competition-math

[royal estuary]

And uh

Have some chocolate

Before the comp

Enhances brain function

[high goblet]

ahaha lol

[mental elbow]

yeah i heard that seems interesting

[royal estuary]

Yeah

[mental elbow]

what’s a reasonable score I should aim for if it is my first time in a math comp

[high goblet]

if it's ur first time, don't really stress about it

just enjoy the exam

[royal estuary]

Idk about amc

Ask someone from murica

[mental elbow]

murica

land of the free

[high goblet]

do as many problems as u can etc.

[royal estuary]

🦅🦅🦅

🔫🔫🔫

[mental elbow]

thanks

honestly i’ve been trying to practice the number theory and probability a bunch

cuz they never taught it in school

[royal estuary]

Do some geometry

From egmo

That helps

[mental elbow]

hmmm okay

[high goblet]

unless i seriously misremembered, i don't think EGMO is appropriate for AMC10 lmao

[royal estuary]

Why

Is it less difficult

[high goblet]

too hard lol

[royal estuary]

Oh

Shoot

[high goblet]

EGMO is more for USAMO/IMO/other international maths olys etc.

[ornate blade]

yeah AMC10 questions are publicly available

just check AoPS

[mental elbow]

yeah been practicing them for around a week

[royal estuary]

I completed egmo for the first selection round in my country

[mental elbow]

i like how they have different solutions

[high goblet]

i'm gonna quickly find a past paper

but yeah like if it's ur first time competing, don't stress too hard

etc.

[mental elbow]

ok by the way what is egmo cuz i searched it up and it gave two results

[royal estuary]

Euclidean geometry for math Olympiads

[mental elbow]

is it girls olympiad or a book

[royal estuary]

Evan chen

Ig

Auhtor

[mental elbow]

oh okay

[high goblet]

if ur looking to improve, probably firstly u'll want to get resillient to like trying for a while without making any real progress

like as u get into harder problems i.e. for USAMO, USAJMO etc. u'll be trying to a very long time without making much progress

[mental elbow]

i feel like resilience isn’t a problem i just am really inefficient at times

[high goblet]

i suspect the later questions for AMC10 will get fairly tough so stick with it and u'll improve

[mental elbow]

meaning i will take too much time on questions

[royal estuary]

The starting questions are really easy tho

[ornate blade]

agreed

like that's the way AMC works

[mental elbow]

yeah they get harder as you go on

[royal estuary]

So make sure you do the first few for sure

[ornate blade]

only questions 20 to 25 are hard I'd say for AMC10

the rest just need some thinking

[royal estuary]

Don't skip the first few problems

[ornate blade]

honestly start off easy

[royal estuary]

And then take your time on the later ones

[high goblet]

basically like u might find urself quite stuck on qs 20-25 - stick with it!

[ornate blade]

this is fairly representative of AMC10 geometry

don't be intimidated

[mental elbow]

bruh

[royal estuary]

Not that hard

[high goblet]

i'm not american so i can't say for sure what they're like but like i don't think they should be too hard, so if u stick with it long enough it should be fine

[mental elbow]

fr

[high goblet]

EGMO over in europe i.e. UK usually refers to European Girls' maths olympiad

[mental elbow]

is it asking for shaded regions area?

[high goblet]

but depending on context, obvs sometimes we'd be referring to evan chen's book

also really don't bother with it yet

[mental elbow]

👍

[high goblet]

like there's no point getting EGMO if u haven't even gotten to the olympiads yet lol

[mental elbow]

i agree

[ornate blade]

yes

[mental elbow]

can you explain the solution to number 16 please

my thought process is that you would obviously find the area of the smaller circle and subtract thirteen of them from the larger circle

[royal estuary]

Coordinate bash

Ik bored

[ornate blade]

hint: ||radius is equilateral triangle + r||

[royal estuary]

Let's complex bash

[high goblet]

bruh

[ornate blade]

yeah so if you can find the radius or diameter of the larger circle you're good

[mental elbow]

hmm

ion get this one

how would you find the larger circles radius

[royal estuary]

Construction or something

Try some construction s

[ornate blade]

bigger hint

[royal estuary]

Which leads you to radius

[royal estuary]

Yeah basically solved the question

[mental elbow]

uhh

[ornate blade]

so ABC is half of an equilateral triangle...

[mental elbow]

yeah

wait lemme think

[white hull]

you can form a triangle with the radiuses of the circle

where the triangle is inscribed in the circle

and to find the median use

the ratio formula

yeah no

i lied

[mental elbow]

idk what allat means bro

[white hull]

ok here

use pythagoras theorem

[royal estuary]

Just use median= √3/2p

[white hull]

so its (2sqrt3 + 1)*smaller radius

[royal estuary]

P is side of equilateral triangle

[royal estuary]

Kinda complicated

Just make one right triangle

[mental elbow]

ohhhhh

[royal estuary]

Then find the perpendicular

[mental elbow]

that’s a very cool solution

[royal estuary]

And add 1 unit

[white hull]

idk that was the first thing i thought of

[royal estuary]

Try seeing the solution of IMO problems

Yeah valid

Just stating the efficiency

For the methods

From comp pov

[mental elbow]

yo south

[white hull]

js wondering

[mental elbow]

can i see your solution

[white hull]

for competitions

[royal estuary]

Yeah probably what I told

[white hull]

would you have to know a lot of niche formulas

[high goblet]

2 nons who clearly don't know how to help someone with AMC10 try to help someone with AMC10

[royal estuary]

Find the perpendicular of the triangle

[mental elbow]

could you show it in a diagram plz

[mental elbow]

crazy lol

[royal estuary]

Yeah ur kinda right

I can't help

Idk why

[high goblet]

but please more seriously, incowl said to let him think

[ornate blade]

https://artofproblemsolving.com/wiki/index.php/2019_AMC_10A_Problems/Problem_16

check out solution 4 here

[high goblet]

please don't just give away the answer/more hints just bcus u can

[mental elbow]

got it

[ornate blade]

I'm loving the 2019 AMC10A for some reason

[mental elbow]

south i was actually kinda close

[ornate blade]

I feel like this is just the right difficulty

[ornate blade]

wow

[mental elbow]

it’s just late at night and i’m reading off my phone so i messed it up

[white hull]

oh are you not supposed to

[ornate blade]

but you see you're more capable than you think

[ornate blade]

I would recommend spoilering the hints

[mental elbow]

yesssir

put an extra s

that’s how capable i am

[white hull]

my fault king

[royal estuary]

Yo solve this

[mental elbow]

vro

[royal estuary]

Kinda looks like a hotdog

[mental elbow]

i am not reading that bro my eyes are so tired

it’s like 1:30 am

[royal estuary]

Oh not you

Just whoever can

[mental elbow]

word

ayo south can you slide another geo problem that you think is good

[royal estuary]

I have one if u want

Amc 10

Level

[mental elbow]

👍

[ornate blade]

maybe this?

[royal estuary]

Try the geo problems from here

[mental elbow]

ok south lemme get a paper

[ornate blade]

I don't want to give ones with too much construction

and that are from AMC10 ideally

[royal estuary]

5,13,14,15 if I remember

[ornate blade]

ah this one uses the angle bisector theorem

or there are definitely other ways but

[royal estuary]

I remember a solution which uses the m:n angle theorem

[ornate blade]

it's like deriving tan of 15 degrees

[mental elbow]

ah shoot my trig is bad

i have ideas tho

[ornate blade]

there is a non trig solution btw

[mental elbow]

ok lemme see if i can find something here

[ornate blade]

diagram if you want it

[mental elbow]

what is h?

[jolly geyser]

Is it possible for one of ϕ∨(ψ∧θ) and (ϕ∨ψ)∧(ϕ∨θ) to be true and the other false? (If not, then the distributive property holds for disjunction across conjunction.) plz help

me with thissssssssss

[high goblet]

that is how it expands, yes

this more belongs to #proofs-and-logic btw

[ornate blade]

h = AF = FD

[jolly geyser]

can u elaborate ?

[mental elbow]

okay

[high goblet]

as in ϕ∨(ψ∧θ) = (ϕ∨ψ)∧(ϕ∨θ), so either both are true or both are false

[jolly geyser]

ohhke i see

[ornate blade]

also like AC = 5, cause the diagram isn't 100% clear

[mental elbow]

yeah

[high goblet]

remind me what age AMC10 is again?

if u want the UK competitions i can link them here, i thought they were quite good

[mental elbow]

9th and 10th grade

[jolly geyser]

can u tell me some lectures or videos for mathematical thinking or proof type question ?

like this one

[high goblet]

what's that in UK years lol 1 sec

[mental elbow]

dw one of my best friends is in the UK

[high goblet]

ok Y10/Y11

[mental elbow]

yeah

[high goblet]

https://ukmt.org.uk/competition-papers/jsf/jet-engine:free-past-papers/tax/challenge-type:70/#free-past-paper-anchor

[mental elbow]

i am Y10

[high goblet]

problems from here should be appropriate then

probably only do them if u run out of AMC10 problems to do tho

[jolly geyser]

can u tell me some lectures or videos for mathematical thinking or proof type question ?

[royal estuary]

Oi

Chewkzday innit

[jolly geyser]

u indian ?

[mental elbow]

nah

[high goblet]

also for ur first year i wouldn't stress too much about trying to do well, cus u still have like many years left

[mental elbow]

bro my friend who is my age already has been to the AIME 😭

[high goblet]

and there was someone 2 years younger than me who already did the IMO twice in my first year of olympiad stuff!

don't worry too much about comparing urself to ppl ur age lol

[mental elbow]

nah bro that’s crazy

IMO is wild

[royal estuary]

Yk what's bad

[high goblet]

some ppl are like late bloomers

[royal estuary]

My friend been to imo

Same class

And won gold

This year

[mental elbow]

tell bro to slide the intelligence steroids

also south

can you tell me if my idea is rational/ makes sense

actually i think i could probably do this with some trig

[ornate blade]

what idea?

[mental elbow]

actually it doesn’t make sense

i was thinking to perpendicularly bisect angle DCE to get the altitude of the triangle

[ornate blade]

sure, you can do that and you'd get the altitude being 5/sqrt(2)

if the midpoint of DE is M though

the problem is that DCM would be 15 degrees

so that's the tan 15 degrees issue I was talking about

[mental elbow]

bringing this down here so i don’t have to scroll

how do you get 5/sqrt2 for altitude

[ornate blade]

oh, it's an isosceles right triangle

so $a^2 + a^2 = 5^2$

[gilded halo]

south's secret twin brother

[ornate blade]

in other words, triangle BMC is similar to BCA

so MC = MB and so on

[boreal sky]

I see, thankyou sir

[mental elbow]

ok

mb i fell asleep

[deft wraith]

i saw roughly that someone was talking about amc10 questions - as ly said the senior maths challenge is probably the right difficulty, but there are lots of mocks on AoPS and a lot of them are collated on MathDash as well (which I reccomend) and possibly the AusMO first round if i can remember correctly

cc: @mental elbow i think

[glad zinc]

Do PUTNAM questions its good prep for AMC 8 or 10

[ornate blade]

yeah AMC12 is probably too hard for SMC

[deft wraith]

yes

even amc10 last few questions might be -- can't remember very well

[ornate blade]

I think AMC10 is just about right for SMC

also both competitions have 5 answer choices

and you get more time for the SMC, 90 minutes vs 75

#serious-discussion message

also check out my solution to an AMC10 question

I feel this is representative of the last few in SMC

[ornate blade]

some geometry questions are more algebra bashing than others

[ornate blade]

no you're right, AMC10 last few questions vary quite a bit in difficulty

SMC is much more consistent

I'd say problem 22 is a fair bit easier than 23

this is an algebra bash

the worst part is yep, no calculator allowed

[winter sable]

i am indian y/o

[winter sable]

easy

[ornate blade]

oh wait...... problem 23 I think I got the method

[ornate blade]

Indian years old?

$\frac{4r^3 / 3}{(1 - k^3)/3} = \frac{1}{2} \implies 8r^3 = 1 - k^3$ and $4r^2 + 1 - 2k + k^2 = k^2 + 2k + 1$

[deft wraith]

i think 20-25 AMC10 is slightly harder than 20-25 SMC

[ornate blade]

I misread my own diagram RIP

[gilded halo]

south's secret twin brother

[ornate blade]

yeah the more I look into this, the more SMC seems genuinely easier

[winter sable]

yes sir

i solved college maths in 8th i am at 9th now

studying on quantum mechanics

[ornate blade]

what kind of uni maths btw?

ok wow

https://www.damtp.cam.ac.uk/user/tong/teaching.html

don't know if you've seen these lecture notes before

[winter sable]

calculus , linear algebra , probability , differential equations i have done

wbu

[ornate blade]

I'm at uni so

[winter sable]

damn

old

[ornate blade]

20

[winter sable]

big brother

[ornate blade]

well I'm not doing maths at uni from next sem

[winter sable]

i am 4

14*

[ornate blade]

but yeah I did some comp maths at high school

[winter sable]

coool

i am studying cs now too

0!

[balmy lintel]

I checked the solutions and they used Vieta and Chauchy-Scwartz ineq. I proved it via contradiction and differentiation, is it still acceptable? I can send the proof too

[jolly solstice]

can't really say without seeing it

[high goblet]

probably send in ur solution and then ppl can check if it's correct

are u US? i would like to warn u that some countries are quite averse to calculus methods for olympiad stuff

(like in particular the UK is quite against calculus methods for pre-uni olympiads)

i think the US doesn't really care about calculus vs non-calculus

but anyway yeah if u have a correct calculus solution then they won't mark it down, but yeah just as a precaution that some countries would prefer non-calculus solutions

[balmy lintel]

Not US but its not something too advanced yk

[deft wraith]

is this from the paul zeitz book

i was doing it earlier

[balmy lintel]

Yeah lol

[deft wraith]

why don;'t you use the 3rd ed

actually it might be screenshot might just be blurry on my end

[balmy lintel]

I didn't know there was a 3rd version

Whats the difference

Oh shoot it's substantial, let me switch real quick

[high goblet]

i didn't actually check ur algebra but ur method seems fine

one note is that u forgot to say at most 1 real root (u said has 1 real root at the start)

oh wait f'' is a cubic nvm

[high goblet]

anyway also what theorem are you quoting? fermat's?

[balmy lintel]

Ye

[balmy lintel]

There's a theorem by Fermat that states that in a closed interval [a,b] s.t a<b if there exists a root of f then there must exist some point s.t the derivative equals 0 (it's pretty easy to see why if you draw a diagram)

[high goblet]

f(x) = -x?

[balmy lintel]

Wait

[high goblet]

do u mean if there exists 2 roots in that closed interval then there exists a point where f'(x) = 0?

[balmy lintel]

Wait hold up

Yeah

In general

[high goblet]

also that's Rolle's thm

[balmy lintel]

If f(a)=f(b)

[high goblet]

unless Fermat proved a similar more specific version of the theorem that i am unaware about

[balmy lintel]

Na cus it's for derivative

[high goblet]

you are using this right?

[balmy lintel]

Ye

[high goblet]

yeah it's rolle

[balmy lintel]

Oh

Damn

Alr anws thanks for the help!

[high goblet]

nw!

[jaunty fern]

25

[high goblet]

oh whoops didn't reply to this

the reason why some countries don't particularly like calculus in olympiads isn't bcus calculus isn't 'too advaned', but more bcus unless u've learnt analysis, ur probably doing calculus without being able to prove any of the facts u use

like rolle's thm is very intuitive, but can u prove it rigorously?

otherwise some ppl view using calculus in general to be a bit like just quoting advanced thms

like it's great calculus works, but if u can't really prove why it works then ur just relying on a lot of previous theory

anyway that's why some countries are sort-of against use of calculus in pre-uni olympiads

[balmy lintel]

Hhmm but dont you already use a lot of preset theories to solve these probs

Especially in geo

[high goblet]

but the thing with geo, students will usually be able to prove the thms they use

like if someone uses i.e. simpson line, you could reasonably expect them to be able to prove it

similarly if someone uses 9 point circle, then it's reasonable that they would be able to prove it exists rigorously

whereas if u ask someone to prove rigorously that if f'(x) >= 0, then f is increasing

not many high-school students would be able to

[high goblet]

as in like in the US, for some reason this is 2nd year/3rd year content (i believe) cus real analysis is a 2nd year course for US students

(for the UK it's basically first year at every uni)

anyway so that's kinda why some countries aren't too fond of ppl using calculus cus it's like u can reasonably expect students to prove basic geo thms that they use, whereas it's a bit harder to expect students to be able to recite a proof from uni content

[balmy lintel]

Fair argument, but still I guess I get the point that they dont want to encourage memorisation over critical however its still a tool in ones arsenal and I personally can say that I dont know how to prove 15% of the stuff I use rigously

[balmy lintel]

I guess I should also mention that here where I live we do proper calc and uni stuff in high school

So I cant really speak for every country

[high goblet]

wait really?

[balmy lintel]

Our entry level exams have calc

[high goblet]

what like defining what a limit actually is

[balmy lintel]

Nono like hard calc stuff

[high goblet]

proving stuff like this?

[balmy lintel]

Hold up let me find some

[deft wraith]

do you have to be able to prove something like fermat's christmas theorem

[balmy lintel]

For example this problem

Given a function f with the following properties

f is continuous in [0,1] and differentiable in (0,1)

f(x)≠0, for every x in [0,1]

f(1)-f(0)=f(1)f(0)

Show that f'(x)-2xf²(x)=0 has at least 1 sol in (0,1)

[high goblet]

oh right interesting

it's not analysis tho so we still get the same issue

[balmy lintel]

3rd year p3/4 whole country level question

Pretty easy tho

[high goblet]

but anyway yeah u'll probs wanna check what ur country's attitude on using calculus in olympiads is

[high goblet]

as in u don't have to prove it if u use it

like the proof is fairly elementary, just a bit boring and tedious

[high goblet]

bruh, this result is from erdos lol

i'm not good at combinatorics lol, try like #combinatorial-structures

[onyx birch]

no

the result is different

cause this is about REAL numbers

[onyx birch]

tried

[high goblet]

oh shoot yeah mb

[cerulean ibex]

see what i posted in combinatorial structures

[stiff zealot]

make a damn help channel abraham

[short condor]

make sure you @ helpers when you do make a channel

[stoic lake]

[rotund edge]

Thank you!

[frozen palm]

Do you guys have any pointers on what to study for a math competition in highschool?

12th grade to be specific

[royal estuary]

What problem set is this from

[swift imp]

Not allowed

To discuss

[swift imp]

It’s a live contest rn

[soft vigil]

LMAO

THIS IS A LIVE CONTEEST

ITS GOING ON RN

[swift imp]

bros boutta get kicked out of the contest 💀

[soft vigil]

ong

also why wait till the final day

theres a full month to do it

[swift imp]

he prob just found out about the contest and asked for the 2 day extension 💀

[crisp sundial]

Lol, I responded

I'll go delete what I sent

[swift imp]

@sick fable there is someone who is sending live contest problems

[sick fable]

and theyve been banned

hence why their messages are gone

[swift imp]

oh

@soft vigil W moments

[soft vigil]

lmao

[crisp sundial]

Was a cool problem tho

[soft vigil]

ye

[swift imp]

yea

he couldve waited legit

3 days

[soft vigil]

lol

isnt deadline soon

[swift imp]

today

theres a 2 day extension period tho

[soft vigil]

yeah

22 minutes

[swift imp]

and next round starts friday

and solutions come out then too

did u do usamts @soft vigil

[shy anchor]

if you guys are so smart, could you pretty please with cherries on top help me with this math problem that Chat GPT called "mathematically impossible"? Someone else in this server couldn't solve it either. Please and thank you!

[swift imp]

no one said we were smart 💀

[soft vigil]

yes

but lets not discus now

[shy anchor]

you're doing math voluntarily

[swift imp]

yes i did all 5 problems

[soft vigil]

https://tenor.com/view/throwing-daniel-stahl-sweden-nbc-olympics-discus-throw-gif-22949868

no discus

[swift imp]

i have been doing math voluntarily for like my whole life 💀

[soft vigil]

ong

[swift imp]

my asian parents kicked me out to go to after school tutoring

[shy anchor]

mind doing my math voluntarily? Pretty please

[swift imp]

err

nrn

[shy anchor]

you finished all 5 of your other problems anyway

[swift imp]

i have 50 calc 3 homework problems to go thru 💀

[shy anchor]

damn

[soft vigil]

💀

[swift imp]

true procrastination

[soft vigil]

spam parallel lines ngl

[swift imp]

too busy grinding geometry

and then forgot calc 3

[shy anchor]

what does that even mean

[swift imp]

it means draw parallel lines

[shy anchor]

this is a diagram that someone else in the server made; https://www.desmos.com/geometry/ptnf091aku. How many parallel lines do you see

[soft vigil]

1 set

lol

[shy anchor]

exactly

[soft vigil]

wait a minute

i made the wrong diagram

oh this is easy right

just 360-139-174

ye

[swift imp]

ok asian

[soft vigil]

im not asian

[shy anchor]

you

[soft vigil]

nice try tho

[swift imp]

i am from asia

am i asian

🤓

[shy anchor]

you're saying the answer is 47?

[swift imp]

(yes)

[soft vigil]

yes

(yes)

[shy anchor]

alright we'll know if you're right or wrong in just a minute

[soft vigil]

ok

[shy anchor]

you were correct

[soft vigil]

nice

just draw the line through C parallel to AB and DE

trivializes it

[shy anchor]

"trivial"

[soft vigil]

ye

this is pretty basic once you draw parallel line

[slender saddle]

Why would you trust ChatGPT??

[shy anchor]

I obviously didn't which is why I'm here

[royal estuary]

Wth

[mental elbow]

you are demotivating asf gang

[soft vigil]

dont listen to the professional troll

[mental elbow]

bro the sad thing is that it is completely possible he is not trolling

there’s a lot of people out there who are like 100x smarter than me at like 8 years old bro 💀

[soft vigil]

the thing is

there is no real way to know if he is truly fully understanding of these topics

i know lots of people who says they know something but have only scratched the basics

[mental elbow]

true

but he is saying that he has done university level math and is studying quantum mechanics, which leads me to believe that if he’s not lying he’s not just learning from a youtube video. he’s actually taking classes on it

[jolly solstice]

I suggest trying to figure out a way not to compare yourself to others. I can't think of a good reason to really

[mental elbow]

lighten up, bro. i’m not genuinely comparing myself to him, i was just making a joke.

[jolly solstice]

sure

[mental elbow]

im gonna take that as a non sarcastic sure

[soft vigil]

yeah no

university level math is very vague

[mental elbow]

it’s interesting, though. i wonder if he just has a natural proficiency for math, he really likes it, or both.

[fossil loom]

quantum physics is quite simple if you don't go into the math part

university level math could just be basic calc which is also not ridiculously hard

[mental elbow]

i guess so

what’s the difference between quantum physics and mechanics

or are they the same

[fossil loom]

i think they're the same

[mental elbow]

hmm

[mental elbow]

this is really impressive though at 14

[fossil loom]

that is impressive indeed

[swift imp]

Net negative if you compare yourself to others

Focus on you

[slender saddle]

They’re not knowledgeable about them dw

Look at their roles

[winter sable]

why sir

[empty skiff]

47??

[mental elbow]

i agree but i wasn’t being fr, was just making a joke

[mental elbow]

was just a joke on how if what you said you did is true it is impressive and demotivating because you’re my age doing much higher level math

[eager root]

yo

[mental elbow]

where is south

[deft wraith]

Can I have a hint for this problem

I'm guessing it's probably induction at some point -- not very good at FEs

[high goblet]

draw a diagram of Z^2

and see what the condition tells you: if you know f(m,n), what does the condition tell u about other points in Z^2

[jolly geyser]

Hey any recommendations for calculus lectures or videos .. i know it doesn’t belong here

[glad zinc]

Angles in a pentagon make 540, AB and DE are parallel so angles A and E add up to 180, thus C must be 540-(174+139+180)=47

Weird how chatgpt cant solve such a basic problem

https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/

This is really interesting though

Saw it a while back

AlphaGeometry first uses its symbolic engine to deduce new statements about the diagram until the solution is found or new statements are exhausted. If no solution is found, AlphaGeometry’s language model adds one potentially useful construct, opening new paths of deduction for the symbolic engine. This loop continues until a solution is found.

[high goblet]

idk sorry, try like #calculus ig?

[jolly geyser]

Thanks buddy

[deft wraith]

hmm okay

it's a tough question

[winter sable]

hehe

[thin stratus]

im ngl i did that at 11

[radiant jasper]

Heh nub, I did that at 4.

[winter sable]

no way

ily

[glad zinc]

I did it before I was born, mom was a math major

[radiant jasper]

Your mom did it not you nub.

[radiant jasper]

Hehe be dazzled!

[glad zinc]

I was a part of my mom back then (egg cell), I just got split from her when I was born

What??

What on earth are you saying?

Oh

I see what you mean

Well yes

the answer is yes

[radiant jasper]

Then

[glad zinc]

Doesn't invalidate my original argument

[radiant jasper]

Soo

[glad zinc]

🤷‍♂️

[radiant jasper]

Heh, you got your dad into serious problems.

[glad zinc]

I think we should just end this conversation here

[glad zinc]

Every man for himself

[radiant jasper]

Ofc that's why I deleted some messages

This escalated quickly though

Delete this

[winter sable]

ssup

[radiant jasper]

Sup inf

[winter sable]

oo

[swift imp]

what heppened

lmao

[solid iron]

Has anyone done the tmua

How was it

[shell mauve]

has anyone competed in mathematics Olympiad.
if so can you give me some tips, my first exam is the 23rd

[radiant jasper]

try your best

[fringe vector]

look at competition problems in topics you dont feel comfortable doing at the highest level

Try attempting lots of geometry questions though as they tend to be the hardest usually

[radiant jasper]

*counting

[mental elbow]

just been trolling you guys, been doing that since the beginning of the universe

[swift imp]

focus on what u need work on,
theoretically it involves more critical thinking but can do more on just stuff u learn in hs

[warped wedge]

what are my chances of AIME qual (AMC12) and how should i practice

[modern prawn]

Not really math related but really productive today for some reason

Been doing my homework for 2.5 hours straight with no break usually i take a break or two

[glad zinc]

apparently was harder this year

[glad zinc]

https://tenor.com/view/lil-yachty-drake-oprahs-bank-account-meme-laptop-gif-20803826

[slender saddle]

It's not weird at all if you know how ChatGPT works

[timber wraith]

would u mind sharing a copy of this? I feel like I'd need snth like it

[radiant jasper]

that symbol is sus

[glad zinc]

I'm familiar with how it works, it's surprising because I've asked it significantly harder math and geometry questions which it has done correctly

[glad zinc]

Just a guy holding a big peach, Im sure it has no other connotations

[winter sable]

nostalgia

[warped wedge]

It’s on this website

https://math.llmlab.io/

[winter sable]

i m backl

[mellow oracle]

who studying for the aime? been slacking off a bit need to lock in

oh yeah I also need to study for amc..

or well not rlly

[gusty verge]

Have u done it?

[balmy lintel]

I got 1 but I'm not sure does anyone know the answer?

[fathom sleet]

it is 1 (from memory), but lemme try it once

[fathom sleet]

yo dude, can u check dm

[ivory ember]

,w minimize x/(y+z)+y/(x+z)+z/(x+y) if x >0, y>0, z>0, xyz=1

[gilded halo]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[toxic imp]

Compute all possible values of x if A = x^2 + 7x is the largest positive angle measure (in
degrees) for which 3tan^2(A)-1=0```

Anyone know a if there is a better way to do the quadratic that comes out?

Or if there’s a trick I’m missing

Ik A=330

[trim bramble]

what quadratic?

i feel like there may be a typo, cause why not just right A = 8x

[toxic imp]

No the answers for x are -22,15

Definitely not a typo but just super annoying

[trim bramble]

i’m confused why did you right A = x + 7x

why not just right 8x

[toxic imp]

Shit I meant to write x^2

x^2+7x

[trim bramble]

lmao okay that makes more sense

so then you would have
330 = x^2 + 7x
0 = x^2 + 7x - 330

[toxic imp]

Fr it’s a bitch to solve

[trim bramble]

then you can use vieta formula to find sum of the roots

[trim bramble]

discord did a weird thing

wait compute oops

quadratic formula

shouldn’t be too hard to solve from there

[toxic imp]

Square root of 1369 😡

[trim bramble]

😓

[toxic imp]

If that’s the best way then oh well

[trim bramble]

it’s just saying to list the roots so there really isn’t anything else to do

[toxic imp]

Yeah ig so

[trim bramble]

actually

it turns out

x^2 + 7x - 330 = (x + 22)(x - 15)

[toxic imp]

Indeed

But how would I find that

This is supposed to be a 3 minute problem

[trim bramble]

are you allowed to use a calculator or no?

[toxic imp]

No

[trim bramble]

uh

pray?

😭

[toxic imp]

It has like 16 factors

[trim bramble]

yeah but like

i tried 30 cause that looked pretty close

[toxic imp]

Might be better to just learn the long square root by hand method

[trim bramble]

and got 30 x 11

then was like i’ll check 15

and it is 15 and 22

which works

[trim bramble]

😓

[toxic imp]

This is supposed to be the easiest of a set of 3 problems

We have 10 mins for all 3 😭

[trim bramble]

it would take like a minute and a half to do all of that

especially cause 6 of the 16 factors can’t work right off the top of my head

actually 8

[toxic imp]

What’s your thought process for eliminating

[trim bramble]

the different between the 2 numbers is 7

that’s pretty close to a square

so let me try some 2 digit numbers that could work

[swift imp]

Forums

Aops forums

[soft vigil]

i think i got all 5

but havent checked answers

[radiant jasper]

anyone have that super long limit problem still?

[radiant jasper]

how do i start with math olympiad specifically our national Olympiad for mathematics i really don't know where to start, but i have read geoff's Smith advice but then uhh it just said to not learn university level math blah2 and just become a better problem solver in Algebra, Combinatorics, Number Theory, and Geometry but i lack theory when i do Problem Solving Tactics by Australian Math's Trust, Art And Craft of Problem Solving and etc..

[vernal storm]

is there anyone here specialised in the game of theory ? please i need some help in a mathematical related problem

[high goblet]

idk what the books u've mentioned are

but that definitely should not be happening

i'm assuming when you say u wanna start with maths olympiads, u mean like at a beginner level?

[high goblet]

if so then consider finding easier books

some books might seem like they're for beginners but r really more for more advanced ppl

idk what round 1 of ur maths olympiad is like but generally you should not be getting stumped at questions bcus u lack theory

https://bmos.ukmt.org.uk/home/bmo.shtml

certainly for the UK, round 1 should be very doable without any theory

(occasionally u'll get the odd question that requires more theory etc.)

[high goblet]

i do wanna highlight that sometimes it's easy to think that a problem requires theory you don't know when really it doesn't

i think like a good example is maybe if u've learnt about fermat's little theorem

and u've learnt what orders are

then if you know $a^k \equiv 1 \mod p$

[gilded halo]

LY

[high goblet]

then $ord(a) \mid \gcd(k, p-1)$

[gilded halo]

LY

[high goblet]

this is technially a theorem, but anyone who's learnt about orders and fermat's little theorem should be able to derive this

basically often, doing problems is how you learn theory

so as i've highlighted above, u might know the basics of orders and modular arithmetic

then you can derive basic results about it etc.

[high goblet]

(similarly, if p = 3 mod 4 and p | a^2 + b^2, then p | a and p | b is also a theorem, but again, you should be able to derive this if u know what orders are etc.)

anyway lmk if that helped!

[high goblet]

i think i can provide more specific advice if u give me examples of what u mean when u say u lack theory

[radiant jasper]

Would doing JEE math for STEP be a waste of time?

[fathom sleet]

bro i missed one square in this

do i lose more than one point?

this what i got, i forgot the top left 3 😭

[deft wraith]

yes

[winter sable]

do u remember me

[radiant jasper]

Really?

Then where the fck should I learn from, NCERT is too plain and boring.

[radiant jasper]

No who are you?

[winter sable]

BRO HOW

I AM THE 14Y/O

[radiant jasper]

Oh

Cool keep studying

And make me proud

Also dedicate your PhD thesis to me.

Also attribute all your subsequent discoveries to me.

And also name your children after me.

@winter sable Will you?

[winter sable]

lmfao

[winter sable]

i can do the first three lines for u

ok guys its maths time 7 hr streak..lessgooo see y'all tmrwwwwww

[radiant jasper]

Name your children after me atleast

[winter sable]

i will see

whats ur name

[radiant jasper]

Zayd

[winter sable]

sounds good

[tired chasm]

send help

@everyone

[fast coral]

why bruh

send 1 w

q

[tired chasm]

i will give share of 100 000 pesos if i win

[tired chasm]

https://pmo.ph/awards/

[fast coral]

no

[tired chasm]

why

[fast coral]

because

[tired chasm]

is it hard for you

[fast coral]

no

its not too hard

[tired chasm]

prove it

[fast coral]

why

i wont do it for u

[tired chasm]

nah you're gay

and happy

[fast coral]

bohoo

solve it yourself

!!!

[tired chasm]

i need help

[fast coral]

in whay

[tired chasm]

i cant

[fast coral]

what

[tired chasm]

im not smart, i only do calculus

[fast coral]

u cant do any one of them

oh

can u do deez

[tired chasm]

wut

[fast coral]

do deez nuts

hah

[tired chasm]

ha ha

but seriously i need help

[fast coral]

like mentally

im no therapist

but i can b a friend

[tired chasm]

then help me do this math

[fast coral]

ok but u sent like a billion qs

[tired chasm]

first question

[tired chasm]

@scarlet root answer

[radiant jasper]

bot can't answer xD

[deft wraith]

past step questions

[novel karma]

me too

[tired chasm]

hello

[pallid ginkgo]

any olympiads thats around amc12 level about proving? (hopefully in aops)

[deft wraith]

BMO1? (Not on AOPS)

[swift imp]

What country

[swift imp]

Look at India math Olympiads

Idk how it works there

Idk

What the topics are

Generally probably it’ll be generic like algebra, geometry, number theory, and combinatorics

[old bay]

when is it due

[tired chasm]

last year

[winter sable]

yay

[royal estuary]

Pls help

4 and 5

Else I'm gonna fail

<@&286206848099549185>

[gusty verge]

What have you tried?

[royal estuary]

Uh tried expansion

For 5

Here's the work

Not sure how to bound the value of the cyclic sum

Tried using limits but I think that won't work

Cuz we don't know the range

[royal estuary]

And I'm still trying no. 4

[gusty verge]

For 4), find a/b

[royal estuary]

Ye I did

What do I do next

[gusty verge]

5. is probably something to do with Cauchy Schwarz

[royal estuary]

Ohh

How did I not think of it

Thanks

I'll try

What do u think of my approach

[gusty verge]

$\frac{b}{a}=x^2-xy+y^2$

[gilded halo]

Max

[gusty verge]

Seems like a logical start

[royal estuary]

But what do I do next

[gusty verge]

Yeah it's good, the roots of polynomial approach, but hard to then optimize as there are a lot of stuff we don't know

[royal estuary]

Hnm

That's what I was thinking

[gusty verge]

Maybe switch to polar coordinates for the simul equation?

[royal estuary]

Like using the ellipse equation

I'm in 8th grade so I don't know complex numbers that well

[gusty verge]

Set $x=r\cos\theta$ and $y=r\sin\theta$, the equation becomes:

[\frac{b}{a}=r^2(1-1/2\sin(2\theta))]

[gilded halo]

Max

[gusty verge]

Hmm idk perhaps try some examples of a,b see where it goes wrong

[royal estuary]

Alr

[gusty verge]

If ur in 8th grade doing this idk why u think ur gonna fail lmao

[royal estuary]

It's a school test

I need like a 30 or smth

To pass

[gusty verge]

What school do you go to... MIT 💀💀💀 8th grade in the UK is not like this

[royal estuary]

Yeah ik

Not even in my country

[gusty verge]

(not actually asking for ur school so don't say lmao)

[royal estuary]

It's for the IMO

[gusty verge]

Ah okay 👍

[gusty verge]

Pretty sure you want to find a formula for $\sin^3\theta$ in terms of $\sin 3\theta$ and $\sin \theta$ using De Moirves theorem, then it will just telescope

[gilded halo]

Max

[jolly solstice]

that's what I was thinking but too lazy to try too lol

I guess if we call the sum S_n then we could look at S_n - S_{n-1} to see what the idenity is

[tired chasm]

this is the most hated sigma

[fast coral]

yep it telescopes

[fast coral]

keep spamming D>0 ig since x, y are real assume quadratic in either

[gusty verge]

As in do discriminant for x and y? But this will depend on the other variable, which we don't know and should depend on a,b ?

I was thinking from the wording of the question it's probably going to be some finite cases.

Ie. a=b=0

[stoic pagoda]

idk where to send this but how do u do 11b

[spice wyvern]

when should i start studying for a math comp? or should i start as early as possible?

[jolly solstice]

,rotate

[swift imp]

Math competitions are year round studying

People spend years studying

Not something you can do well on in like a few weeks

Most of the time

[spice wyvern]

oh ok

[hearty tendon]

try subbing x+y = p, xy=q

[tawdry agate]

python says the answer is 1001, but not sure how to approach this combinatorially?

[gusty verge]

Treat them as letters: U, D and B.

Place the B first as there is only one of them.

Then think about how many Us and Ds need to be placed (this is fixed!)

Then identify where in the word the B can be placed.
Treat them as letters: U, D and B.

Place the B first as there is only one of them. Identify where in the word the B can be placed.

Then think about how many Us and Ds need to be placed (this is fixed!)

[sleek ivy]

If the sum of the first from 0-2020 of f(n) is 0, and f(n+1)=(f(n)-1)/(f(n)+1), find f(0)

Chat anyone have any ideas on how to solve this?

[royal estuary]

Can u write the question clearly

[sleek ivy]

You're given this and have to find f(0)

[royal estuary]

Alr

[royal estuary]

What have u tried

Till now

[sleek ivy]

i tried expressing f(1) and f(2) in terms of f(0) but idk how to use the information for the sum to find it

[royal estuary]

Try doing it for general n

[sleek ivy]

f(n)=f(n-1)-1/f(n-1)+1 ? isnt that already pretty much given

[royal estuary]

Maybe could make a telescopic sum

[sleek ivy]

whats that

[royal estuary]

Like rearrange such that when u add the terms the terms cancel out

So only the starting and the last term is left

[sleek ivy]

I found that f(0)=f(4), so it recurs every 4 terms, meaning that the sum of the first 4 terms is equal to 0 and f(0)=f(2020) so f(0)=0, would this logic be correct?

[fast coral]

yeah

looks correct

just formalise it

[royal estuary]

Nah

Sometimes it doesn't

Ig

[fast coral]

if you cna do f(4k)=f(k)

[royal estuary]

Yeah if u can prove it

[fast coral]

oh

i got it i think

f(n+4)= f(n) i think

[ocean narwhal]

Proof?

[fast coral]

keep applying

the thingy

[ocean narwhal]

Thats surely not the best way...

[sleek ivy]

well

it works

[fast coral]

f(x)= ax+b/ cx +d f(f(x))= x if a+d=0

[ocean narwhal]

Uh i thought of subbing f(0) tan^2(x)

[fast coral]

this is basically that

[ocean narwhal]

That gave f(1) = - cos(2x)

[fast coral]

i dont want to do the calculation but ok let me try

[sleek ivy]

isnt that the requirement for a rational function to be even

[ocean narwhal]

F(2) = tan^2(x) and so on

[fast coral]

n

o

[ocean narwhal]

So it repeats every two thingies

[sleek ivy]

are we still talking about my problem? if so where tf did the trig functions come from

[ocean narwhal]

No shit i kinda just remembered the trig formula and it looked similar so i just subbed f(0) = tan^2(x) so i dont need to do the calculations again

[fast coral]

yeah

[sleek ivy]

huh

[fast coral]

just keep applying

[ocean narwhal]

Youre welcome to do the calculations tho

[fast coral]

f(n+2)= f(n+1) -1 / f(n+1) +1

then f(n+1) = f(n) -1 / f(n)+1

[ocean narwhal]

Yea so its just tan^2(x) , -cos(2x), tan^2(x) again and so on

[fast coral]

yeah i guess

[ocean narwhal]

Now we know that tan^2(x) = f(0) and -cos(2x) = f(1)

Just write back in that form

F(0), f(1),f(0),f(1)....

[sleek ivy]

im not familiar with the trig function formulas but if yuo do the calculations you get f(x+4)=f(x)

[ocean narwhal]

Use the sum

To get a quadratic(is a quadratic or a cubic? In f(0))

[ocean narwhal]

Nah

You get f(x+2) = f(x)

[fast coral]

yeah

that

[fast coral]

no

f(n+2)=-2/f(n)

[sleek ivy]

uh no you dont

[ocean narwhal]

Too lazy to verify

Argh

[ocean narwhal]

Makes sense

[fast coral]

yep

[fast coral]

looks correct

[royal estuary]

Im getting f(0) = 1/f(4)

[fast coral]

u should get f(0)=f(4)

[royal estuary]

How

[fast coral]

algebra

[royal estuary]

I did

Algebra

[fast coral]

express f(4) in terms of f(3)

f(3) in terms of f(2)

f(2) in terms of f(1)

[royal estuary]

Maybe calculation mistake

[fast coral]

f(1) in terms of f(0)

yeah

[royal estuary]

Maybe could use a cubic equation

And then use the cubic formula

[fast coral]

i think u should get 505f(0)+504f(1)+504f(2)+504f(3) =0

[ocean narwhal]

Ugly

[sleek ivy]

That looks right but how do you find f(0) from that

[fast coral]

f(1) in terms of f(0)

f(2) in terms of f(0)

f(3) in terms of f(0)

f(2) = -2/ f(0) , so f(0)= 0 seems incorrect

[sleek ivy]

Yea my logic was wrong be4

I’ll do the calculations and see the answer

[fast coral]

alr

[sleek ivy]

would it not be 506 f(0) and 505 for the others

since 2020/4=505

[fast coral]

yeah

i think

im bad with shit like this

its either 505 or 506

[sleek ivy]

506 for 0 and 505 for the rest

[fast coral]

yeah

ok

[sleek ivy]

and its a cubic

how tf am i supposed to do all this in a non calculator contest wtf

its actually a quartic

[ivory ember]

Write it as the product of two quadratic factors

It also might be symmetric, so you can invoke that trick

,w (a+(a-1)/(a+1)-1/a-(a+1)/(a-1))(a)(a+1)(a-1)

[gilded halo]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[ivory ember]

Oh wait it’s a quadratic in (f(0))^2

Yeah just do that then

@sleek ivy

[sleek ivy]

how so?

its a quartic in terms of f(0)

[ivory ember]

.

Notice the square

[sleek ivy]

oh im blind

[fast coral]

also you could have also used ferarri if u didnt spot that

[sleek ivy]

ferrari?

[ivory ember]

You can also divide by $(f(0))^2$ and do $$(f(0))^2+\frac{1}{(f(0))^2}=6$$ $$\left[f(0)+\frac{1}{f(0)} \right]^2-2=6$$

[gilded halo]

Civil Service Pigeon

[ivory ember]

Not particularly useful here

But the technique is useful with more … funky symmetric polynomials

[sleek ivy]

right the x^3 cancel out

[fast coral]

u can sometimes factorise quartics nicely

[radiant jasper]

bro what

[next sorrel]

If I were to discuss a potential partnership with this discord server, who would I discuss it with?

[radiant jasper]

@quick aurora

why did you send that in competition math

[pallid tundra]

hey at least they didn’t send some basic mechanics question here LOL

[high goblet]

it's the quartic formula lol

[frozen pendant]

If all the six digit numbers x1 x2 x3 x4 x5 x6 with 0 < x1 < x2 < x3 < x4 < x5 < x6 are arranged in the increasing order, then the sum of the digits in the 72th

[radiant jasper]

i guess this is enough for my hypotension

[hushed cosmos]

https://youtu.be/bw9KSFZuAJU?feature=shared
i tried

[gray heart]

Can someone help me with this?

[high goblet]

you can get f is bijective quite quickly

and then also f(0) = 0

might be useful, i'm gonna go to bed now

[jolly solstice]

yeah and slightly stronger ||it's its own inverse||

[high goblet]

yeah and you can also get |x| = |f(x)|

ok i should actually probably head to bed

bye

[gray heart]

yes i can see it's an involution

[rough anvil]

Guys

What’s the best aime prep

For 2 weeks

Cuz that’s how long I have 😭

I did Alr on the last one but I wanna do better

[high goblet]

ok i said i was gonna go to bed

but here's another idea

if you set x=0, the f(yf(y)) = |y|^2

so if we set y = rexp(iθ)

then you can find an expression for f(y) in terms of f(r)

anyway maybe let theta be a function of r and then see if u can solve for theta like that?

if u still need help on the question i can think about it properly tmr rather than just some random ideas i have whilst in bed

[gray heart]

imma try that

thanks

[high goblet]

ok i said i was gonna go to bed

but i cooked some more

[high goblet]

yeah you can then finish the question with that

in case you need a hint, i'll spoiler it here:
||consider f is injective. if f(r) != +-r then we get a contradiction||

[high goblet]

||you still have the piecewise trap, but i suspect you can easily resolve the piecewise trap||

[radiant jasper]

take mock test

[dusky whale]

i took the amc 12 last yr and got a 66 w/ no prep. im trynna get a 100+ this yr but i only have about 2 weeks left. how can i maximize my score with the time i have left (not looking for a miracle, but a fast and efficient way to practice)?

[gray heart]

actually I got f(r) to be ||the conjugate of r||

[naive pasture]

Try solving 3 problems of a model, then after u get accustomed to it, check if u can solve the same type in ur head

Keep repeating

[soft vigil]

fr?

[dusky whale]

what do you mean by “of a model”? i’ve just been looking at past AMC tests

[naive pasture]

Well a model means

A type of question

Usually, I can say finding maximum and minimum of a quadratic equation is a model of question

[soft vigil]

best way is making sure you have a strat