintry kiln]

okok

[royal estuary]

Everyone does that

Then if ur done with amc 10

Go to amc 12

[shy meteor]

Ah okay thanks

[royal estuary]

For geometry u can use books like Evan chen

[wintry kiln]

whats does the number after amc mean???

[royal estuary]

Grade wise

[wintry kiln]

the grade?

[royal estuary]

Ye

[wintry kiln]

okok

[wintry kiln]

Ty man

thanks for the tips

[royal estuary]

Nw

[shy meteor]

Would you suggest the school ones

Like hmh

[royal estuary]

What's that

I'm not a Yankee so idk

[shy meteor]

Textbook brand

😭

It’s used in schools

[royal estuary]

I'm from a third world country

With no food

Water

Electricity

[shy meteor]

Oh

Sorry..

[royal estuary]

Nah

Just kidding

[shy meteor]

I knew it…

Would u recommend tho

[marble grove]

I have like 2 weeks for amc 10

and im tryna study for it

but i don't know the topics cuz yeah

anyone have a good studying website or sum

or like what topics on khan they r on

cuz i looked at question 20 from 2023 amc 10 b or a i think b and I did not get it

[radiant jasper]

If one does well on STEP, yet messes up the a levels, does one still have a good chance of getting into a top 10 British University?

[ornate blade]

for Cambridge they'd still consider you

but other unis don't really use STEP, so you would have trouble

depends what you mean by mess up also

like are we talking one grade below the entry requirements in 1 subject

or that you got something like A* C C

[winter sable]

i hope you guys rememeber me

[ornate blade]

hopefully

depends on how long you leave us

[ornate blade]

more like they can consider STEP cause it's well-known, but they have no obligation to

they can say nope you don't have the A level grades so you can't get in

only Cambridge has STEP as a part of their admissions methodology
cause Cambridge designs it ofc

[winter sable]

i m sorry

bro yk what i did a 12 hr maths streak

yeolpumta

[radiant jasper]

Thanks for your reply.
Cambridge requires me to get at least 95 percent in aggregate, now by "messing up" I meant getting a 99 or 100 in math, yet 90ish in other subjects.

[winter sable]

Ohh

study then

[radiant jasper]

I'd be grateful if you could mention some site where I can read about the admission process.

[winter sable]

yeoulpumta

[ornate blade]

ah India

man

[winter sable]

same

i m india

from

[ornate blade]

https://www.maths.cam.ac.uk/undergrad/admissions/files/admissions/admissionsguide.pdf

https://www.undergraduate.study.cam.ac.uk/courses/mathematics-ba-hons-mmath

the second link is a brief summary

[radiant jasper]

Tysm bruder this'll help a lot!

[ornate blade]

the solution is to apply to a range of unis

specifically, you can apply to two courses at the same uni

and then yeah you only have 5 choices on UCAS

use them wisely

basically don't laserfocus on Cambridge only

[ornate blade]

life is not Cambridge or nothing

there's always opportunities eventually

[radiant jasper]

Ok, I'll remember that.

You are Aussie no?

[ornate blade]

yep

[radiant jasper]

@ornate blade Also what makes a good personal statement?

Does it matter much?

[ornate blade]

personal statements do matter a fair bit but the format is changing

you'll be answering 3 open-ended questions instead

https://www.thestudentroom.co.uk/university/personal-statements/mathematics/ - here are some exemplars in the old format

https://www.ucas.com/undergraduate/applying-university/writing-your-personal-statement/new-personal-statement-2026-entry

details for the format change are here

also yeah you only get one personal statement for all the unis you apply to

it shouldn't matter that much as to what you want to say

as you'll be talking about your motivation for studying your degree, super important

as well as other extracurriculars and non-academic things
although those are not as important, if you show you've been reading and working with maths texts, so just something else other than your grades you need to talk about

[radiant jasper]

Thanks again.

[deft wraith]

Depends, yes if you already have a STEP offer and no if you're applying otherwise. It's quite a difficult question because it's case by case, and also it's very rare to mess up A Levels and do well on STEP.

[ornate blade]

it's just that for India you don't really have much choice in your 5 subjects

maths, 3 sciences, but then people take Hindi or English I think

and you need to score 95%+ at least

[radiant jasper]

What does "case by case" mean there?

[deft wraith]

like they consider your step mark, a level grades, interview scores so on and so forth

there's not an overlying general set in stone rule

[radiant jasper]

@deft wraith You are grade 11 too?

[deft wraith]

no

[violet lichen]

hello! i have a problem with complex numbers and i don't know how to solve it. can you help me pls?

The problem is: let w a complex number, w^13=1 and w isn't 1. Then, how much is the product (2-2w^k + w^2k), where k take all values from 1 to 12 (k is an integer)?

[royal estuary]

Youtube

[jolly solstice]

do you know the geometric series

[high goblet]

i mean it probably doesn't really matter for cambridge

depends exactly what you mean by mess up, but like if u get SS in step

and ur a levels looked like i.e. A* A* B

or A* A* C then they'll probs still let u in

at worst u'll get pooled to a different college

the SS in step and doing well in ur interview is a lot more important to them basically

[high goblet]

(also realistically if ur doing a levels, ur probs doing a level maths&further maths and it's like u should be able to get double A*s on those if u can do step)

[radiant jasper]

Is this a reference to contest math?

[high goblet]

yh

[radiant jasper]

Urgh I hate contest math

[high goblet]

u don't have to talk abt contest maths

basically they're just saying don't waste ur time talking abt ur a level grades etc.

[radiant jasper]

What if I don't have "any relevant educational achievements"? Is that a handicap?

[deft wraith]

you're international right?

[high goblet]

probably not, they don't really care abt personal statements anyway

[radiant jasper]

Yes

[high goblet]

r u applying for 2026+ entry?

[winter sable]

u am back

[radiant jasper]

I'm in 11th grade (year 12 in UK), so probably.

[winter sable]

m for maths

indian

[high goblet]

in which case i have no idea how the PS equivalent is gonna look, but whatever the case it'll be dumb lol

[radiant jasper]

Wdym?

[deft wraith]

they're changing the personal statement format

[radiant jasper]

Ik it's changing

[high goblet]

cambridge don't really care too much about ur personal statement, as long as u put in a decent amount of effort

unfortunately i'm not sure what they're changing it to, but i doubt cambridge maths will particularly care

[radiant jasper]

Cool, I'm glad I don't have to do contest math.

[radiant jasper]

I'm sorry for bugging you, but wdym by "a decent amount of effort", put in a decent amount of effort in what?

[deft wraith]

Into writing the new personal statement I'm guessing

[shadow spruce]

really

[high goblet]

i mean i'd like to preface this by saying i'm talking about cam maths here

but like why would they care?

like a good personal statement shows that ur good at bragging abt how good u are at maths

but like they don't want ppl who are good at bragging about how good they are at maths when they can do zilch for actual maths

like they have the interview and STEP

they can judge how good ppl are at maths based on those

so like cambridge ppl won't say that the personal statement doesn't matter bcus

• it may matter for some sbjects
• other unis may care abt ur personal statement

(and also bcus a bad personal statement will hurt ur chances, but a good one won't help u)

apparently one of my supervisors last year got in a bit of trouble with cambridge cus he seemed to imply that cambridge don't care abt ur personal statement on TV or smth lol

[ornate blade]

the personal statement is also important in filtering out motivations

do they want to do maths cause their parents told them to or something, even though they may be really good at maths

it's a sampler platter of the person's personality before Cambridge interviews them

[glad zinc]

Apparently there’s also this new thing in which your school must send your class rank for each subject

[ornate blade]

I can't confirm if that's true or false, but that sounds very un-UK to me

or that thing has always existed behind the scenes, but if so, I've never heard of that for the UK

that's standard for US elite unis for example

[glad zinc]

Yeah that’s what I thought but I’ve had multiple teachers in my school say that

[ornate blade]

it is possible that your teachers are just as uninformed as you

[glad zinc]

I don’t bother doing any research on whether it’s true or not because it’s good motivation to do well in tests 😭

[glad zinc]

Weirdly enough my school doesn’t send them for US unis but they re (they as in the teachers I talked to) saying UCAS is forcing them from next year to send rankings from next year

Hopefully it’s not true though because there are a lot of sweats in my year

[ornate blade]

okay then yeah I don't know then, if it's really a new change then that sounds normal

[glad zinc]

Btw are you in sixth form or uni?

[ornate blade]

that is also how news of new changes spread, like it always starts with rumours

uni

[glad zinc]

True true

I like how this channel has kinda become a UK uni admissions channel

[ornate blade]

lmaoooo

so true

[violet lichen]

no... can you explain pls

[shadow spruce]

same ratio？

[glad zinc]

How does one manage to get A in normal maths and S in step

[ornate blade]

ask them lol

[ornate blade]

maybe they're scared to admit A level maths wasn't challenging enough

and so they underachieved cause of boredom and not high enough expectations

[glad zinc]

I feel like it’s bait

[ornate blade]

or that

[deft wraith]

it's definitely bait

anyway they need to learn the art of alpha farming

[ornate blade]

oh yeah their comment is bait

[olive bay]

what in the world is STEP? can someone explain to me??

[ornate blade]

https://www.maths.cam.ac.uk/undergrad/admissions/step

read this

[olive bay]

is this for students? ive never heard of Math having levels

[ornate blade]

yes, high school students looking to enter Cambridge

it's just different question papers

STEP 2 is based on less advanced maths than STEP 3

but both are the same difficulty

[olive bay]

oh i see

[ornate blade]

so in A level Further Mathematics you learn additional content

I wouldn't say it's harder

just extending the maths you know a bit further

[olive bay]

we dont have much of that here in the philippines

also not a lot of math competitions here...

[ornate blade]

sad

there is SEAMO I know

[olive bay]

as if im actually good enough at math to actually be in a competition

[ornate blade]

you start small and work your way up

[olive bay]

what i am looking for here though is an entire.... how do i say this, curriculum

i want to start literally learning math in advance

[ornate blade]

https://artofproblemsolving.com/store

ah try these books

[olive bay]

oh

damn

oof, are those locked behind a paywall?

[ornate blade]

yeah you need to buy them

but the AoPS forums are very nice

there's AMC question papers since like 1990 or something

and solutions free online

[olive bay]

sounds fascinating

[ornate blade]

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

basically if you're just starting try doing AMC 8

then AMC 10 or UKMT's SMC

AMC 10 and 12 are challenging by international standards: the corresponding UK competitions are easier by far

well I mean other Asian countries are just as challenging

[olive bay]

wait these are actually fascinating

they dont visualize problems like this over here

thanks!

[glad zinc]

a levels are the standard exams sixth formers (grade 11 and 12s) study for in the UK

STEP is the cambridge math entrance exam

[olive bay]

oh i see

[glad zinc]

Theres also stuff like O levels and AS levels which are easier versions of it

this isn't only for maths its for all subjects

The Further Maths a level is probably the best structured A level, as it, in theory, allows you to pick what you study, there's further mechanics, further statistics, decision maths and further pure maths

Im saying "in theory" because in practice alot of sixth forms pick for you what selective modules you have to do

like my school forces everyone to do further mechanics 1 and further statistics 1

which is ideal for the engineers and all but I would rather be doing further pure 1 and 2

further mechanics is just yuck and Im doing AP Physics C:mechanics anyways

[gusty verge]

Literally every school does this I swear 😂 so rare to find further pure or decision schools

[gusty verge]

Further mechanics is a gift, lowest grade boundaries but super repetitive

[glad zinc]

I asked my teacher about why we do what we do, he said that the math department thinks we're too dumb to do the further pure vector topics because most students struggled with it the most in gcse and he said decision isn't real maths (something around those lines) 💀

tbf decision has alot of cs topics in it too, so it can get repetitive if you also take cs

[gusty verge]

Decision is by far the easiest option

[glad zinc]

for sure

[high goblet]

my school did:

1. AQA FM which is already very unsual and
2. mechanics & discrete

[high goblet]

also this is for sure bait

if ur not getting any alphas on past tripos papers that's not even a first class

(you can't get a first class degree without a single alpha, we calculated last year)

so if u're not even getting a first class degree there's no point wondering if ur gonna get 1st in the year lmao

[glad zinc]

wonder how aqa compares to edexcel in terms of difficulty

[gusty verge]

AQA is pretty common? I did AQA and have some AQA students

[high goblet]

AQA maths is not very common

the statistics say apparently

[gusty verge]

Yeah unexpected

[high goblet]

~13% of FM maths entries are for AQA

[gusty verge]

Edexcel leading probably

[high goblet]

i don't remember what the stats were for the others

[gusty verge]

Then OCR A?

[high goblet]

i know it is edexcel then OCR yeah

(idk what OCR A/B are)

[glad zinc]

its kinda weird and obscure, ocr a is done entirely by ocr and ocr b is organized by ocr and MEI together

ocr b has this paper 3 called Pure mathematics and comprehension instead of the normal just pure maths paper 1 ocr a has

they have some very interesting selective modules

ones called Further Pure with Technology

modelling with algorithms is an individual paper for some reason

[deft wraith]

i do further pure

[barren grail]

it looks terrifying

[barren grail]

my school offers it

[glad zinc]

have a look at the fp1 or fp2 papers

[barren grail]

no like d1 looks terrifying but its not so hard

fp1 is quite easy

fp2 i could learn in a few months

[glad zinc]

Whatever you say mate

[barren grail]

sorry thats like kinda wrong to say ngl

i already know a lot of the content of fp1

so i find it easy

[deft wraith]

i think it's pretty interesting

things like t-sub and lhopital are really useful

[plain jacinth]

So I took like 5 of the amc 10 practice tests and my scores are all in the range of being 15 points below the qual score to 5 points above the aime qual score. Are there any tips I could almost guarantee aime qual?

[swift imp]

See what you missed

Gain key ideas

And always remember you have next year (: even if nothing works out

[plain jacinth]

Thank you 🙏

[keen wasp]

dm me if someone figures it out pls

[glad zinc]

try asking in one of the available help channels like #help-14

[ornate blade]

someone has answered already @glad zinc

[karmic rune]

if only people bothered to follow up on their own posts...

[glad zinc]

oh alright

imagine asking a question multiple times in different channels then not even bothering to read the replies

yikes

[winter sable]

i m back

[cunning onyx]

Hello

[pallid ginkgo]

any olympiads thats around amc10 level about proving?

[modern prawn]

giys dumb question but

is amc 10b and amc 10a the exact same and only so students can take both amc 10 and 12

[pallid ginkgo]

what

[modern prawn]

is amc 10b and amc 10a tests made with the exact same type of questions and stuff, just different problem sets and given over different time periods

because what i’ve always thought it they have different topics and they were meant to be studied differently

[ornate blade]

yes, Canadian one

https://cemc.uwaterloo.ca/resources/past-contests?grade=All&academic_year=All&contest_category=25

click FGH

or for the upper end of AMC 10 there's the Euclid contest

[ornate blade]

I'd say this is the most comparable

[ornate blade]

yes that's the only difference

so you can take AMC 10 and 12 twice a year

however most schools only offer either A or B

but technically there's nothing in the rules that says it isn't allowed

reach out to other schools or other tutoring centres

[glad zinc]

How do I sign up for AMC as an intl I wanna do it for fun

[shadow spruce]

Grade 8 AMC10 how’s that

I think it is completely preposterous: shouldn’t be a test you study for, or at least should not be a test that you go take it and aim for a specific mark when you should not👀

[modern prawn]

i had a stroke reading this, why would u not want to aim for a specific score

[reef condor]

??

[swift imp]

what are you trying to say

it's always good to have goals but amc is like a week away so theres not a lot of chance rn

but its a year long contest studying so for the next few months just study how to do problems and when contest is near u just work on speed

[drowsy bough]

????

[vital mason]

add all equations

then u get (a+b+c)^2 = (x+y+z)^2

[drowsy bough]

i know this but whats next

From this what you wrote i got this: a+b+c=x+y+z

But that's not the same as what I have to prove

[drowsy bough]

anybody pleas?

[hidden fog]

bro ap stats is so boring

[untold thunder]

If you manage to show that 2xy+2yz+2zx-2ab-2bc-2ac is zero that's good but I am not trying that rn

with the a+b+c=x+y+z or -x-y-z

[surreal willow]

Yo chat like a week till the amc 10a, 12a

any of yall got plans on how to get into the AIME?

[sleek ivy]

Hope I’m better prepared next year that’s the plan

[high goblet]

we'd like to work in the variables a+b+c, ab+bc+ca and abc (and similarly for x,y,z)

this is quite common/a good thing to try if u've had lots of experience with symmetric polynomials

so you've added the equations up to get (a+b+c)^2 = (x+y+z)^2

what happens if we now add up the squares of the 3 equations?

[untold thunder]

That's smart

[idle halo]

Add the equations and then compute individual components

[surreal willow]

lol

What about this year?

[marble grove]

🆗

my friend said you guys are all cracked and that is why amc 10 is not competitive for u

[fathom sleet]

someone explain 5.2 rq pls what does mod cycle mean

[sleek ivy]

This year I’m cooked

[jolly solstice]

post the question idk what they're talking about

[slender saddle]

2%7=2
4%7=4
8%7=1
16%7=2
32%7=4
...

[winter sable]

do u guys remember me

[ornate blade]

yes

it's not like you were gone a year

[winter sable]

yyay

what the f(x)

[deft wraith]

what haha

[ornate blade]

@undone spindle

reposted your question here since the help channel got closed

!help

[scarlet root]

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

[ornate blade]

you should post in an open channel next time

[undone spindle]

Ok

[ornate blade]

I have an idea actually

from componendo and dividendo, $\frac{x + y}{x - y} = \frac{a}{b} \implies \frac{x + y}{(x + y) + (x - y)} = \frac{a}{a + b}$

so we just need the value of $1 + \frac{y}{x}$

now let $y = kx$ and thus $x^2 - k^2 x^2 = 2k x^2$

[gilded halo]

south's secret twin brother

[radiant jasper]

x,y>0

[vague temple]

Factor the LHS. We get a difference of squares.

[ornate blade]

alternatively, yes

[radiant jasper]

or both x and y should be less than

[vague temple]

It would we nice to have (x-y)^2 to divide. We can add 2y^2 to both sides

[radiant jasper]

0

since

we get

(x+y) ^2/2xy

[vague temple]

Divide through, consider cases, answer is (1 + sqrt(2) + (-sqrt(2)) = 2.

[radiant jasper]

divide through?

[vague temple]

Divide equations

[radiant jasper]

what equations?

like which equations

[drowsy bough]

I dont understand. can you explain it to me in more detail?

[vague temple]

What I described gives you (x^2-y^2)/(x-y)^2 = (x+y)/(x-y) = x/y

If you consider the cases in (x-y)^2 = 2y^2, you get the answer

[radiant jasper]

why

is

x+y/x-y = x/y

[vague temple]

Did you write out the steps I described? It should clarify

[radiant jasper]

i dont understand

why

[radiant jasper]

this

[vague temple]

Here: factoring 5e original equation, we have (x-y)(x+y) on the LHS. It would be nice to have another equation in (x-y)^2 so when we divide the two, it would give us the desired expression. Conveniently, we can do this by adding 2y^2 to both sides and rearranging and factoring

[radiant jasper]

shouldnt we

subtract

2y squared

but damn

thats nice

[vague temple]

No, we do add it.

[radiant jasper]

why tho

[vague temple]

Did you write out the math?

Try doing both and see which ones works to confirm

[radiant jasper]

brother

do you not want

x-y

in the RHS

[vague temple]

It does work out nicely since in most competitive math questions like these, it is designed to be this way.

[vague temple]

No, we are putting (x-y)^2 in the LHS.

[radiant jasper]

putting as in

adding or dividing?

[vague temple]

Creating it artificially by adding 2y^2 on both sides

Try it

[radiant jasper]

so ur trying to acheive

x^2 + y^2 in the LHS

right?

[vague temple]

What does moving the 2xy over to the LHS then allow you to do?

[radiant jasper]

wiat what

[radiant jasper]

thier ight or worng?

[high goblet]

add up the squares of ur 3 equations

so (a^2+bc)^2 + etc. = (x^2 + 2yz)^2 + etc.

then simplify

[glad zinc]

Met tom rocks maths today

such a cool guy

[ornate blade]

wtf

lucky

[glad zinc]

yeah bro idek how to they got him to come all the way to dubai just to visit our school 💀

he talked about his PHD thesis and how he worked with mr beast

then in another presentation today (the other one was yesterday) he did mock interviews with some y13s applying to oxbridge in front of an audience

was pretty cool, the y13s did really decently too

I asked my teacher and next year they may try get grant sanderson (3blue1brown) to come, Im literally praying every single day it happens

[ornate blade]

wait what

since when did that even happen

[ornate blade]

how rich is your school

cause we had people come to our school but they weren't famous

they were from like important charities but no one knows who they are

[drowsy bough]

thank you

[drowsy bough]

And whats next?

I developed the expression from the shortened multiplication formula

And I got

a^4 +4a^2 bc+4b^2 c^2+...=x^4 +4x^2 bc+4z^2 x^2+...

And i dont understend how can I simplify this more

[high goblet]

^

rewrite that in terms of our elementary symmetric polys

[drowsy bough]

So a=ab?

I dont get it

[glad zinc]

He worked on the ocean thing that they did where they took out 1 pound of trash every 1 dollar donated, and his thesis is about how water and trash moves around the world and looking into stuff like if you have the outflow of a river where would most of the current and trash flow to and group up. So they used that and worked with another company to maximize the efficiency of where the cleaning boats went. There was some interesting math involved but because the first session he had had everyone in it he didn't go that deep into math, he just showed some of the ODEs and the solutions he got. He also did a demonstration of the coriolis effect which was pretty cool

At the end I went up to him to ask whether he could come to my presentation for a club but it was at the same time as the oxbridge interview session he was doing so he couldnt : (, I ended up cancelling my presentation to go to that too 💀

overall was great experience

[drowsy bough]

Could you describe this solution to me in more detail?

[glad zinc]

dubai

[high goblet]

i mean i think he is like one of the maths outreach ppl for oxford so it sorta makes sense

i missed the oppourtunity but a few of my friends met tomrocksmaths and james grime last year cus they filmed a video in front of trinity

https://www.youtube.com/watch?v=1S-BeWzpU5s&ab_channel=TomRocksMaths

it was this

[high goblet]

i mean just expand and write in terms of a+b+c, ab+bc+ca, abc etc.

or even more explicitly, define s=a+b+c, t=ab+bc+ca, u=abc and rewrite

(a^2+bc)^2 + (b^2+ac)^2 + (c^2+ab)^2 = (x^2+yz)^2 + (y^2+xz)^2 + (z^2+xy)^2 in terms of s,t,u (i.e. eliminate a,b,c)

and then do the same for x,y,z

i can't give u anything more without just telling u the answer

[drowsy bough]

I have this

And what should i do now?

[high goblet]

let's try to get rid of the a^4 + b^4 + c^4

so maybe we should try using (a+b+c)^4 first

what do we need to do next

[drowsy bough]

i have no idea how can i simplify it to the (a+b+c)^4

[high goblet]

subtract off (a+b+c)^4 then see what u havve left

then try to simplify that

[balmy lintel]

Solve 273x +1003y=1 over ints?

[drowsy bough]

If I understand correctly, I have to subtract from (a+b+c)^4 the (a^2+bc)^2 + (b^2+ac)^2 + (c^2+ab)^2???

[high goblet]

yeah

[balmy lintel]

Nvm its with Euclidean algorithm

[drowsy bough]

And what can i do with this

i dont see this

[high goblet]

let's try getting rid of the 4a^3b terms instead

that suggests adding 4(a+b+c)^2(ab+bc+ca)

anyway i'm busy working but you should find

it equals that

anyway idk what sort of level of maths competitions ur doing

but if ur doing like harder olympiads for ur country, being able to rewrite symmetric polynomials like the ones u have into this form is a very useful skill to have

[drowsy bough]

I got this, but whats next with that

[high goblet]

we know (a+b+c)^2 = (x+y+z)^2

so then use that to finish

[drowsy bough]

Can I just do this like that?

[high goblet]

how did you get bc+ca+ab = xy+yz+zx

[drowsy bough]

bc+ca+ab=yz+zx+xy is a consequence of the fact that the sum of the three equations results in a single combined equation.

But idk

Im not sure

[high goblet]

as in you have (a+b+c)^4 - 4(a+b+c)^2(ab+bc+ca) + 6(ab+bc+ca)^2 = the same with x

now (x+y+z)^2 = (a+b+c)^2 := K

also for convenience, set ab+bc+ca = S, xy+yz+zx = T

then we get

6S^2 - 4KS = 6T^2 - 4KT

so (S-T)(3(S+T) - 2K) = 0

if S - T = 0 we are done, so we want to show S-T = 0

if S-T doesn't equal 0

then 3(S+T) = 2K

i cba to do the rest but you just get a contradiction

since 3S <= K etc.

[fathom sleet]

so remainder basically

[hollow berry]

This is cheating as its an ongoing contest

https://om.sem.edu.pl/static/app_main/problems/om76_1.pdf?series=2

[cerulean ibex]

<@&268886789983436800>

the cheating guy and also the other server

[orchid sentinel]

Hi, I have an olympiad problem I am trying to solve, and am wondering if anyone wants to work on it with me. I am just looking to bounce ideas around or something, we dont have to rigorously solve it

There is no obvious way into the question it seems

[radiant jasper]

Post it!

@orchid sentinel

[radiant jasper]

Maybe try a proof by contradiction?

Is this imo

[orchid sentinel]

I am new to these kinds of questions, but my basic insight is that if we fix $N$, then we have say $r$ distinct variables, which we could express as $x_1^{\alpha_1} + \ldots + x_r^{\alpha_r}$ where $\alpha_1 + \ldots + \alpha_r = N$.

[gilded halo]

Tear

[orchid sentinel]

Yes

It could be generating function question

[radiant jasper]

Idk

There may be some induction or something’s

[orchid sentinel]

Yes sure, but to actually attempt to solve a question you need to know roughly what area of math you need

[radiant jasper]

I only have experience with olympiad geo proofs lmao

[radiant jasper]

This is algebra no?

[orchid sentinel]

What makes you think it is algebra

[radiant jasper]

Okay i have no clue

Sorry

[radiant jasper]

Ok i dont know what i was thibking this is combinatorics

[orchid sentinel]

Yeh I'm starting to think combinatorics too

A bit of number theory as well since we are dealing with eventual periodicity

[radiant jasper]

Maybe visualizing the problem would help

[glad zinc]

oh yeah he talked about that, wild how he teaches at cambridge and oxford now

[high goblet]

bruh

my olmpiad NT and olympiad algebra are much better than my olympiad combinatorics so i didn't give this question much thought

[high goblet]

i mean the first thing i thought when i read the problem is this thing is true???

so i just tried computing some small things by hand

i set N=4, a1 = 1, a2=2, a3=3, a4=4

you'll have to do it for a while but eventually it does repeat

and then i also tried proving it for N=1

proving it for N=1 isn't too hard

it's been quite a while though

so the first thing i would recommend is to just compute some smaller values

(honestly i need to do that asw cus i don't think i tried enough values to get a sense of idea for the problem)

[high goblet]

how exactly does this help?

[high goblet]

i mean... this is completely combinatorics

there is no world in which this is algebra/nt

[reef condor]

Isn’t this imo 3…

[winter sable]

i m back

what the f(x)

[winter sable]

sir galhand u r the best

[fiery minnow]

https://tenor.com/view/nerd-emoji-nerd-emoji-avalon-play-avalon-gif-24241051

[radiant jasper]

That's the truest thing you'll ever say.

[winter sable]

yes

[vague temple]

Looks like each a_n is bounded, could it be possible to apply the Pigeonhole principle? Then, using the recursive nature, determine periodicity

[high goblet]

wdym by each a_n is bounded?

[vague temple]

Bounded between 1 and n - 1

For n > N

[high goblet]

why?

oh wait nvm i see what ur saying

hmm might be useful if we could achieve a better bound

actually i do know that step one of what to do is show that one of the sequences is unbounded

so that tells us there are infinitely many 1s in one of our sequence

if we could bound this other seq. that'd be good

wrong channel, go to #probability-statistics

[whole hornet]

Thanks no problem

[glad zinc]

Just found out a couple goldman sachs IB and other department reps/employees are coming to my HS, i cannot fathom what on earth my school is doing to attract these people 😭 Hopefully they have a quant guy with them so I can bombard him with questions

[jade widget]

i just look up the amc question for my first time, i feel so cooked

especially geometry😭

how do u guys prepare for it?

[vivid ingot]

<@&268886789983436800> spam

[fallen magnet]

did anyone do the senior maths challenge for ukmt?

if yes, what score did u guys get?

[deft wraith]

i did

[fallen magnet]

i was wondering when the olympiad challenge is and what score was needed for it?

bc i got 113

[radiant jasper]

ERM

WHAT THE ORZ

[fallen magnet]

what

[radiant jasper]

ORZ

[fallen magnet]

tf is orz

[fallen magnet]

tf lmao

ezzz

i left 3 questions so that means i basically got full marks

[radiant jasper]

used to show respect to someone who is very good at math or some subject

"orz" resembles a person bowing

[fallen magnet]

i see

[radiant jasper]

i hope you make the british imo team :)

[fallen magnet]

do i get money?

[radiant jasper]

what

[fallen magnet]

do i earn money if im in the team?

[radiant jasper]

no?

[fallen magnet]

then id rather not

lol

[radiant jasper]

💀

[soft vigil]

first thing is to not start prepping 1 week befor ehte contest

second is to learn the theory

third is to do problems

[fallen magnet]

unrelated but i didnt revise or anything for ukmt 💀

[jade widget]

oki thx

[soft vigil]

also mock tests are important

make your own strat to maximize score

[jade widget]

oki ill try it

[glad zinc]

You do it for the love of the game not money

I’m not British so I can’t make the team

[fallen magnet]

u need to be 17-18 to do the senior maths challenge

[glad zinc]

Tbf I’m probably not good enough either but I would’ve actually worked on comp math if I knew I could

[glad zinc]

That’s not true

[fallen magnet]

idk about the team

[glad zinc]

I did it at 15 and this year at 16

[fallen magnet]

well its targetted at that age

[fallen magnet]

wtf

what score did u get tbf

[glad zinc]

Full 😭

[fallen magnet]

nah ur capping

[glad zinc]

On god i got full bro

[quick frost]

Ouch.

[glad zinc]

It was easy this year

Last year I did worse

Hoping for BMO2 qual and merit this year

But it’s looking rough as BMO1 is soon and I have not done any prep as always cause I’m fucking stupid

[fallen magnet]

bro is not doing this question at 16 😭

[glad zinc]

12

[fallen magnet]

i didnt revise

[fallen magnet]

i refuse to believe u

[glad zinc]

Give me a minute

[fallen magnet]

damn

ima sleep

[glad zinc]

lol

[soft vigil]

this has got to ba a troll problem

just 24*1/2 makes the most sense

[fallen magnet]

3am for me 😭

[glad zinc]

Oh fair enough gn

[slender saddle]

!noans btw

[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.

[slender saddle]

Wait what’s the helper version of this

!nosol

!nosols

[scarlet root]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[slender saddle]

Ah

[ornate blade]

AMC12 is harder

[swift imp]

Oh yea amc like next week

Time to prep

[ornate blade]

good luck!

[fleet grotto]

How did you calculate that?

[ornate blade]

also consider the shapes (P + Q) and (Q + R)

[fleet grotto]

Thank you!!!

[ornate blade]

no worries!

[quick frost]

I still don't get it. 💀

[ornate blade]

I am green and I am not easily fooled

[soft vigil]

🤯

[quick frost]

Oh the triangles on the right have the same area

[ornate blade]

indeed

split the equilateral triangle in half then join the two shorter sides

[quick frost]

Hence P + S + R = 3P

[ornate blade]

yes!

well I cheated, looked at the sol

[quick frost]

You can also reflect S about the line joining Y and the common vertex of Q, R, S; then observe that the left-out part of Q is (after breaking into two pieces and separating them) the same as the extra part of R to the left of the radius from X.

[ornate blade]

T is different though, cause it has a straight side

oh

ah that's insane, it works

so you get half the semicircle exactly

[ornate blade]

interesting q btw

3bc = 10b + c for example implies c = 10b/(3b - 1)

now gcd(3b - 1, 10b) = gcd(3b - 1, b + 3) = gcd(3b - 1, 3b + 9) = gcd(10, 3b + 9) and we want this not to equal 1

since 10 is not divisible by 3, 10 and b + 3 must have common factors

that leaves b = 1, 2, 7, but if we sub back into the original equation for c, we can't have b = 7

2bc = 10b + c can be factored as (2b - 1)(c - 5) = 5 btw

so that gives a = 2, b = 3, c = 6 only

I mean somehow the product of these numbers is always divisible by like 6

612 is the other answer

[high goblet]

if u make trincamp trinity give u £120 lol

[high goblet]

nah any age is possible

alex chui has been doing SMC since y9 and he's made IMO team every single time