competition-math

[severe eagle]

i only enjoy them when theyre d6+

potds are fun, when you grind more youll improve

gl with oly

[neon summit]

let u=(x-1)(x-6)=x^2-7x+6, eq above=>u(u+4)(u+6)=720 => u^3+10u^2+24u-720=0 => (u-6)(u^2+16u+120)=0
the quadratic has no real solution, u=6 => x^2-7x+6=6 => x^2-7x=0 => x=0, x=7

ergo 2 real soltuoins

or smth

idk what's a solution

[wet otter]

You already solved...

İdk too

[brisk dirge]

Can somebody help with this problem:
Prove that for the same perimeter a right angled triangle with two same sides have the bigger area than other right angle triangles.

[latent mango]

i cant give out the entire explination bc ur not allowed to fully answer questions BUT u can derive the steps from the final equasion:b = P(1 - sqrt(2)/2).

[brisk dirge]

Thanks for idea

[agile gazelle]

Hi

[inland totem]

ok it's back

[inland totem]

[olive haven]

Hi 👋🏻

[radiant abyss]

did anybody here mop ?

in competition math ?

[inland totem]

probably

[neon summit]

what's a solved

[neon summit]

huh

[little wraith]

patrick li

[inland totem]

hi

[thorny tusk]

not me thats fs

[viral sierra]

Not me, but probably

[viral sierra]

Halloa

[trail sluice]

what's the best way to format partial solutions (mainly to save the trouble of the examiner having to figure out that it's a partial solution)

[lament swan]

What did you know about online math olympiads, dm me

[neon summit]

depends on the question although you want to place
casework, geometry diagrams, assumptions on short figures on the top right while everywhere else would be the bulk (idk)

[near hill]

Write Partial solution: at the beginning?

[neon summit]

I exist to be bored

very fun problem

[vernal axle]

||198?||

[dense latch]

is there a way to access aops books for free?

[frank hornet]

hmm no I don't think so...

[neon summit]

👍

[marsh sluice]

hey chat, soi'm going to this team math contest event tomorrow and i wanted to ask if anyone has any tips on how to prepare??

[near hill]

At less than a day, the most important thing is get enough sleep, etc.

[woeful sleet]

which contest??

[marsh sluice]

CTMC

canadian team math contest

[woeful sleet]

where i it held?Online mode or offline?

[marsh sluice]

offline, in person

competing against other schools

[tiny eagle]

As troposphere said and also work on teamwork identify individual strengths (geo, combo, etc) and make sure those ppl do those problems

[zinc ridge]

cool problem rbo

is there a way to do it without getting your hands on some bash

[inland totem]

hmm

[zinc ridge]

like with multiples of 11

[warm rock]

hey, i'd highly recommend using usamoguide.com to prepare! its designed entirely for competition math and has curriculum written by US national math olympiad medalists!

i personally like it

[zinc ridge]

i mean pirating exists but its illegal

so yeah

[marsh sluice]

i'll def check it out, thank you!!

[inland totem]

wait i js realized

i've been kinda neglecting comp math for higher math this past week

[tiny eagle]

I meannnn I can’t blame you

Integrals so fun

I’ve been neglecting math in general tho cuz AP exams coming up 🫤

[viral sierra]

I've been doing the opposite its comp season

[reef jay]

i think the best possible scenario for you is if the examiner does not realize it is a partial solution

[thorny tusk]

i just write some random shi at the end and try to format it as a full solution

[rugged solstice]

Lol

[tired raptor]

guy i need help in this problem

[ivory ember]

complex numbers

[tired raptor]

what

[ivory ember]

you could also write each term as an integral

[tired raptor]

ok

thx

but wait how

[ivory ember]

I leave it as an exercise for the reader

consider the "standard" integral representation of 1/n ig

[tired raptor]

ok

that means the answer will be

wait for 5 minutes

the answer is pi/3√3

am i right

please check

yoo

[ivory ember]

,w sum of \frac{1}{3n+1}-\frac{1}{3n+2} from n=1 to inf

[gilded halo]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[ivory ember]

image compression

[tired raptor]

brother i calculate thx to the help of Civil Service Pigeon it's pi/3√3

what is the that webpage you are using the showing me that calculation

[ivory ember]

wolfram alpha

[tired raptor]

thx let me check

k it's quite nice

but any for raw calculations

anyways thx for the help

i will try finding some question to solve

yoo tell a channel that give question like this

[sonic grove]

for any function that is differentiable over the interval I, there exist $J={ \frac{f(b)-f(a)}{b-a} | a,b \in I , a < b}$ such that $f'(I)-J$ has at most 2 elements(where f'(I) refers to the set of values of f'(x) for evey x $\in$ I)

[gilded halo]

Respectful_mathematician

[sonic grove]

that has 2 elements when I is closed... if it is open then I is essentially same as J...

Is this correct?... I am just wondering can every secant line slope over I captures every derivative over I...

If this is not the place for this specific question, please redirect me. thanks.

[neon summit]

carry the team on your back

[neon summit]

I'm pretty sure they're addable

[trail sluice]

true...

[tired raptor]

hey guys

i have a doubt

on what are tensors

[sharp dawn]

From the multi equation, we get: 6/u=2/t
So: u=3t
Now you substitue it into the equations

[spark scaffold]

My idea was subtract 6 to u^2-ut-6=0 and t^2-ut+2=0

And try to factor

[white heart]

Add the 2 equations and multiply by 2

Should be 8

[sharp dawn]

there are several aproaches for 1 problem

[spark scaffold]

Okay

[steel bay]

128

[spark scaffold]

I got 8

Cuz I made it t^2=-2+ut and u^2=6+ut

And expanded (u-t)^2=u^2-ut+t^2

[oak tartan]

yeah thats correct

[spark scaffold]

Yay

Then it’s 2u^2-4ut+2t^2

[oak tartan]

should expand to u^2-2ut+t^2

[spark scaffold]

2(6+ut)-4ut+2(-2+ut)

[pine geyser]

answers 8 i think

[spark scaffold]

It is 8

[spark scaffold]

After simplifying its 2(4+4ut-4ut)

“4ut” cancels out

Into 2(4) which is 8

[zinc ridge]

i got that

[spark scaffold]

Good

[round crater]

8

[round crater]

if sm1 gets this shit

ur cracked

at math

[dusty sundial]

Come private

[olive haven]

Does AP mean arithmetic progression?

[round crater]

Yurt

[olive haven]

@round crater I think I got it. Do you have the answer? I got || 3/2 ||

[olive haven]

For some reason I’ve never seen geometric progression and arithmetic progression abbreviated as GP and AP lol. But it makes sense. Immediately realized what those were because of “common difference”

Good to know, I don’t need to write out long words anymore

[olive haven]

It took me a while, but I finally wrote it out neatly

[gilded drift]

Heyyy

[inland totem]

hmm

[inland totem]

hmm

ig ill do some today

[olive haven]

Hello 👋🏻

[gilded drift]

Whats upp

[fallen apex]

This is probably something you see on the easiest stage of math contests ngl considered “easy” in competitive math

Probably would see that in amc

[novel karma]

Where did you get that problem?

[round crater]

😂

i cud give ya harder ones

just ask

[round crater]

im studying for IPMAT

[proper fable]

I don't know about all that but what I do know is that atp I can only do cbse boards lvl maths

Maybe I could do better but I only got like 49%ile in jee math and even if I solved the questions that I couldn't do cuz of time limit ,I would still only get like 85ish %ile

Maybe if I study for that then I might be able to do that

But I won't do it if I don't need all that in engineering

[neon summit]

add u^2-ut to t^2-ut, you get u^2-2ut+t^2 which is (u-t)^2

[spark scaffold]

Yea

[neon summit]

weird I wonder if this is where they took that one problem from

I think I lowk have seen that b4 lol

[neon summit]

||3/2|| after a bit of weird typing

I got it wrong initially but eh

somehow got 1/2 1 1/2 but then realized I multiplied a 2 in the denominator weirdly and then it fixed itself

[spark scaffold]

Which one is easier

[daring sparrow]

there's another real solution to this

[hearty needle]

Anyone has ANMC pyq pls send

[neon summit]

(3^x)^2=3^2x=9^x=(x^9)^2 and like that should be easy enough ig

wait

that should intersect at 2 points mm

[restive anvil]

Aren’t these questions meant to not be solvable since e is transcendental or whatever

Lambert w for the other root ig

[fleet drift]

literally solved it in my head

[heady summit]

Yeah we aren't good like that

[neon summit]

is it possible with accurate hitboxes

[fleet drift]

tbh idk that's y i sent it

[radiant shoal]

what

[pallid dragon]

he means passable

[neon summit]

lowk don't remember where I found this

a1=1, a2=1/2, a3=2, a4=1/5, a5=5/4, a6= 8/7, a7=7/13, a8=13/6, a9=6/17, a10=17/11, a11=11/16, a12=16/5, a13=5/19, a14=19/14 hmmmmmm
alr I think I've been calculating wrongly for a bit but I think I see a way

hmmm

a6

7/4 it shoudl be 4/7

1 1/2 2 1/5 5/4 4/7 7/3 3/8 8/5 5/7 7/2 2/7 5/7 7/2 2/7...
so prolly 7/2 idk

huh weird the answer is ||13/46|| but like I swear isn't this how the thing goes

idk maybe I'm stupid

[ivory ember]

$a_4=\frac{1}{3}$, not $\frac{1}{5}$.

[gilded halo]

Civil Service Pigeon

[neon summit]

oh yeah

I'm blind

1/3 3/2 2/3 3 hmmm

[spark scaffold]

I wonder where is other 3 solutions

I get x=6

[novel karma]

Can you send the solutions

[near hill]

it's x=-6, not x=6, and that is a double root due to the symmetry of the equation.

There are two further roots between -10 and -9 and between -3 and -2, respectively.

[sinful current]

I am enough pro to say these typa questions has 2 rational and two 2 non rational roots

Pretty easy tbh

I solved there are three solutions x= -6,-6+√10,-6-√10

One rational and two conjugate pairs since they are irrational

[mighty pine]

you can probably just guess them

[scenic sun]

This deals with the || stern-brocot sequence ||. You should look into the || binary representation of n || and assert a claim on a_n depending on || parity ||, via || strong induction ||, from which you can then compute a_2024

[mighty pine]

neither of the factors can be even

so x can't be odd here

and if any are negative, another also has to be negative because otherwise it wouldn't be in N (which 9 is)

x = -6 works here

[inland totem]

idk why i was doing aime mocks at 11 pm

[zinc ridge]

is it ||72+-sqrt(26)||

[near hill]

Definitely not, that isn't even roughly in the right range.

[spark scaffold]

Correct

you get -6,-6+√10,

Two irrational that has x^3-10=0

[restive anvil]

whats like the smart way to do this

pair them up and let u = x^2 + 12x?

[spark scaffold]

Set y=(x+6)

(y+3)((y+1)(y-1)(y-3)

[restive anvil]

hm and then expand to get a quartic missing a degree 3 and 1 term?

ah that works nicely

[zinc ridge]

shoot

i made a mistake with quadratic formula

wait i literally made a mistake with every single step in the quadratic formula

first, i thought 26*4=116, then i squared b instead of making it negative

then i thought 144-116=26

also sqrt(26)/2=sqrt(26)

[spark scaffold]

Then it turns into perfect square

When it’s (y^2-9)(y^2-1)=9

y^4-10y^2+9=9

9 cancels out

y^4-10y^2=0

y(y^3-10)=0

[neon summit]

oh no wonder there was a 2024=1101010100110 smth on the solution

how does one even recognize that

[neon summit]

I literally just saw this on facebook

[neon summit]

let u=x^2+12x+35, u(u-8)=9 => u=9, -1
9=x^2+12x+35, -1=x^2+12x+35 => x=-6, x=-6__+__sqrt(10)
hence (x+3)(x+5)(x+7)(x+9)-9=(x+6)^2(x+6+sqrt10)(x+6-sqrt10)=0

[neon summit]

to which ones

I don't have soltuions for the minimum value of m and n that sort of thing cuz who would bother thinking about that

[novel karma]

All except the ones you don’t have

[neon summit]

I ain't doin all that the entire document is like 890+ pages long 😭

brb in like 5 minutes if I can manage to scour it for the problems again

note that my solutions may not be entirely right

b

majority of these are probably made up answers

I was also probably drunk making them

making the solutions* I didn't make the problems

[inland totem]

hmm

[graceful vine]

Awesome!

[tired raptor]

hey guys what are tensors

[mental cove]

uh simple idealogy is its 4D vectors

But they are more complex

You should check in a physics server or other math channels

[lost sapphire]

Well clearly Tensors are objects that transform like a Tensor

[tired raptor]

ohh

but how can 4d object exsit

i did see an video on quaderions by 3b1b

[untold wing]

TSTs are just brutal, Espicially when you think you solved something but get omitted so much points for missing to prove something

[severe eagle]

gl for results

[untold wing]

No I received them

[severe eagle]

never thought youd rant here instead of mods tho

[severe eagle]

oh

do you have next year?

[untold wing]

I could have gotten 11/21 and be in top6

I got 6/21

Am going to PAMO

[severe eagle]

your tst is 3 questions?

pamo

[untold wing]

Pan African mo

[severe eagle]

oh

[untold wing]

Yeah

[severe eagle]

can i ask which country

[untold wing]

I have 2 more years

[severe eagle]

oh orz then

[untold wing]

Algeria

[severe eagle]

[untold wing]

I just hope I get a perfect score in PAMO

[severe eagle]

i need to cook tstst

[untold wing]

U have high chances

Ur orz

Did I forget to mention ur VERY young

Like all of that and ur 13 is phenomenal

[severe eagle]

i don't actually

[untold wing]

May I ask you what did you do ? Or was it just starting early

[severe eagle]

theres at least 6 people my age better than me

[severe eagle]

im asian

[untold wing]

Oh rly ?

[severe eagle]

of course

were a top 10 imo country

i am very worried rn

[untold wing]

You have 5 more years so it’s ok no ?

[severe eagle]

idk man

[untold wing]

Oh but they also have 5 more years

[severe eagle]

yes

[untold wing]

Idk u have soooo much potential just grind

[severe eagle]

i dont rlly

like

it feels very demoralising

but i will heed my teacher's (china mo gold) advice

of not comparing to others

[neon summit]

they don't

[untold wing]

Man trust me you can do it, I remember getting into MO for the first time and seeing orz people in nationals yet I got 4th place

My age obviously

[severe eagle]

man

you're orz

theres at least 3 people better than me in geom my age

[untold wing]

It was d4 max

[severe eagle]

and my geom is the only thing im good at

[severe eagle]

ah

[untold wing]

Dude grind until ur eyes start to bleed

[neon summit]

doubting yourself does not help you

[untold wing]

Watch whiplash it’s very relatable

[severe eagle]

but i could be enjoying my life

[untold wing]

For u

[severe eagle]

instead of grinding everyday

i could ba hanging out

[untold wing]

And every mo nerd

[severe eagle]

if i dont make IMO im dead

[severe eagle]

i will see it

ty

the #1 in my year is a/c/g/n 8/7/9/9

what am i to do

[neon summit]

rest and take a break

[untold wing]

Ur better no ?

[severe eagle]

im 6/5/9/7 at best

[severe eagle]

no im not

[severe eagle]

im losing timeees

like

im bad

😭

[untold wing]

Am pretty sure ur problem solving skills are very good, youre easily d6 combi

[neon summit]

hm this is making me start to wonder about something

[severe eagle]

my combi is horrible

like actually

thanks for encouraging though

[untold wing]

Combi is just problem solving

[severe eagle]

i struggled on 2024 C1

yesterday

😭

[untold wing]

It was overrated

Underrated*

[severe eagle]

i think i have to switch my focus

i need to stop doing geom

the time i would take to make my geom go from d9 to d10

is equivalent to making my combi go from d5 to d7

[untold wing]

Yeah Thats reasonable ur d9, d9 is enough

[severe eagle]

i must do combi

[neon summit]

I wonder what that d thing means

[severe eagle]

but i hate it

[untold wing]

Trust me combi is very upgradable

[severe eagle]

math olympiad discord server ratinf

[untold wing]

MODS difficulty rating

[severe eagle]

d9 ≈ 35 mohs

[neon summit]

oh ok

[severe eagle]

ok i hope

[neon summit]

dt I can solve even a singular problem from there

[severe eagle]

i need lock in

[neon summit]

so all of them are beyond me ig

[severe eagle]

there are easy problems

[neon summit]

give me an example

[severe eagle]

aiyo just come to

[neon summit]

that isn't geometry proving logic number theory or combinatorics I'm weak in those 🥀

[severe eagle]

https://discord.com/channels/533153217119387658/1423326377762881637

@neon summit

[fair bronze]

I love functional equations

[untold wing]

NT functional equations are fun

[fair bronze]

gimme some

[untold wing]

Find all functions f:N—>N such that
f(m) + f(n) | m+n

It’s a simple introductory NT Fe

[neon summit]

||6sqrtpi/2sqrtpi||

is it possible with accurate hitboces

hitboees

hitboexes

ok vro

[sinful current]

Easy question mate , the ans.is The value of the integral is 3.

[lost sapphire]

Whiplash is not supposed to be a motivational movie 🫩

[untold wing]

Brochacho everyone has different feeling

[lost sapphire]

it's meant as a cautionary tale iirc

[untold wing]

Well theyre warning me of something and am falling for it

[lost sapphire]

you can grind, just avoid unhealthy practices 🙏 🙏

[unborn cairn]

is that actually properly written? seems like dx should not be in the root

[fleet drift]

yh its not

[inland totem]

yaey another graph theory problem

[fallen apex]

want more? go to #discrete-math

[inland totem]

hmm

[rough anvil]

Yo is there any way to see how many aime quals came from your state

[neon summit]

huh

idt that's even possible

[neon summit]

actually it is we have to find the integral with square root respect to x

[scenic sun]

It’s possible. The integrand can be simplified further

[neon summit]

yeah it's 1

wait

oh yeah

nvm

no wait a minute

[neon summit]

nvmthought it was another number

[neon summit]

I mean I don't think it's even possible for the answer to be 3 mm my original ans was wrong

I've changed it now

[winter lake]

Does anyone knows a good handout/ressource to learn :

1. Geometry of numbers: Lattice points. Pick's Theorem. Minkowski's Theorem. Geometric interpretation of the Farey sequence and continued fractions. Geometric proofs of the two square and four square theorems.

2. Finite fields: Characteristic. Frobenius map. Counting irreducible polynomials. Uniqueness Theorem for the field of p^n elements.

3.Orders of elements

[inner swift]

what i should study if i want start compete in math?

[lost sapphire]

Algebra, Geometry, number theory, combinatorics. The level of which depends on your level of competition.

[neon summit]

math

[untold wing]

the basics of algebra and geometry and number theory and combi is what you need

other than that are just optional

in geometry you just need to know angle chasing, i solved multiple IMO problems with just angle chasing

in algebra, you need to know some basics abt factoring, inequalities, functions and polynomials(even tho they're getting less trendy)

in number theory; you just need to know what primes are, whats divisbility, gcds, lcms and other stuff

in combi u need to know abt counting, and maybe the pigeon hole principal

for geometry, the first chapter of EGMO is awesome
for algebra, learn the topics independetly(idk any alg book)
for NT: first chapter of MONT
for combi : since there isnt that much theory to learn, you can learn it just by problem solving, if you really want to learn theory use "an exploration of olympiad combinatorics"

again , dont expect theory to solve all ur problems, mo is literally 90% problem solving and motivating ur solutions(unless ur regional competitions are multiple choice questions wich require speed, those require u to just do past papers of them(i hate them so much))

for more info u can join the math olympiad discord server

[inland totem]

[thorny tusk]

for inequalities just do muirheads

thats like the only reason they're not trendy

[untold wing]

Btw do u know why polynomials no longer exist ?

[thorny tusk]

no?

[untold wing]

Theres some advanced shit called Lagrange interplotation, it’s a fricking machine it kills almost every problem

[thorny tusk]

oh yea

that

[untold wing]

It’s very VERY bashy

[thorny tusk]

i didnt learn taht yet 😔

thats the only reason why i didnt solve cmo p5

official solutions

were so

advanced

[inland totem]

isn't that the one which finds the function of degree n which passes through a given set of points?

[untold wing]

Yeah but I heard elsewhere you can use it in different ways

[inland totem]

hmm might have to look into that

[untold wing]

Ohhh Wair mb mb

It’s not Lagrange interplotation

It’s multipliers

They kill inequalities

Not polynomials

Wait wtf I though ur pfp was a cat 😭

[inland totem]

lagrange multipliers ok

thankfully i know abt that

[neon summit]

oh this is just some fancy way to term 2 points can determine a line 3 points can determine a quadratic and so on

again we should stop giving everything names

I remembered searching how to do this in 8th grade I genuinely still remember it every now and then

cuz it also kills patterns

[inland totem]

orz

[thorny tusk]

whats ça

[neon summit]

note for primes depending on ur country you might wanna memorize the years prime or fun facts about the year

what's the 2027th prime and you lowk just look at the organizers like that was a fair problem

[thorny tusk]

2025 was cool

perfect square

[neon summit]

2025 shouldn't exist

bad number

worst year of my life >:(

[thorny tusk]

why?

[neon summit]

for the sake of my sanity I choose to be ignorant towards my own issues

[thorny tusk]

why?

[fallen apex]

N>>>>>>>>>>>>>>>>>>>>>>>…

[worn flax]

rising 10th, planning to take the AMC 10 ts year; to those who have taken the test or also quali'd for AIME, what were your study sessions like, and how much did you spend studying?

hoping to get some useful tips because im just grinding through the AOPS intro books and taking mock tests, but im having issues on my speed and test taking strategy 😔 always get nervous when i take certain tests and i waste time

[empty cairn]

NK>?

[inland totem]

i forgot complex bashing existed for a full few minutes while doing a problem

[neon summit]

k=nk(k=p)

[neon summit]

as a person who knows people who do that
15 hours a day

[thorny tusk]

i did a bunch of aime mocks

that didnt work out very well

[inland totem]

haiya

u did great on aime

[thorny tusk]

yes thanks

[neon summit]

oh wow nevermind AMC doesn't look that hard, AIME is pretty hard tho

correction, AIME would need like 15 hours a day

[ashen hatch]

so if school is 7 hours a day i just need to sleep 2 hours and spend 15 hours studying- /j ik im not qualing for aime next year

[neon summit]

Ionknow bro other countries are a mystery to me

how unsurprising my country copied AIME's format

[inland totem]

yeah doing a butt ton of practice tests just stops working after a certain point

[neon summit]

wow I'd hate to do these

source 2001 aime 2

[neon summit]

they help if your competitions have oral rounds for NO REASON(I AM FORKING ENRAGED)

[inland totem]

hmmm

[thorny tusk]

oral?

that reminds me of

like

sharygin

[inland totem]

geo 🤤

[little wraith]

help pls is it B i don’t even know how i got to that i think i guessed

[ivory ember]

No, as per the solution packet that you can Google.

[little wraith]

yes but ik i can google the answer and i read the solution but i still don’t get it which is why i askwd

[thorny tusk]

what is this sneajer thing

[ashen hatch]

oh icic ur not in US

[near hill]

<@&268886789983436800> another raid (search back for "sneajer" in the channel).

[acoustic jetty]

oh dear

measures have been taken

[near hill]

Ah, it was even the same person, just with a new display name.

[fast atlas]

Given integer n≥2, S is the set of the first 2n natural numbers. F is the family of subsets of S containing 2 elements. Prove that F can be partitioned into partitions of S.

[fallen apex]

[knotty yoke]

Show $K_{2n}$ has 1-factorization.
This one is a known thing, ig, where you construct a $(2n-1)$-gon, having vertices $0, 1, \dots, 2n-2,$ and a special vertex at the center

[gilded halo]

LemmaLover

[knotty yoke]

You connect the special vertex to vertex $0$ to get first factor

[gilded halo]

LemmaLover

[knotty yoke]

Then generate the rest by rotation

[rugged solstice]

"LemmaLover" lmfao

[orchid raptor]

Hi, can someone help me understand the question ( without solving it)?

I don't understand how the answer is not just simply ∞

Like in this case, can't we just move the plane a little bit each time getting closer or further from the fourth vertix of the cube?

[scenic sun]

Wdym?

You would need to consider that a plane here is essentially a flat 2D surface that extends ‘indefinitely’ in 3D space

[orchid raptor]

I think I'm just having a problem visualizing it

[fallen apex]

well think of some examples that you can pass a plane through a cube and have it 3 of the cubes vertices

[lost sapphire]

this guy is going on a tangent 🥁

[silver forge]

Ahem

I have returneth

[silver forge]

do tree diagram

[echo ocean]

why do these problems look like it come straight out of my math hw, like the format, the type of questions

[scenic sun]

That’s fine. You can go on Desmos 3D, type in “max(|x|,|y|,|z|) = 1” which represents a cube of side length 2 units that is centred at the origin. Now a plane can be described as the following equation: ax+by+cz+d = 0 for any real a,b,c,d. Just to make sure that this plane actually intersects the cube, check that |a|+|b|+|c| ≥ |d| for your choice of a,b,c,d. Desmos 3D cannot capture the infinite 3D space, so you might need to zoom out in order to see the plane extending indefinitely

[silver forge]

they are from cayley contest

[echo ocean]

interesting, I'm not that surprised tho they even handed us AIME problems as hw

[silver forge]

bru wutt

[echo ocean]

we love counting/ probability problems, so what would be a better place to find counting problems other than competition

Also ig students are getting better so they have to level up the game

[silver forge]

what grade r yall

[silver forge]

true..

[echo ocean]

I'm 12th kek

[silver forge]

o then aime makes sense

[clever kernel]

hello im jackie chan the math teacher

[inland totem]

hmmm birdli rejoined

[silver forge]

indeedeth patrick

https://klipy.com/gifs/l-death-note-3--k01KQSRXXXR54YTK30WT5J0NQTA

[radiant shoal]

is #1 ||224||?

[inland totem]

<@&268886789983436800>

[zinc ridge]

oop i got ||161|| smhow

[radiant shoal]

you might be right

wait

[neon summit]

why does it need to indicate area as positive
fake
the right angle one is pretty well shown, that the square of the hypotenuse is greater than that of the sum of the squares of the other two sides so x^2>10^2+17^2=389 so x__>__20 and with triangle inequality x<27 so you have the values

bro what is that combinatorics question

you can do the funny with the cube and find the plane PFM is in and then use fancy vector formulas to find the normal vector passing through the point G and then finding the distance fairly easily

oh wait no I misread

the cube part is hard mm

I'm pretty sure there's a formula for distance of a point to a plane iirc

[neon summit]

brotato chips isn't it 1/2 chance
either even or odd 😱

oh wait

ohhhhhh

I'm stupid

gosh I hate combinatorics

[neon summit]

2nd one is like casework
since they're independent the order doesn't matter so just do the probabilities that 2 people picked odd 2 people picked even 4 people picked even or 4 people picked odd

I don't know the formula for combinatorics or quite frankly anything related to probability, it's prolly some ||(5/9)^2(4/9)^2+(4/9)^4+(5/9)^4=400+256+625 /6561=like 1271 so 1+1+4+49=55 or smth||

[zinc ridge]

maybe if it was even

[neon summit]

I see what you did there

oh no the probability missing something

oh wait no it isn't

[zinc ridge]

i would probably js do for each dice the probability depends on the parity of the previous sum

idk

[silver forge]

i did some bs assumptions and it worked

[silver forge]

i forgor

triangle inequality theorummmm

and pythagorean theorum i think

thats all u need

[zinc ridge]

take a croos section

[silver forge]

median of triangle

then midpoint of that median

then pythagorean theorum on the isoscles triangle

[fallen apex]

Most important thing ever

[neon summit]

it is a cube
that

prolly works

imagine cross section of the cube thing on the plane with LKHG and it kinda is just a line and a point so easy enough ig

[echo ocean]

There is,1/PG^2 + 1/FG^2 + 1/MG^2=1/distance(G,PFM)^2 iirc

[neon summit]

hmmm

||200-100sqrt2=x~=69|| which is kinda super far

[severe eagle]

So civilised

[neon summit]

shut up d9 farmer

[severe eagle]

??

combi is stupid

why are you telling me to shut up 🥀

[neon summit]

agreed

[severe eagle]

smh

[neon summit]

because I suck

now solve the cube thing

[neon summit]

the 3rd one here

[severe eagle]

i dont think i will

im learning algo

[silver forge]

muahahahahaha

[silver forge]

Multiple choice = bs until you get smth

[silver forge]

wait what u didnt solve it

[echo ocean]

Dude....

,w 200-100sqrt(2)

[gilded halo]

Results provided by WolframAlpha

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

Requested by yobi_fx.

[silver forge]

um

[echo ocean]

How did you even get 69

[silver forge]

let me see my answer

[silver forge]

good job

[echo ocean]

[silver forge]

but dont be too excited cuz this is grade ten math contest

[echo ocean]

I don't lol

I do these type of problems like 5 times/day

[silver forge]

https://klipy.com/gifs/my-reaction-to-that-information-death-note--k01KQSRXXXR54YTK30WT5J0NQTA

[echo ocean]

[zinc ridge]

ooks

[neon summit]

the magic of 100*1.414 and me thinking hmmmm

I got an extra 1

[neon summit]

they know more than me they prolly have a better solution than I would've

I can solve it it'd just take me a while and paper and it's not really gonna be instantaneous

[amber finch]

lambert w function

,w x^x = 3x

hm.

[fleet drift]

what is the value of x

[knotty yoke]

If $x \neq 0,$ then:
$$ x^{x-1} = 3 $$
So, $x < 3.$ That is something I can conclude.
Use Newton-Raphson atp.
$x_1 = 0.23697$
$x_2 = 2.31197$

Or just use a graph

[gilded halo]

LemmaLover

[inland totem]

hmm

[untold wing]

i jusr HATE those "olympiad" problems, its almost always lamber w function or some ln shit

[silver forge]

hmmm

[spark scaffold]

I got this b4 too

[zinc ridge]

frel

[mighty pine]

it's a bit tricky to use the lambert w function here

because for like $x^{x}=ax,a\in\mathbb{R}\setminus(-\infty,0)$, you inevitably end up with $\ln({x}) e^{\ln({x-1})}=\ln({a})$

[gilded halo]

chudcel

[orchid raptor]

Ty i tried it and it was helpful!

[quick juniper]

lmao lobster when chkn was alre addy 2 be eaten then raw lobster instead of chkn ! added ! gratz.

therefore 3 is 3 and 3 = 3 just not for me but I'll tell you three of climb a tree IIV just don't climb ivy even tho it's 3.

| | |

up up and away !

[severe eagle]

Help is available

[quick juniper]

I saw

if I were to say he went to club fed would you know?

and that's why things are posted and not said, and I don't say things on here since ♬♪ ♬♪♫♩ ♪ ♫♩ you may never know. and I do not tell you, and we can't talk about it here... get it please be aware I am not that dolt.

2 3 1

ooos, I'm already not interested

[inner hazel]

does anyone know how i can build olympiad style reasoning in my brain bc whenever i see an olympiad / quant interview question or anything of the sort i get stuck and dont know where to start

[knotty yoke]

The easiest thing one could do is: Breaking into Cases.
I think this is a strategy that works in a lot of beginner/intermediate problems, and is the easiest to learn and internalize for a beginner

Like, break it into some $n$ finite cases, and see what happens in each of them.

[gilded halo]

LemmaLover

[knotty yoke]

A more powerful method is: Invariance and Extremal Principle.
Basically, either consider what does not change, or, consider, what is the minimum or the maximum (the extremes) of a configuration. This gives insights that simplify a problem tremendously.

For this, just read up on Chapter 1 and Chapter 3 of Arthur Engel Problem Solving Strategies.

I think they are great resources.

There is one thing that I'd want to tell you. You might think those who do well in Olympiads have a brain that thinks on levels that is outside your reach. While this may be true in some instances, it is not universally. With practice, most of the low-level stuff (SFFT, modular arithmetic, breaking into cases, invariance, coloring, pigeonhole, bijection, identities like Sophie Germain, inequalities like AM-GM, etc.) become automated, so their brain is free to think on higher lines, and reduce them into patterns they have already seen. With practice, these people probably have a LOT of patterns distilled in their mind. Even if they don't outright reveal it, it is just baked into muscles.

So, again, an overused word, but is appropriate here:** PRACTICE**

[inner hazel]

ahh i see thank you so much for this advice

i'll try doing maybe one problem every day

[knotty yoke]

Do not force it. If it becomes unenjoyable, there's no point chasing it.

You should do problems if you feel like it.

The really important skill to cultivate here is patience.

[inner hazel]

is it fine if i spend more than like 2 hours on a single problem

[knotty yoke]

It's perfectly fine.
I have spent much more than that on a single problem.

[inner hazel]

is art of problem solving a good place to get problems from

[knotty yoke]

100%.
Just look at their contest archives

For olympiads

They got a comprehensive archives for years and years of most olympiads you'd be concerned with.

[knotty yoke]

Coming with the expectation that you'd figure out the answer to a problem is something that might lead to hundreds of heartbreaks.
You should always try to make some progress, or at least eliminate some methods that do not work when dealing with a problem. if you can do that, you can always look back, and be happy that you did something

[inner hazel]

ahh i see thanks for the help

[neon summit]

spam pattern recognition

[neon summit]

you should be asking people for help if you can't get it in like 40 minutes 😭

I tap out quicker than 40 minutes I'm just gonna ask without thinking whenever

[fallen apex]

dont memorise

memorise = u wont do well

u need to actually understand

[echo ocean]

it pmo when people say there's no need to memorize things in math comp, ofc you do, remember as many known results, lemma and theorems as possible and also common/unique approaches and sub problems is such a big deal

Derive them on the exam would take ages even if you understand them clearly

[fallen apex]

if all u do is memorise then you wont do well

[echo ocean]

that's said, you need to do both

Understand and memorize

[fallen apex]

in olympiad and contest prep yes, you memorise but when you are just buildling reasoning, there is no reason to memorize anything

[echo ocean]

And people say memorize is not needed

really pmo

[fallen apex]

the only reason you need to memorize is cuz its timed
in reality you dont need to memorize anything

thats just the reality of all maths

[neon summit]

you memorize a lot

you'd be surprised

[echo ocean]

no, you need to memorize thing to make a connection to new problems. If you have a known result already in your head, you can connect them to other difficult problems

[neon summit]

sure it may "come" as natural after a long time practicing but a lot is genuinely memory and studying

[fallen apex]

and imo theres a differnece between active recall and straight up memorization those are two different things

[echo ocean]

you can't do that if you don't memorize them all

[fallen apex]

you probably referring to recall more than memorisation

[neon summit]

in both general kinds of competitions, long-form and fast/oral, you need the memorization

[fallen apex]

memorisation is just like what u do when u cram right before a test and forget it after a few days

[neon summit]

you can't recall what you don't memorize

what

[fallen apex]

yes you can

[neon summit]

I think you're mistaking recollection with finding something familiar

[fallen apex]

lemme formulate my thoughts more but i usually refer to memorization as just what ppl do as cramming and thinking they can do well just memorizing a bunch of formulas

like ik ppl thinking they could do well in amc just by memorizing a book of formulas and theorems and they were sorely disappointed

[neon summit]

memorisation literally takes root in the word memory which would imply it's long-term

[neon summit]

both understanding and memorization are needed

[echo ocean]

they, in fact, CAN do well even if they only memorize the theorems, even if they can't derive them, they only need to apply them well enough

[neon summit]

gimme the formula for ptolemy's theorem on cyclic quadrilaterals

[fallen apex]

who am i to argue against the goat terrence tao who doesnt memorise 😮‍💨

[neon summit]

that reminds me what was that 1/3 things in the median of a triangle

[fallen apex]

whats the statement of the theorem

i dont know names anymore

💀

pov: <-- this person hasnt done any competition maths in 2 years

[neon summit]

there's like two cyclic quadrilateral theorems

[neon summit]

same

[fallen apex]

is is the relation between diagonals and sides

[neon summit]

there's like only two* I'm sure your recall can remember the both of them's formulae

[neon summit]

I can't derive half the formulas I use/would use
we let the people 670 years ago deal with that

and euler

[fallen apex]

other one is just opposite angles sum to 180 surely but thats easy to see

[echo ocean]

You have been taught that volume of the pyramid is 1/3 h Area right?? did you known how to derive them ?

When you were taught?

[fallen apex]

yes

[neon summit]

we use integration and viewing

frfr

[echo ocean]

huh, so you were taught integral huh

In 8th grade, i see

[neon summit]

huh no I just cheatcode with calculus

[fallen apex]

no?

u dont need calculus

just use geometry

well i mean calculus is just geometry in some way

[echo ocean]

show me then

[neon summit]

added bonus of being a larp I self taught myself extremely elementary calc in 8th because nikola tesla did the same thing

I was 12 and edgy

[tiny eagle]

My friend did this and brought me along for the ride lmao

[neon summit]

I mean the main named ones used in competition, that one doesn't count that has practical applications in most curriculums

I would suppose if we include the angle things, it'd be 4 theorems on cyclic quadrilaterals

[echo ocean]

wao, I didn't even know what calculus is in 8th grade

[neon summit]

you should've spent more time being on facebook

[fallen apex]

if euclid can do it then you can to

!

[echo ocean]

[neon summit]

I used to think people just filled up a mold with sand and individually count how many sand pieces long were the sides and height and derive formula from the relations lmao

[echo ocean]

I was still struggled with euclidean geo at the time

[fallen apex]

i mean thats definitely a way u could do it

[neon summit]

just call it geo vro we know that 3 lines make a triangle

[fallen apex]

but also a lot of the formulas can be derived once you know some simpler stuff

[fallen apex]

diffgeo:

[neon summit]

derive the formula for the area of a square-based pyramid now

without using calculus

should be easy enough

[echo ocean]

you haven't shown me how to prove it's true , yet

It's not physic mate

Can't just do experiment

[fallen apex]

euclid already did it

why should i

who am i to argue against euclid

[echo ocean]

to show that you can

[fallen apex]

🤣

idc about euclidean geo

i do diff ge

[neon summit]

so would you say the memory is recalling or memorizing

[fallen apex]

none

i just dont know

[echo ocean]

honestly, euclid geo sucks, idk why carbonite is so passionate about it

[neon summit]

but you know the logic behind it don't you?

[fallen apex]

and n>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>cag

[neon summit]

Carbonite stop enjoying d9 geometry /j

I would like to be good at geometry but I deadahh forget every triangle and circle related shi(every geo problem ever) every 5 seconds

[neon summit]

tf is cag and n

[fallen apex]

💀

[neon summit]

I'm not familiar with terms I've only ever seen once

[tiny eagle]

Combo alg geo nt..

[neon summit]

oh combinatorics

right

[fallen apex]

wlog assume square pyramid (because nautilus told me to)
but it works for all bases if u adjust the argument carefully

blah blah blah

qed

[echo ocean]

combinatoric is better in everyway

[fallen apex]

there

[neon summit]

why is nt>alg alg>n

[neon summit]

erm

alg>nt>geo>combinatorics

[tiny eagle]

Geo > alg >>> Nt >>>>>>>>>>>>>>>>>>> C

[echo ocean]

nuh uh

[neon summit]

whoever says algebra isn't easy is high, whoever likes number theory is higher, geo is bad enough but manageable, combinatorics is just plain worse than geo

[echo ocean]

you lwk don't have to memorize that much for combi

compare to others

[neon summit]

the only time I'd apply just using logic for a problem is combinatorics because IT IS JUST USING LOGIC AND USING LIKE 3 DIFF FORMULAS

[fallen apex]

lokey

[tiny eagle]

Case bashing gives me horrors

[neon summit]

IT'S TOO INTUITIVE

[fallen apex]

idk how to do square pyramid

need more machinery than my brain can handle

ik triangular tho

u ujst use geometry

[echo ocean]

I do math very intuitively

so that's good

[fallen apex]

well im high

[neon summit]

the size of the square base increases by a certain ratio when you increase the height, an infinitesimally thin slice/cross section of the pyramid parallel to the base would have a volume of dh*(s)^2 so dV=s^2 dh now you express s in h and

wait

is that how it geos

I think it is but I'm probably wrong

[fallen apex]

well yea ik how to do with calculus

can u do it without calculus?
exercise: prove, or disprove

[neon summit]

vectors are also calculus

[echo ocean]

yeah, that actually applies to any base

[neon summit]

probably

[fallen apex]

not vectors needed

just trianlges

oh i just describe all of euclidean geometry

[neon summit]

I would imagine you can imagine a cube can be cut into 6 equal square pyramids but that only covers 1 case of s=2h

[fallen apex]

all u need is trianlges

[neon summit]

well, one could imagine an extension into a

nope nvm

[neon summit]

can do it in one specific case

probably it's possible to imagine smaller of such cases but as of the moment I'm stupid

[neon summit]

yeah it's how I remembered how we did it

[fallen apex]

yea the goal is to not use machinery beyond precalculus ig

or i guess trig idk

[primal bridge]

hello does anyone wanna participate with me in the MPL? its a great math competition I am trying to make a team if you would like to participate message me

[spark scaffold]

How can u factor x^pi=1

[rugged solstice]

Wdym

[spark scaffold]

Like can we use perfect of squares

[rugged solstice]

What

Like factor $x^{\pi}=1$?

[gilded halo]

Tangent

[spark scaffold]

Yes

[rugged solstice]

Hmm

$x^\pi=e^{i*2\pi k}\x=e^{i*2k}\iff k\in\Z$

[gilded halo]

Tangent

[rugged solstice]

There you go

@spark scaffold

[spark scaffold]

Thanks

[spark scaffold]

Ik x=1

[rugged solstice]

...

If you were asking I assumed you also wanted complex roots

[near hill]

Most of those e^i2k won't have i2k as their principal logarithm, though. So there's a threatening morass of pedantry about equations between multi-valued expressions.

[inland totem]

hmmm

[rugged solstice]

True except NT is the best

[inland totem]

nt is fun

but geo is best

[rugged solstice]

True

[rugged solstice]

No

[rugged solstice]

Wdym

[silver forge]

yes

[near hill]

For example, it if you set x=e^4i, then what is x^pi?
According to the most general single-valued definition of exponentiation I'm aware of that applies here, that should be e^(Log(x)·pi).
However, Log(x) is not 4i, but rather (4-2pi)i, since the principal argument is the one between -pi and pi.
So x^pi in that case ends up being e^i(4pi-2pi²) = 0.63 - 0.78i, which is not 1.

[rugged solstice]

Huh

[near hill]

The basic problem for your reasoning is that you cannot rely on (e^a)^b = e^(ab) when there are complex numbers involved.

[silver forge]

troposphere still carrying

[rugged solstice]

What if we limit k to a range

[near hill]

Yeah, we'd need to do that.

In fact it will only work for k in {-1,0,1}.

[rugged solstice]

k∈{-1,0,1} I'd think

[rugged solstice]

Yh

[fallen apex]

true

[fallen apex]

u get 🦧 🦧 🦧

[inland totem]

🦧

[glad flame]

true

[neon summit]

tangent line and extended line hell

[inland totem]

hmm

[neon summit]

is a kettle without the cap at the top and the handle included homeomorphic to eyeglasses without lens

[inland totem]

uhh i dont think so

[thick onyx]

hi

i'm new

[neon summit]

you enjoy geometry u should like this too

[inland totem]

ok

[quick juniper]

n - 2 ( 180 )

where n is the number of sides.

[thin pumice]

im sry for this but correction: the formula is 180(n-2) bcuz u need bedmas and order of operations or else it would turn into n-360 or unless ur doing (n^2-360)/n thingy

[radiant shoal]

unfortunately a triangle does not have -357 interior angle

[zinc ridge]

u mean the interior angle isnt -357 degrees right

[radiant shoal]

ye

well

both

[quick juniper]

cool... and yea teamsters... unlike how it's good in some situations . I wouldn't be good at competitive math it's healthy to tho to keep mind working as good as possible.

sorry whoever else don't like humor

[quick juniper]

I think the interior is in total 360 so one may be -357 then 358 then 359

[fallen apex]

What if we define it to be

[obtuse aspen]

Hey guys
How do you prepare for maths olympiad?

[rugged solstice]

With a smile

[neon summit]

what if hyperbolic geometry

[neon summit]

I larp and appear cool asf to every1 in my province because we appeared in a van with our school's name

[severe eagle]

https://tenor.com/view/gigachad-chad-gif-20773266

[neon summit]

chop chop geometry man/woman/equivalent is it possible for a triangle to have -357 interior angle in hyperbolic geometry

[severe eagle]

Anything is possible if you believe.

[neon summit]

but is it possible

with accurate hitboxes

[mental cove]

you are not wrong

[tired raptor]

hey can anyone explain the gaussian intergral??

[mental cove]

#multivariable-calculus

[urban ingot]

I challenge every1 to solve ques 2.

[urban ingot]

My progress

Of hour

<@&286206848099549185>

[urban ingot]

This ques is impossible

[urban ingot]

I do

This is Olympiad ques

[azure island]

67

[echo ocean]

lwk look like my 8th grade exam

[echo ocean]

do you know vector? this problem can be solved easily with vectors

[urban ingot]

Idk vector

[echo ocean]

hmmm

[urban ingot]

Pure geo ik

[azure island]

vectors and ratios in geometry

[urban ingot]

🫡

[echo ocean]

a hint would be: take advantage of area ratios and here're some constructions you might need

[urban ingot]

Dayum

[urban ingot]

Good approach

[echo ocean]

should have label the intersection

[urban ingot]

Bro u are pro

V clever approach

[azure island]

1/X = AC/AT = 67

[neon summit]

I got an unreasonably large number

[neon summit]

vro be making lines 🥀

[neon summit]

I wanna do number 5 because number 5 is algebra and it doesn't suck
so obviously we can tell from the get go that
(m+10)(m+11)(2m+21)/6-(m-1)(m)(2m-1)/6=n^2
(2m^3+63m^2+(220+231+210)m+2310-(m^3-3m^2+m)=6n^2
66m^2+660m+2310=6n^2 => 11m^2+110m+385=n^2
11(m^2+10m+35)=n^2
11(m+3)(m+7)=n^2
so now ||m=15, n=22 => m+n=37||

[neon summit]

no 6
||a>b, a=6 and a=5(assume b=a-1 since that maximizes b^3+ab) don't wor, a=4 leaves the only possible solution which then gives b=3 so now 16+27=43||

No 4. is just 81M+80=16N+540 leading to 81M=16N+460 which you then do fancy mod stuff and get ||N=275, M=81||

never doing geometry

[grand ember]

1+1=_

(Hint: )

[mighty pine]

$1+_{2}1=0$

[gilded halo]

chudcel

[mighty pine]

those who know

[fair bronze]

who?

[fleet drift]

derivative of x^(x^(x^(x)))

[inland totem]

hmm

[inland totem]

hmm lemme try

[fallen apex]

just use multiple logs

btw

theres only one log

and thats the natural log

all other logs are unnatural

[neon summit]

let y=x^x^x^x, u=x^x^x, v=x^x
lny=(x^x^x)lnx
lnu=(x^x)lnx
lnv=xlnx
(dv/dx)/v=lnx+1=> dv/dx=(lnx+1)(x^x)
(du/dx)/u=(lnx+1)(x^x)lnx+(x^x)/x => du/dx=((lnx+1)(x^x)lnx+(x^x)/x)(x^x^x)
(dy/dx)/y=((lnx+1)(x^x)lnx+(x^x)/x)(x^x^x)(lnx)+x^x^x/x => dy/dx=(((lnx+1)(x^x)lnx+(x^x)/x)(x^x^x)(lnx)+x^x^x/x)(x^x^x^x)
is the general way to do it

you have the funny blackpenredpen option

wait no blackpenredpen did like 2^x^2^x

[fallen apex]

now find a recursive formula

essentialy find the derivative of $^n x$ where $^n x = x^{x^{\cdot^{\cdot^{x}}}}$ ($n$ times)

[gilded halo]

kate (online)

[neon summit]

well I assume it's just (x^x^x^x^... n times)(x^x^x^x^... n-1 times/x+(
no I'm not writing that down

[fallen apex]

u can probably just use pduct notation

product

when i get home ill do it

[neon summit]

pi from i=1 to n (x^x^x... (n-i+1) times/)
nah I'm not doing all that

[fallen apex]

ill do it later

looks interesting enough that idm

and im bored and tired

[inland totem]

<@&268886789983436800>

[thorny tusk]

what happened

[neon summit]

I happened

[thorny tusk]

wat a great thing to happen

[dim garden]

x tetrated n times= xxx.... x times to equal x^x, and that amount of times to equal , yk the amount of products is 1 less than the tetration

so product rule wont simplify it enough

you need to make sure there is a derivative first

[neon summit]

suppose it's for values of x >0

[spark scaffold]

How can we solve x^x=3^(324)

[fallen apex]

would you say 2^2 = 4^1 ? Try using that idea

[spark scaffold]

After a brainstorm

It’s 3^(4x81)

Then 3^4=81

Therefore x=81

[fallen apex]

Yep

[molten wedge]

Quick question would an 8th grade putnam style question count as competition math

Since well
-# its a putnam style question

[thorny tusk]

putnam is a competition right?

[fallen apex]

Wdym

Just send it

[sinful current]

The William Lowell Putnam Mathematical Competition is the premier North American undergraduate mathematics exam, held annually on the first Saturday of December. It consists of two three-hour sessions (12 problems total) challenging students' mathematical ingenuity, typically in calculus, algebra, and combinatorics. The competition is notoriously difficult, with a median score often at or near zero, yet it is highly esteemed

I myslef gave one of its test for fun and got 4 marks , even though I am a full on Olympiad student although I am only 17

The age is range usually lies between 17-22 ( u just shouldnt have any college degree )

[oak tartan]

i think the answer he was looking for is yes

[mighty pine]

lambert w function

[neon summit]

give me enough time and I'll solve 1% of a putnam problem in NT or algebra give or take

[blazing coral]

send the q

some putnam questions are moderate but ive never done one at "8th grade level"

but tbf i flunkedd ts and got a 6/120 💀

[spark scaffold]

100% will be x=81

[mighty pine]

yes

i think it just returns 81 here

because the argument is positive

[thorny tusk]

is this an orz imo guy responding to my message?

[calm grove]

I need help with how to solve an non homogeneous differential equation with constant or variable coefficients with the right hand side needing the use of a convolution method when solving it with the method of laplace transform (LAPLACE ONLY!!!!!) please im curious on how the problem looks when solved

[shy raptor]

This doesn't really belong here - I see you've posted in #odes-and-pdes, which is more fitted to your question
(if you have a specific question, it would be helpful to also post it in there too!)

[novel karma]

Is anyone going to mao nats this summer

[knotty yoke]

Solve this one guys!

[sturdy knoll]

Isn’t that good in Putnam

[sturdy knoll]

Do you need help with this

?

[spark scaffold]

Yes

[spark scaffold]

But wait I need to do it and u check it

[sturdy knoll]

Uh sure

Where this problem from

[spark scaffold]

Insta

[spark scaffold]

Question on d

If they say f(x+5)=0

[sturdy knoll]

Obly that one?

Okay

[spark scaffold]

Is it mean do synthetic then set it as zero

[sturdy knoll]

I see

[spark scaffold]

And solve

Looks like right now

[sturdy knoll]

Idk

I would js plug in simplify and aolve

[spark scaffold]

My idea was

Still do synthetic and plug it in and set (x+5)=0

So that’s the remainder is the ans

[spark scaffold]

^

[sturdy knoll]

I don’t think that’s right

Cuz what I would do

Is plug x-5 into the equation you get in b

And one of the parts becomes (x-2)

Which gives you x=2

As a rral root

[spark scaffold]

Yes

[sturdy knoll]

No

??

[spark scaffold]

Bc it’s a horizontal shift of 5