competition-math

[delicate basin]

do you have a list of them

i can’t find it

What score are you aiming for?

[barren iron]

Perfect

[willow anvil]

p5 is well known troll

only 1 person on South Korea got it apparently

[brave heron]

WHAT?!?!

HOWWWW

Well tbf it relies on the clearing part

Playing a lot of minesweeper and some pacman and other clearing games probably helped my cause

I'm gonna be disappointed in my country if they didn't perfect 7 P5

[acoustic nova]

what score do u get as of now?

[zealous violet]

this is what i plan to use: https://bcmath.ca/competition-math-formulas.pdf

[zealous violet]

a qualifying score, which is usually around 100-120

[brave heron]

I still don't know why someone put an easy "combi" problem in a P5

[zealous violet]

70-80 😔

[brave heron]

Read it and you'll see why it's so easy

I'll be hella disappointed if someone in my country got 6/42 because if you just put me, i'll get 7/42(hey atleast an honourable mention)

Cutoff is probably 32+

They said P6 and P2 is kinda easy too

[delicate basin]

same lmao

I did 1 practice and got 91.5 😭🙏

[acoustic nova]

ok that is a guide, but pls do not study at all with that

[delicate basin]

but I have no idea how to improve

[acoustic nova]

thats ok

[delicate basin]

I would say try not to guess unless you’re sure it’s 50/50

[acoustic nova]

have u looked into aops?

[acoustic nova]

have u looked into aops?

[delicate basin]

the aops books are ok

[delicate basin]

i got sent copies of the books

my number theory is really weak

[zealous violet]

oh yeah fs, it was a link for a formula chart

[delicate basin]

because it’s never taught at school

[acoustic nova]

the inter alg one and inter combo books in particular are very good

[delicate basin]

I’ve been using the intro books

😭

[acoustic nova]

the algebra and geometry introductory ones are great in my opinion

thats cause richard wrote them

[delicate basin]

real

[zealous violet]

yeah ive taken a couple of their classes and also have 5-6 of their books
i plan to go through all of them (self study) to practice, deciding which order would be optimal though considering i only have a few months left

[acoustic nova]

if u study those well thats a large part of the test u can be confident about

[delicate basin]

OMG TYSMMM

[zealous violet]

np, i found it today as well lol

[acoustic nova]

oh u have already studied the books?

[brave heron]

Geometry introduction book feels like reading an enchanting table

[delicate basin]

i forgot about amc for a long time

until someone reminded me

and then I found that I’m not too far off the aime score

[acoustic nova]

im taking the 12 this year. i got a 96 last year so i missed a bit narrowly but i should definitely get it this year

[delicate basin]

so now I’m kind of dead set on it

[zealous violet]

i took classes for a couple of them but it didnt really stick, so I plan to go through all of them so i can cover the ones I havent gone through as well as revise the ones i already "went through"

[delicate basin]

this is my only shot at 10

[acoustic nova]

indecipherable is that supposed to mean? no i think its very good

[brave heron]

Yeh, my geometry skills are below abysmal

[acoustic nova]

then, when you do the introductory books, go through all the exercises and review problems and challenge problems and especially for the challenge problems, stick with them until u get it

[zealous violet]

I plan to first go through volume 1 as I heard it was the most beneficial for amc 10

[brave heron]

Give me combi and number theory, i'll eat those

[delicate basin]

i still don’t get how to use the number theory rules

[zealous violet]

oh the challenge problems 😔 jk ill try my best, theyre hella tough tho

[delicate basin]

anything with fermat’s little theorem

[acoustic nova]

u will have to put in a lot of effort since the test is kinda soon but if u do that (i didnt go through all the exercises when i did it, which is why im forced to go back to them, but im doing it now)

[delicate basin]

makes my head hurt

[delicate basin]

i have other exams too so

whidoejrnrkfkgtkit

[acoustic nova]

like what?

[delicate basin]

i can’t spend that much time on amc so i can’t do all the problems sigh

[zealous violet]

yup only got around 100 days

[brave heron]

Use smaller examples and you could see the applications really quick

[delicate basin]

school

[acoustic nova]

well you were looking at imo problems before so better than me probably

[zealous violet]

prob cant even get through a full intro book by then

[acoustic nova]

no school now though

not in us

[acoustic nova]

oh you can certainly get through an intro book

[brave heron]

Wdym, I forgot what even an orthocenter and incenter means😭

[zealous violet]

even the big ones?

[acoustic nova]

you can get through at least a chapter if u put in a few hours

[delicate basin]

im also not in us

[acoustic nova]

oh

[delicate basin]

i have exams for a load of subjects at school aaaaa

[acoustic nova]

what country

[delicate basin]

hk

[acoustic nova]

oh cool

[delicate basin]

my issue with fermat’s little theorem is

sometimes the mod base is not what I want

😭😭

do I manipulate the powers or smtn

[acoustic nova]

do u know things like finding the number of total divisors?

[acoustic nova]

the base can be anything u want

as long is the prime number doesnt divide the base

oh

[brave heron]

Yup

[acoustic nova]

oh the mod base

oops

[brave heron]

That's just most number theory. Manipulate the powers and some mods idk

[zealous violet]

so overall, how would you reccomend me to study for the next few months? (books to do in order, other stuff, etc) @acoustic nova

[acoustic nova]

well i have to see a particular problem, but the chinese remainder theorem is also handy

(not that i know how to use it well, but i know what it does at least 😞 )

[acoustic nova]

u live in the us right?

what grade?

[zealous violet]

yeah in summer break rn, entering 9th grade in a month

[acoustic nova]

for number theory, have u heard of michael penn? also the intermediate number theory aops class is supposed to be decent

[delicate basin]

I remember that’s like.. take each power of the prime factor and add one

then sum the up

[delicate basin]

nope lol

[acoustic nova]

no its the product. but do u know why it works for example?

[delicate basin]

oops

[delicate basin]

kind of..?

[acoustic nova]

https://www.youtube.com/@MichaelPennMath

[delicate basin]

it’s the number of ways you can combine them

the +1 is because you can have powe if 0

[acoustic nova]

pls watch this guy he is very good

[delicate basin]

i still haven’t gotten to that oops

[acoustic nova]

yeah to come up with a factor of a number, u go through each prime number and take a possible exponent for it

and you multiply cause its independent so thats how it works

add one cause if the exponent is e, u can choose the exponent to be from 0 to e

[delicate basin]

yea I kind of figured it out after I saw it in a book

[acoustic nova]

ok

[brave heron]

Not really sure if that works because theres a case where you could easily die if the monsters are in some diagonal state

[delicate basin]

😭

[acoustic nova]

so i would recommend algebra geometry combo then nt in that order

are u prepping for amc also?

[acoustic nova]

u should aim to finish all of these books or as much as u can, but obviously that will take a lot of effort (if u get to a chapter a day, which is definitely reasonable if u r dedicated, u will have a lot of extra time at the end for practice contests). go back to older material from the books if u need review, etc.

start doing more amc practice tests as u get closer to the date. aops releases their own "official" mock one, do that one seriously

[zealous violet]

hmm okay gotcha, don’t got combinations should I do volume 1 instead?

[delicate basin]

my school uses a system where all the topics are covered together

[acoustic nova]

honestly i dont find volume 1 very helpful. volume 1 would only be useful if u like discovered the amc the day of halloween (it would be too late to sign up at that point, but its just a joke). the book series has harder problems and goes in more detail

i would try to buy it if u can

[acoustic nova]

do u have the other intro books?

[delicate basin]

so the basics of differentiation is 9th
trig addition formula is 11th

its interesting..

[acoustic nova]

the algebra and geometry books are very good though the combo and nt are slightly worse but still good

[zealous violet]

books I have are: intro to algebra, intermediate algebra, pre-algebra, intro to geometry, number theory, volume 1

[delicate basin]

doom

i personally just get walled

by the last 7 amc problems

[acoustic nova]

10 years? idk

[delicate basin]

especially in the time limit

[acoustic nova]

they have a class though

[acoustic nova]

yeah definitely

[brave heron]

Which amc?

[delicate basin]

10

😭

[acoustic nova]

i would say this problem, #21, is easily doable though

[zealous violet]

okay got it then, I’ll start by revising the intro to algebra book while doing practice tests

anything else I should be looking at?

[acoustic nova]

have u looked through the intro to alg book already?

[brave heron]

2024 or 2023?

[brave heron]

0,9,4 are roots?

[zealous violet]

yeah but as I said it didn’t really stick too much yk, I wouldn’t mind revising the whole book

[delicate basin]

||4 is root of 4P(x) -> 4 is root of P(x)
3 is root of P(3x) -> 9 is root of P(x)
2 is root of P(x-2) -> 0 is root of P(x)
P(1) = 1
x(x-4)(x-9)(x-y)
1(1-4)(1-9)(1-y) = 1
-3 * -8 * (1-y) = 1
1-y = 1/24
y = 23/24
23+24=47||

[delicate basin]

Is this correct?

Shoot should have thought of that 💀

[delicate basin]

gonna sign up for this November probably

I think I solved it

[acoustic nova]

yep

[delicate basin]

Cuz my final answer is in the answer choices

yay!!

[acoustic nova]

i mean u dont have so much information about coefficients but its easy to find the roots themselves

[acoustic nova]

ok

[delicate basin]

Yea my idea was just finding every root I could

[acoustic nova]

i can understand that actually

[delicate basin]

and then trying to use that

[acoustic nova]

see

thats a final 5

[delicate basin]

I think that’s one of the nicer final 5 ones though 😭

[brave heron]

Yup

[delicate basin]

https://artofproblemsolving.com/wiki/index.php/2019_AMC_10B

[acoustic nova]

i think this problem is also very solvable

[delicate basin]

this is the one I practiced

I did not even have time for the last 6

[acoustic nova]

lets just say someone at my school a few years ago got a 150 on this test ...

oh oops not that test

https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B

this test he did

the 12

even harder

[zealous violet]

alr then, Ty man

[delicate basin]

(floorx)^2 = 3x - 2
x = 2/3 definitely works (eliminate E)
so does x=1
and I think it’ll start growing away
Id just guess C

[acoustic nova]

yeah np

gl

[delicate basin]

nah im cooked

i got low 90

[acoustic nova]

its 100% not c u just contradicted yourself

no

[delicate basin]

nvm I just remembered negative numbers exist

[acoustic nova]

well the expression ignoring the floor is factorable and that immediately tells u there are two solutions

[delicate basin]

wait no

[acoustic nova]

integer

solutions

[brave heron]

mfw

[acoustic nova]

but there are more total

[brave heron]

I hate negative numbers tbh

[acoustic nova]

the way i did it was rewrite the expression as floor(x)^2 = 3x - 2

[delicate basin]

😭🙏

im silly

[acoustic nova]

and then the LHS is an integer so u realize that x = r/3 for r in the set of natural numbers

[delicate basin]

I kind of figured that out

[acoustic nova]

LHS is also nonzero so x >= 2/3

[delicate basin]

do you guys think it’s a good strategy

[acoustic nova]

and also clearly there are no solutions for like x > 4

[delicate basin]

if i just ignore the last few and try to get the rest right

[acoustic nova]

so u have only a few solutions to check

and its easy

solutions take less than 10 seconds to check each, basically

[radiant jasper]

I think doing piecewise stuff might work

[delicate basin]

😭

[acoustic nova]

maybe that looks hard though

[radiant jasper]

Yeah but it’s the surest method

Slice the function into each interval

[delicate basin]

😭😭

[acoustic nova]

I wonder how it would be different if the square was inside the floor

[radiant jasper]

?

[delicate basin]

the math is hurting my head rn

[radiant jasper]

There’d be infinite amounts of answers

[brave heron]

I'd say just graph it

[acoustic nova]

u could use a similar approach as I described but it should be fine

[radiant jasper]

Oh I misread

Interval thingie could still work though

[acoustic nova]

yep there are still four solutions, one of which differs from the solution in the actual problem

[acoustic nova]

that’s pain

a proper solution I think would be to use the fractional part, but that would take more time

[radiant jasper]

That’s actually easier

[radiant jasper]

That’s just piecewisey with extra steps

[radiant jasper]

The graph would be many linear piecewise graphs

and you might select a few nice points to see its behavior

[acoustic nova]

then what I proposed, no. can you show me the piecewise approach though how exactly are u doing it?

[brave heron]

not really, 2 and 1 are solutions so there has to be additional roots near it

[radiant jasper]

With the square inside the floor?

[brave heron]

test -1,0,3,4, then you get 4

[acoustic nova]

wdym 3, 4

those don’t work?

[radiant jasper]

test

[acoustic nova]

no that would be a similar problem I’m talking about the approach of realizing the floor must be an integer so all x’s are of the form n/3 and then basic bounding

what does testing those do though?

[radiant jasper]

Oh then that’s easier

[radiant jasper]

To look for roots near it

[acoustic nova]

there are clearly no more integer roots

[radiant jasper]

The function is also continuous in an interval so you can quickly apply IVT on some test interval

[acoustic nova]

sure

but that’s more annoying but anyway

[radiant jasper]

It just looks annoying but if you do it in your head it’s trivial

[brave heron]

Where did you learn this?

[hidden sigil]

What will be the ratio of in radius and exradius of right angle triangle?

[radiant jasper]

Hey anyone

Who loves maths

[delicate basin]

kind of

on the amc 10/12 does anyone know if its a bad idea to just skip the last 5 questions if i only want aime cutoff

[brave heron]

There are some amc 10/12 last 5 question which had a trick up its sleeve

I'd say most

Then there are some midling questions which have a lot of whatever

It's a bad idea for sure

Best luck to figure out what you can answer

[delicate basin]

yea, i've found every now and then there is a final question i can do in 2 minutes

but i straight up do not have the time for most of them...

do you think it is a good idea to spend 1 minute on each final 5 q in the last 15 minutes?

[willow anvil]

Aops

[brave heron]

A lot of people got trolled aint no way

I can't wait to see my country's result

[craggy grotto]

quick! what is 3↑↑↑↑3 known as?

dang no one is here

[novel karma]

what do those up arrows mean? lol

[willow anvil]

knuth up arrow

[brave heron]

Tetration typa stuff

[craggy grotto]

nuh uh

[brave heron]

it is, its a knuth up arrow notations for stuff like hyperoperations which includes tetration and pentation

[craggy grotto]

i meant the number

what is the completed equation equal to

[craggy grotto]

🥶

[obsidian cloud]

Hi;
How do I get better at c&p topics? They feel more unintuitve to me than geo or alg based problems so it tends to tank my score a lot. On a related note, how do I do better on case counting problems?

[brave heron]

combi should be more intuitive, just practice yourself with lots of caseworking problems

apply complement principle

tbh when you know how to multiply and add probabilities then you know like 60% of it

[craggy grotto]

no one ever gonna asnwer my question? 😭

[radiant jasper]

all calculators respond with error unless I can find one that doesnt alr

[craggy grotto]

🤦‍♂️

prob cuz too many digits

[radiant jasper]

yea

because its like 3 to the power of 3 to the power of 3 to the power of 7625597484987

[craggy grotto]

?want to know answer

?

[radiant jasper]

no

[craggy grotto]

ok

[brave heron]

its G1

[craggy grotto]

correct

grahams number

[radiant jasper]

welp then I didnt go through wikipedia enough

[craggy grotto]

larger than googolplex

[brave heron]

its not grahams number though, graham's number is G64

[craggy grotto]

then whats G1?

[radiant jasper]

alr I was right thinking thats hexation

[brave heron]

TREE(3) still better

[craggy grotto]

TREE(4) is better

[brave heron]

TREE(TREE(TREE(TREE...) better

[craggy grotto]

TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100)))))))))) better

[radiant jasper]

∞↑↑↑↑↑∞ best

[acoustic nova]

why’s that useful

[craggy grotto]

infinity isnt a number

[radiant jasper]

oh well

[obsidian cloud]

SSCG(3)
Also ty for the tips

[radiant jasper]

I guessing this is a discussion of the biggest numbers that are still finite

[craggy grotto]

it is

[brave heron]

an infinite series of tree is still bigger than that

[obsidian cloud]

Would that produce a finite result tho?

[radiant jasper]

yea

[craggy grotto]

if its infinite it isnt a number

therefore it is disqualified

[brave heron]

2095 IMO gonna have infinite tree in P1

[radiant jasper]

isnt there some rule with relativity that infinite finite numbers can add into a finite number

[craggy grotto]

yes

[radiant jasper]

some zenos paradox stuff

[craggy grotto]

it is called irrational numbers 🤯

[obsidian cloud]

That's for convergent sequences of sums tho right

[craggy grotto]

cause pi=3+0.1+0.004...

[radiant jasper]

but infinite of them right?

[craggy grotto]

its infinite decimals yet smalller than 4

its is real

[radiant jasper]

eh but thats one division equation

[craggy grotto]

idc it still real

SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100)))))))))))

big number

[acoustic nova]

there’s no rule just common sense 1/9 = 0.1 + 0.01 + 0.001 + …

if that’s what u mean

[obsidian cloud]

Generalizing, some infinite decimal n.n1n2n3n4... can be expressed as a sum of 10^-k *n
Where k is the position? Of n
So yeah generalization

[brave heron]

I hate graph theory

[acoustic nova]

why? there are infinitely many numbers larger than any of the ones discussed so what’s the point

[radiant jasper]

eh yea prob just something I heard in a dream then

[craggy grotto]

ima make a really large number

[radiant jasper]

well anyone can just say ∞ better than everything, not making it a very good argument

man does anyone else hate the type of people who heard some big math name in middle school and thought they would take some khan academy course, just to flex that they "learned" that subject in middle school

[acoustic nova]

like wdym?

I know people who pretend to know calc in my hs and use it in problems

when it’s very much not necessary

[radiant jasper]

yea but they learn some rules, not actually being able to build on from it well

[brave heron]

funny story but a freshman in my school flexes about knowing calculus and stuff in the math club and he joined a team selection test in my school for competitions representation, then he got 0/100 and he put a lot of trigonometry stuff in an all integer answer test

so awful

[radiant jasper]

yea thats what I am talking about, those people

[acoustic nova]

a guy at my school that I know took calc freshman year and took linear last year

[brave heron]

"I know how to do derivation" man you couldn't even solve basic probability wdym?!?!

[obsidian cloud]

Damn do you guys have courses after that or is it w a local college

[acoustic nova]

nah not a local college

also multi and complex is offered

[obsidian cloud]

I'm surprised they found good teachers for that

[radiant jasper]

the real accomplishment that is from saying you "know calculus" is that you know everything before it, atleast when refreshed

[acoustic nova]

why wouldn’t u?

[acoustic nova]

why?

[radiant jasper]

huh?

[obsidian cloud]

Maybe it's my area lol but usually people who can teach topics like complex and multi would be at the very least grad students to non tenured professors and they wouldn't teach on high school leve salaries

Idk

[craggy grotto]

SSCG(10^10^100^(TREE(SSCG(10^10^100^G64^SSCG(SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100))))))))))))))))
goes hard 🗣️ 🔥

[acoustic nova]

I mean people who teach math at colleges for a living are unfortunately not getting by very well either

but I can see your point

[acoustic nova]

what?

[radiant jasper]

Im tired and wanted a more through explanation of what you meant by those 3 words

[acoustic nova]

what does this mean?

[radiant jasper]

anyone can learn some rulesets, and some symbols that are affected by rules, but anything before using the same symbols they wouldnt know

[acoustic nova]

huh?

[radiant jasper]

I dont know just forget it

[acoustic nova]

ok dw

[radiant jasper]

I am too tired to explain my thoughts

[acoustic nova]

what time is it for u?

[radiant jasper]

uh like midnight

[acoustic nova]

oh it’s like 1 for me I’m getting off soon though

[brave heron]

he probably its a real accomplishment if you know the fundamentals behind and not just some memorization learning stuff

[radiant jasper]

but my brain stops running efficacy around this time

yea

[brave heron]

apply formula guy

[radiant jasper]

the real thing that makes me mad is when they flex it as some accomplishment

[acoustic nova]

hard given how the schools are structured to teach

[obsidian cloud]

To be fair though at some level they have to understand what they're using right? Like at the very least in a where to use the formula sense

[radiant jasper]

yea when they get to that level they would know it

that doesnt make me mad

just when they gain an ego from it

-big ego

[obsidian cloud]

Makes sense

[brave heron]

I agree, in a school only about like 0.1% join competitions and only a few of those 0.1 can be considered as an expert of the fundamentals

[radiant jasper]

get into a student paced learning class

[brave heron]

and then theres teachers too

[craggy grotto]

i just went on a whole journey to make a big number

Ω↑↑↑↑↑Σ(Σ(SSCG(SSCG(G64)^SSCG(SSCG(10^10^100^(TREE(SSCG(10^10^100^G64^SSCG(SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100)))))))))))))))))))) is the number

[radiant jasper]

aint no way you use omega in math

[craggy grotto]

just did

still finite so i used it

[radiant jasper]

the end of all numbers

[brave heron]

how much of these googology stuff is actually canon in the context of theoretical mathematics?

[acoustic nova]

Ω↑↑↑↑↑Σ(Σ(SSCG(SSCG(G64)^SSCG(SSCG(10^10^100^(TREE(SSCG(10^10^100^G64^SSCG(SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100)))))))))))))))))))) + 237

better

[radiant jasper]

why 237?

[craggy grotto]

😭 HOW DARE YOU

MAKE A BIGGER NUMBER

GRRRRRRRRRRRRRRRRRR

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[radiant jasper]

wait no

if you added a nonzero number to omega, it would make infinity

[obsidian cloud]

MIT professors had a big number duel once

Beyond that idk

[craggy grotto]

no because omega isnt the last number

[radiant jasper]

well it literally means "end" in some cases

[craggy grotto]

well its not

[obsidian cloud]

https://web.mit.edu/arayo/www/bignums.html

[craggy grotto]

that would make infinity finite if it was the last

[radiant jasper]

I mean can you make the biggest number that isnt infinity

no

because it would have infinite digits

[craggy grotto]

omega isnt infinity digits

omega isnt last

[radiant jasper]

im saying that Omega is the represention of that number

[craggy grotto]

of infinity?

[obsidian cloud]

It would have a finite uncountable number of digits

I think that's how the terminology works anyways

[radiant jasper]

well the square root of -1 is representated by imagination

[craggy grotto]

omega isnt last though

[acoustic nova]

is that a thing?

[radiant jasper]

well so would infinite

[acoustic nova]

No a finite uncountable set isn’t a thing I don’t think

[radiant jasper]

I am saying Ω+n>0=∞

[obsidian cloud]

Maybe I'm wrong tbh I didn't look too deep into it

[craggy grotto]

omega isnt the last number

[obsidian cloud]

Well I had the terminology wrong so oh well

[craggy grotto]

there is no last number

never will be

[radiant jasper]

well there is no square root of -1

you cant write the square root of -1

just the thing that represents it

[acoustic nova]

I just wrote it

[craggy grotto]

💀

omega+1 does nto equal infinty

if it would omega would be infinity

[obsidian cloud]

Finite and uncountable are literally opposite in definition mb

[radiant jasper]

well my mathematical headcannon says Ω+n>0=∞

[acoustic nova]

yeah basically lol

[radiant jasper]

because you brought up omega in math

[craggy grotto]

there aint no last number

[radiant jasper]

yes there is

[craggy grotto]

nuh uh

omega+1 is finite

because both finite

thats how it works

[acoustic nova]

no

[craggy grotto]

no lst number

[acoustic nova]

If there is a largest natural number, it’s 1

[craggy grotto]

2?

[obsidian cloud]

There can't be by definition right? Since if a finite number n is the last number, n+1 is the sum of.2 finite numbers and is forced to be finite therefore no last finite number exists

[radiant jasper]

Ω+n>0=∞

well im saying omega is the number before infinity

because there isnt a number for that

[craggy grotto]

there is no number before infinity

[radiant jasper]

why isnt there then?

Omega would be the perfect fit

[craggy grotto]

well omega+1 is finite

omega is finite

one is finite

finite+finite=finite

[radiant jasper]

you cant square root a negative number

[obsidian cloud]

Omega is literally the term for absolute infinity lol
So it's not a finite number by definition

https://en.m.wikipedia.org/wiki/Absolute_infinite

[radiant jasper]

oh

i didnt know that lmao

[obsidian cloud]

I had to look it up lol

[radiant jasper]

alr then Ig omega is already used in math

[craggy grotto]

ah so its the opposite of infinitsmall

well its still technically finite

[radiant jasper]

is that alpha lol

also whats the point of this text channel I just joined

[acoustic nova]

comp math

[craggy grotto]

we are using different omegas 🤦‍♂️

[radiant jasper]

I can read

[acoustic nova]

not rlly this discussion I will say

[craggy grotto]

im stupid

[radiant jasper]

i just mean what does that mean

[acoustic nova]

so u have your answer if u can then

[acoustic nova]

one sec

[craggy grotto]

the omega im using is the set of all possible outcomes

we use different omegas

[radiant jasper]

for earlier saying that omega is finite, I say that omega isnt finite but it also isnt infinite

for my version of omega

[craggy grotto]

we just had different definitons

so my omega is stll finite

[radiant jasper]

yea

[craggy grotto]

yours is none

the other one is infinte kinda

[acoustic nova]

high schools math topics are often investigated in greater detail in competition math, which is what it sounds like. In many countries, there are local and then national competitions so that participants from each country can be selected for the International Mathematical Olympiad (IMO), the most prestigious math competition in the world

[craggy grotto]

so in my equation my omega is just all possible outcomes in the universe

[acoustic nova]

but this is shouldn’t be the channel for this discussion technically

[craggy grotto]

womp womp

we just arguing about a nonexistent number frfr

[radiant jasper]

I thought this was a channel for one-upping eachother in actual intellectual conversation

[acoustic nova]

@radiant jasper here was the “lowest” level test for the USA team, the AMC, from last year. I bet u can do many of the early questions

https://artofproblemsolving.com/wiki/index.php/2023_AMC_10A

[radiant jasper]

ok

[craggy grotto]



googolplex symbol

[acoustic nova]

look at the later questions though those are hard

[radiant jasper]

yea

[craggy grotto]

Σ(Ω↑↑↑↑↑↑↑Σ(Ω↑↑↑↑↑Σ(Σ(SSCG(SSCG(G64)^SSCG(SSCG(10^10^100^(TREE(SSCG(10^10^100^G64^SSCG(SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100))))))))))))))))))))))

[radiant jasper]

567

[craggy grotto]

here is big number

[radiant jasper]

not even close to the level of my aura

Im sorry

[craggy grotto]

💀

i have Σ(Ω↑↑↑↑↑↑↑Σ(Ω↑↑↑↑↑Σ(Σ(SSCG(SSCG(G64)^SSCG(SSCG(10^10^100^(TREE(SSCG(10^10^100^G64^SSCG(SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100)))))))))))))))))))))) social credit

frfr

no cap

on skibidi gyatt

[radiant jasper]

I cant handle this much brainrot

[craggy grotto]

its fun to talk with smart people who have brainrot as well

[obsidian cloud]

Oh god the brainrot is spreading

[craggy grotto]

REAL

i have Σ(Ω↑↑↑↑↑↑↑Σ(Ω↑↑↑↑↑Σ(Σ(SSCG(SSCG(G64)^SSCG(SSCG(10^10^100^(TREE(SSCG(10^10^100^G64^SSCG(SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100)))))))))))))))))))))) rizz

no cap

[radiant jasper]

still not even close

[radiant jasper]

true

[craggy grotto]

,w Ω↑↑↑↑↑↑↑Σ(Σ(Ω↑↑↑↑↑↑↑Σ(Ω↑↑↑↑↑Σ(Σ(SSCG(SSCG(G64)^SSCG(SSCG(10^10^100^(TREE(SSCG(10^10^100^G64^SSCG(SSCG(TREE(100^100^100*G64^(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(10^10^100)))))))))))))))))))))))+5

evil to bot

i might go to bed soon

[radiant jasper]

same, that was a fulfilling and thought provoking conversation, made my day

[craggy grotto]

same

[delicate basin]

[radiant jasper]

<@&268886789983436800> is this against the rules?

[barren iron]

[acoustic nova]

why against the rules?

[pallid ginkgo]

spam ig

[radiant jasper]

"ig"

https://tenor.com/view/dungeon-meshi-wachipiolas-falin-touden-sere-moment-gif-10372151276077328308

[cursive flower]

any recommended book to get good with olympiads questions

[radiant jasper]

guys I have AMC in like 2 weeks, anyone know a schedule I can follow to get high distinction?

or any resources I could use

[acoustic nova]

AMC in two weeks?

[limpid shore]

Probably australia

[brave heron]

I am so disappointed that P5 has 30% solve rate for IMO Participants(wtf)

For real, they probably don't know how to apply those calculus things in real life

Memorizing kid

he actually went inactive in the club probably because he got called out by one of the club members also planner of the team selection test

he got called "zero"

[lunar fulcrum]

you want to know why theres 2 solutions to the first image but only one to the second?

my best guess is just providing multiple ways to solve the question

since both problems involve expressions equal to zero, i imagine you can zero product property everything

as long as your answer is right i dont think anyone'll take issue with how you get there

[brave heron]

does the system solution works on the 2nd?

[acoustic nova]

for the first one, look at the second solution

[brave heron]

they DID NOT

no country did

[still geode]

what

[still geode]

ok but usually "omega" is used to refer to lowercase omega which in this context is a countable infinity

[inner blaze]

yo guys how should I prepare for high school math competitions such as HMMT and AMC12? I mean like, where do I even begin? I search up past problem sets and they're so hard I don't even know what to start studying. What are some good starting points and can someone make me like a mini roadmap? this is kind of a specific question to a more broader question of how do I become really good at maths? I would be willing to do anything to become really good at maths this year, as it's something I find to be genuinely fun and interesting.

[untold thunder]

I think AoPS books and AoPS Alcumus are good as they use those problems, but that's just my opinion.

[pallid tundra]

those are fine for getting your feet wet with the canonical contest curriculum

but your best resource is usually past contest papers

[acoustic nova]

there is some 3d geometry but all within euclidean geometry

[vale pecan]

Is 126 a good score for AMC 10?

[acoustic nova]

certainly lol

[vale pecan]

Will that get me a distinguished honor roll though?

(its past test)

[pallid tundra]

AoPS wiki has past DHR cutoffs

126 on a modern AMC10 is certainly sufficient for DHR

[leaden herald]

I was trying to do some exercises from my country's math competition and came across this

find the numerator of this sum, reduced to lowest terms

[gilded halo]

Rubix

[leaden herald]

how would you start?

I tried to simplify it, but I realised there's no formula for the finite sum of 1/n

[untold thunder]

Have you tried partial fractions?

[leaden herald]

you mean decomposing it?

I tried one way

[untold thunder]

yeah

[leaden herald]

there are others probably..

but all involving a fraction

[untold thunder]

I think if you decompose it, it might telescope

[leaden herald]

well one turned out to be

1 sec

$$2\cdot\sum_{n=1}^{99}\frac{1}{n} - \sum_{n=3}^{101}\frac{1}{n} - \sum_{n=2}^{100}\frac{1}{n}$$

[gilded halo]

Rubix

[leaden herald]

I think this is correct

but even now I can't proceed

[untold thunder]

I think you can break apart the first sum into to sums because of it's coefficient of 2 then telescope both series

[ornate blade]

so all the terms from 3 to 99 get cancelled out

you are left with 2 * (1/1 + 1/2) - (1/100 + 1/101) - (1/2 + 1/100)

[leaden herald]

not really

[leaden herald]

not even this

I'm plugging it in wolfram alpha 😂

[leaden herald]

this reduction is correct

[ornate blade]

,w 2 * (1/1 + 1/2) - (1/100 + 1/101) - (1/100 + 1/2)

,w 2 * (sum 1/n from 1 to 99) - (sum 1/n from 3 to 101) - (sum 1/n from 2 to 100)

[gilded halo]

Results provided by WolframAlpha

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

Requested by sooouth.

[ornate blade]

hmmm

ah I forgot that n = 2 was there in the last summation

[gilded halo]

Results provided by WolframAlpha

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

Requested by sooouth.

[ornate blade]

that's correct now

[leaden herald]

oh ok

there was no need to solve the sums individually

[ornate blade]

exactly

with telescoping you're guaranteed a lot of the terms cancel

it's just a matter of seeing which terms survive

[leaden herald]

it's still a rough calculation to do in comp, but not as hard

[ornate blade]

yeah when I saw the reduced form I knew that it would be super easy from this step

[leaden herald]

it'd take 5 to 10 minutes

k

thank you

[ornate blade]

npnp

[untold thunder]

I am wondering if I can get help on this problem: I got immediately stumped and I tried some cases like $p(1)=p(2)=p(3)=0, p(4)=p(5)= \dots =p(9)=1$, but even there I still couldn't find $p$. Any hints?

[gilded halo]

Cube

[odd plover]

Say we have 3^(1/3) then there exists a k^(1/k) = 3^(1/3) where k does not equal 3 and is a positive real number. What is k?

[untold thunder]

$k=\frac{-3W(\ln3)}{\ln3}$?

[gilded halo]

Cube

[odd plover]

What is W

@untold thunder

[untold thunder]

The inverse function of $f(x)=xe^x$

[gilded halo]

Cube

[untold thunder]

If you don't know what it is my answer is probably wrong

Rather it can be simplified further

[odd plover]

No I am just a high schooler that’s all

[untold thunder]

Do you have an answer on hand?

[odd plover]

Nope

[untold thunder]

Oh

[odd plover]

Is W(x) Multi valued?

[untold thunder]

yeah

[odd plover]

I see

[untold thunder]

On the interval $[-1, 0)$ I believe

[gilded halo]

Cube

[odd plover]

Mmm I would have thought $(- \infty, 0)$

[gilded halo]

dabeastmode_the_wannabe_nerd

[untold thunder]

Here's the graph: It has an asymptote at $x=0$, and its domain is $[-1,\infty)$.

[gilded halo]

Cube

[untold thunder]

Also I meant $(-1,0)

[odd plover]

Oh oops I was thinking about xe^x

[untold thunder]

The answer is approximately $k=2.47805$ by graphing but I don't know how you would find a closed for for $k$

[gilded halo]

Cube

[odd plover]

Maybe there isn’t an arithmetic answer:/

[untold thunder]

Where did you find the problem? (Or did you make it)

[odd plover]

I made it

[untold thunder]

Oh

[odd plover]

:/

[untold thunder]

You can tell it's probably not gonna have a nice answer because with some manipulation you find $k^3=3^k$ which is not very solvable sadly

[gilded halo]

Cube

[odd plover]

How do you know it is not very solvable?

[untold thunder]

Well those types of equations excluding the integer answers need to be solved with the "W" function which doesn't have a closed form.

This is its Taylor series I think

[ivory ember]

Hint: Consider the factored form of the polynomial $p_s (n)-a_n$

[gilded halo]

Civil Service Pigeon

[untold thunder]

Oh yeah

That's a very nice hint

[leaden herald]

an italian won a gold medal at the IMO

:)

[ornate blade]

mamma mia

[barren iron]

[soft vigil]

nice

[reef condor]

A Chinese “won” a silver medal at the imo 😠

Jk still very impressive

[leaden herald]

lmfao

some of those people are incredible

they're so good that even IMO questions are a limit to their actual skill

[late wren]

hi guys i was doing the amc10 mock test and i scored so low 😭 😭
i did past exams & usually scored around 95-100 (but they were kinda old so the problems were easier) do u guys have any book / video recommendations for probability as i feel like thats def my worst area

if i drop a 50 on the amc10 this fall idk what im gonna do 😭

[late wren]

woah gjgj

i should do that :,)))

i feel like for the old tests i can solve until question 20 but then for the newer ones i tweak so hard 😭 😭

why are teh tests getting sm harder bro

i can not catch up

[dapper magnet]

It says whole number 💀💀

6×5 + 3÷1-4÷2

[peak kestrel]

how do you know?

[near hill]

By construction yellow=green. If additionally yellow=blue, each colored area must be a third of the square.

The problem statement tells you.

[ocean narwhal]

What if the problem makers made a mistake (im sorry for the shitty joke in advance)

[junior zodiac]

Quadrilateral DIHS has ∠DIH = ∠IHS = 135°,DI = 3, HS = 10, and DS = 17. Find the numerical value of
IH^2

is there a non trig solution?

[ornate blade]

https://www.desmos.com/calculator/byposg5ick

there is an approach using coordinate geometry

by Pythagoras we need $\left(h + \frac{13}{\sqrt 2} \right)^2 + \left( \frac{7}{\sqrt 2} \right)^2 = 17^2$

[gilded halo]

southy

[ornate blade]

,w (h + 13 /sqrt(2))^2 + 49/2 = 17^2

[gilded halo]

Results provided by WolframAlpha

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

Requested by sooouth.

[ornate blade]

so IH^2 = 50

[junior zodiac]

where did all that values come from?

[ornate blade]

you start by setting I to be the origin

then because you have angles of 135, which are really exterior angles of 180 - 135 = 45

you can use the properties of the 45-45-90 right triangle

$1:1:\sqrt{2}$ scales up to $\frac{3}{\sqrt 2}: \frac{3}{\sqrt 2}: 3$

[gilded halo]

southy

[junior zodiac]

oh okay then?

[ornate blade]

yeah and then you let H = (0, h)
we don't know h of course

then S = (h + 10/sqrt2, 10/sqrt2) similarly

and then you find the distance between D and H and set it equal to 17

[junior zodiac]

ohhhhhh

[junior zodiac]

whats the reasoning for this scale up?

[junior zodiac]

ok nvm I got it, thanks!!

I have another geom problem where I'm stuck too

An equilateral triangle PQR of side 10 is inscribed in circle O. Suppose Y is a point on minor arc PQ̂ such
that PY ∙ QY = 81/4. Then, the numerical value of RY^2 may be expressed in the form m/n where m and
n are relatively prime positive integers. Find m + n.

I found the circumradius to be 10sqrt(3)/3

then got stuck

hmm

[ornate blade]

I'm also stuck but 10sqrt(3)/3 for the circumradius is correct

[junior zodiac]

is it power of a point?

PY*QY = R^2 - RY^2

[ornate blade]

bruh why even compete if you don't have an idea of your own

[novel matrix]

I have

I'm looking for more ideas

[glacial notch]

I think we should help him don't demotivate him

[barren iron]

Draw a circular square

[glacial notch]

wow

jannat

[exotic creek]

well you could do something like this

but ofcourse youd have to change some stuff or have a really good indepth explanation of how it works

copy pasting the image alone wont do obviously

[glacial notch]

what is this

[novel matrix]

I will merge

[exotic creek]

wait wrong image sorry

this is the one i was talking about

it looks like its always going up thats the illusion

[novel matrix]

hmm nic

[exotic creek]

yeah both

yeah

[prime whale]

I mean the mobius strip isnt really an illusion id say

Oh this was active 6 hours ago lol

[fossil loom]

what's the competition called?

[frozen rune]

uhm hello guys, I published a digital book, and I'm taking a survey about it, it's about vedic mathematics, where there are plenty of shortcuts and techniques that makes calculations easier, mind if i send the copy and the survey here?

if u know about vedic math I'm pretty sure it will help you guys

[barren iron]

I use calculator

[true kernel]

many comps such as amc dont allow calculators

[young echo]

Looks interresting

[barren iron]

Okay

[frozen rune]

wait

https://forms.gle/mpYtfNLmfH8JQz3B8

I'd appreciate it if you would answer the survey, it's alright if you put a random name

[brave heron]

Oh I joined vedic math but I just tend to brute force it

[ocean narwhal]

Aint that what we all do lmao i enetered an abacus competition and didnt even bring the instrument they use and still had like rank 3 or some shit lmao

Tbf that was a competition for third graders so i mean

[brave heron]

I just joined because of the medal

Their aim was for you too solve 999*999 in 5 seconds then I just do it for 15 seconds rather than waste my time shortcutting

And then lost time trying to do so

[ornate blade]

998001

999000 - 999

[brave heron]

Oh yesss

Then they do stuff like find the remainder when quadratic given x+1, then I saw that they set as x as -1

I was like, that's like the factor theorem not vedic

Why is it a vedic shortcut

Oh I screwed

*remainder theorem

[ornate blade]

Nah it's a factor here lol

But yeah same thing

[brave heron]

Tbh the local vedics are mostly about the actual vedic, then when you got to IVMO, it's like a normal competition with some wtf geometry which can'y be solved by any vedic shortcut

[frozen rune]

true it's crazy

[frozen rune]

i just compiled all the techniques i use to solve during the olympiads

[brave heron]

If anyone is up to the task, let s be the set the set of relatively prime to 2025 less than 2025, for each integer x which is part of set s, x⁵⁴⁰ is taken, find the remainder when the sum of all the resulting numbers is divided by 2025

[gilded halo]

Max

[gilded halo]

Max

[gusty verge]

Sorry for spam realized there was a mistake in my original latex but editing had run out

[junior zodiac]

Define s(n) as the sum of the digits of a positive integer n, for the first 999 positive integers n, we write n + s(n), how many of the resulting numbers are written more than once?

[ivory ember]

@gusty verge @brave heron

If we consider $x^{540} \pmod{25}$ and $x^{540} \pmod{81}$, we get that both are $1$, meaning $x^{540} \equiv 1 \pmod{2025}$ for all $x \in s$

[gilded halo]

Civil Service Pigeon

[ivory ember]

If we let the integers which give the same number be $m$ and $n$, then $$s(m)-s(n)=n-m$$ Hint: think about how this relates to carrying in the subtraction algorithm

[gilded halo]

Civil Service Pigeon

[junior zodiac]

Hmmmm

How?

[round lance]

Hey

I need help

[scarlet root]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[round lance]

I wanted a guide to participate in IOQM(india)

M a complete newbie with no guide rn

[gusty verge]

So the answer is just 1080?

[ivory ember]

yeah

[wary magnet]

what do I need to do to qualify for MC Nats. I already qualled in california state competition but I want to see if anyone has any reccomendations on what more I can do for nats

[wary magnet]

I'm already in Aops Mathcounts/AMC 8 class, and have number theory and precalc aops books.

Yeah I'm going in 8th grade this year

Thank you for the reccomendation to practice mental math

I'm not that good at mental math 😅

[reef condor]

It’s impossible unless you are xiooix

Don’t worry too much about it. In a state like California you have to be probably usajmo qual at least

[wary magnet]

thanks

[wary magnet]

what is xiooix?

and why would it be impossible to get into nats?

[mellow portal]

I’m trying to get better at problems for AMC 10 but I dont feel like I’m making any progress. I’ve done 10 practice tests and I can’t figure more than half of the problems out on each one. Is there anything I can do to improve?

[acoustic nova]

what scores are u getting around?

@mellow portal

[mellow portal]

Idk how to calculate that

[acoustic nova]

for each question u get right u get 6 points

each question left blank 1.5

each question wrong 0

[mellow portal]

K

Imma calculate for my most recent test, give me an sec

[acoustic nova]

if u didn’t know u get points for leaving things blank that’s a separate thing

did u?

how many questions did u get right on this last one? did u spend 75 minutes?

[mellow portal]

I didn’t time it

I get around 75 each time

It’s prob really bad

Oh ok

[acoustic nova]

no that’s kinda a lot but it’s ok

[acoustic nova]

how many questions answered and how many wrong each time around?

unreasonable at this point I would say unless the person took this test without any prep yet

[mellow portal]

On the last one I got I did
10 right
12 blank
3 wrong

[acoustic nova]

which test was the last one u took

[mellow portal]

2006A

K

[acoustic nova]

oh 😭

don’t worry though u will make a lot of progress if u put in the effort

[mellow portal]

K

[acoustic nova]

and are reasonably good

[mellow portal]

Is there like a textbook to learn from for methods on how to solve?

Bc some questions I just sit there and don’t know where to even start

[acoustic nova]

that problem is kinda simple but yeah

[mellow portal]

Wait what other topics are on amc

[acoustic nova]

not exactly

u should know trig actually

definitely law of cosines

u don’t “need it” but it’s definitely better to know it

there’s not so much of a point of worrying about the last 5

maybe try one or two if u actually think u can get it

[mellow portal]

Ye I’m really solid on my algebra and trig

I’ll look into the aops books tho

Tysm

K thx

[reef condor]

You should read aops books

You probably have enough time to make aime and get like 8 on it

Or even JMO if you rly grind

Start by using aops books. When you finish all of them, then grind problems

But it’s better to use books at the start

[soft vigil]

oops i gsolved j5 today

[torpid igloo]

Hi - anyone want to try this 5 minute speed contest - https://mathdash.live/contest/2024-kmmc-2a
(400 people have already competed - making it I think one of the largest online math contests I can think of!)

[royal estuary]

Hey guys

Can anyone help with this

[brave heron]

That's exactly the sum of consecutive squares for a

[royal estuary]

Ok

I figured it out

But i cant proceed further

[leaden herald]

I'll say 55 but it's pretty random

[reef condor]

guys this is good

[brave heron]

find the number of nonzero coefficients of (A+B-C)^49 - (A-B+C)^49

[ivory ember]

Hint: For the terms not to cancel, what must the exponents on the B and C factors be?

[brave heron]

different?

[ivory ember]

assuming the corresponding terms in the two expansions are like terms *

What is the condition on the exponents for them to not cancel?

[brave heron]

I don't really get was you mean by that

[ivory ember]

Consider a term in the first expansion

And the corresponding term in the second that is like terms with said term

What is the condition on the exponents of A, B, C for those two terms not to cancel when being subtracted

[junior zodiac]

Okay lets change the exponents quite a bit, just make it say 3, is it possible what you mean?

[brave heron]

wait

the corresponding terms making me confused

[brave heron]

I supposed in different combinations(idk what you really mean) , say one has 9x^3y^2 and the other one is 9x^2y^3, they wont be cancele

but you said its like

[gusty verge]

From what @brave heron pointed out:

It makes sense then to maximise the sum you will probably want to get equality from that, which suggests you take $x_i=i^2$.

The sum then becomes easy as you are doing the sum: $1+2+3+4...+2023=2023(2024)/2$

But obviously that is not the only way to get equality in the first sum. Ie. Swap one square with the number before it and swap another square with the number after, how would this change the sum of square roots?

Also keep in mind... whatever happens $x_i$ must be a square otherwise lambda is an irrational number

[gilded halo]

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

[brave heron]

you mean a corresponding term in the second expansion?

I just know when their exponents differ, they won't cancel out

if they are lik, they should be able to cancel out unless one is on the same sign

or not the same coefficients

[gusty verge]

Mao >>>>, played it at the IMC 3 years ago

[junior zodiac]

I'm so clueless rn

[brave heron]

is that what you mean?

[ivory ember]

I did say like terms tbh

[ivory ember]

Focus on this

[brave heron]

they will not cancel if the numerical coefficients are either different in value or their sign are not inverse(add minus), if they are like then idk the "exponents" affect it so that's part where i'm confused

[ivory ember]

If the exponents aren’t the same

Ex. $A^1 B^2 C^{46}$ and $A^2 B^3 C^{44}$

[gilded halo]

Civil Service Pigeon

[ivory ember]

Then you don’t even need to worry about cancellation

Hence why I said to focus on like terms

Take that as you will

[ivory ember]

or their sign are not inverse(add minus),
This is the same as
they will not cancel if the numerical coefficients are either different in value

So imma just focus on

they will not cancel if the numerical coefficients are either different in value

When does this happen

[ivory ember]

Am I high or does considering $\sum^{\alpha}{i=1} x_i-\sum^{\alpha-1}{i=1} x_i$ give you $x_i \leq i^2$

[gilded halo]

Civil Service Pigeon

[gusty verge]

Oh that's nice

Cool spot, I haven't checked the algebra but makes sense

Don't need to check the algebra... nvm definitely correct

[royal estuary]

[brave heron]

when some order of - + + when expanded doesnt correlate to the others combination too of - + + when expanded?

I can't put it in proper terms sorry

[ivory ember]

tldr parity yeah

[brave heron]

yup, that's the term I forgot

so you Mean, i just need to find all different combinations of parity?

[ivory ember]

There’s only 4 so just do it

The rest is trivial

[brave heron]

what are those?

++, -- andd

[ivory ember]

+-, -+

On B and C ofc

A clearly doesn’t matter

[brave heron]

how would you continue from here?

[ivory ember]

Once you find the exponents on B and C, the exponent on A is fixed

[brave heron]

the only thing I can see being canceled is A

anything else is, i'm clueless

[brave heron]

how do you find the exponents of b c?

[ivory ember]

Wait a minute

You know I’ve been referring to the multinominal theorem this whole time, right?

[brave heron]

i'm familiar somewhat with the trinomial case

[ivory ember]

Yeah that’s it tbh

As long as the exponents have the appropriate parity, you can let them be whatever you want

As long as their sum is no more than 49

[brave heron]

that's the problem, how do I do it when there are 4 different parities

[ivory ember]

If you consider the term $A^m B^n C^p$

[gilded halo]

Civil Service Pigeon

[ivory ember]

It’s easy to see that you don’t get cancellation if $(-1)^n=(-1)^p$

[gilded halo]

Civil Service Pigeon

[ivory ember]

So n, p have the same parity

(They’re both even, or they’re both odd)

I’ll do the even case as an example

We know that if we pick the exponent of B to be n, then m+p=49-n, and this there’s 25-(n/2) possibilities for p (and m is clearly fixed at that point)

So for the even case, it’s just $\sum^{24}_{k=0} (25-k)$

[gilded halo]

Civil Service Pigeon

[brave heron]

325

[ivory ember]

Now just do the odd case and you’re done

[brave heron]

okay okay

m+p = 49-n?

is it also 325?

[midnight frigate]

Help for usage!

[gusty verge]

Wow

[exotic creek]

cant wait for google gemini to prove the riemman hypothesis

(/j)

would they just give the million dollars to the ceo of google in that case?

[reef condor]

Google would donate it probably

[gusty verge]

Just wild that it did it in 19 seconds lmao

Imagine in the future with quantum computers and AI:

"AlphaProof20 proved the Riemann Hypothesis in 0.5 seconds"

[junior zodiac]

Still werent able to solve P5 in a faster rate

I saw a video, that said that if indeed it proved it, it will not be elegant, basically solved the whole thing with like 100+ propositions, it's so ugly and not elegant

[gusty verge]

This was P4 btw

[gusty verge]

Oh that's lame

So over kills on the proofs?

[junior zodiac]

It's a different imk problem though

Wait I'l the video

[gusty verge]

Surely with time it will be able to see what parts are redundant, that might be their first proof but they can definitely make an AI to simplify proofs

[junior zodiac]

https://youtu.be/ZrjarkXS0Fo?si=cg4DspMEPlGJySGO

[gusty verge]

Algorithm/game problems will always be super difficult for an AI

[junior zodiac]

This thing had like 3 cases and the diagram is very very much simpler yet they still suck at it

I'm actually surprised that combinatorics or number theory is not the first thing ai will be able to solve but actually geometry

[reef condor]

Nah it’s not that surprising

90% of theorems in geometry are just five-step angle chasing or a short proof from other theorems

So it’s really just a “simplifying” tool

But AI can run thousands of steps without issue so it is just OP in geo

The only “smart” part is when it creates extraneous points, which takes intuition

And that is where the “AI” comes in (other than that, it’s basically just spamming angle chasing + random theorems - of which it has a bank of millions)

[junior marsh]

Hello! Finally a Discord server that will appreciate my username. 🙂

Any tips for AMC 8 preparation?

[barren iron]

Yes only one

Prepare well

[soft vigil]

19 seconds is a lot of computing time

[gusty verge]

Yeah true, it's still a break through, maybe algebra problems will be next?

[limpid shore]

The more reducible a problem is to applying the same few steps over and over the more attackable it seems with the AlphaGeometry approach

But I don't think that's really plausible with algebra or number theory (definitely not combi)

So they'll have to cook something new up

Which they did with AlphaProof but that seemingly came at the cost of speed

[brave heron]

in the near future, there will be AI math competitions just like how in chess there is alphazero vs stockfish

[barren iron]

No

[brave heron]

they'll have to push them to the limits, well maybe nor competition but there will be someone in near future where they could compare each\

[gusty verge]

Considering what happened with chess, I think in 5 years the AI models will be better than the winners of the IMO

Well... isn't the winner a perfect or near perfect score

So maybe will need to create a new competition for it lol

[brave heron]

that's so crazy

[gusty verge]

You don't think? Everyone said the same with chess, that the computer would never beat the world champion

[brave heron]

no I meant that it's crazy that in a span of years, we could already see it happening

and we can't do anything about it

were entering a new wave of technology

Just like how the internet was introduced in the 90s

If AI can solve G8 ISL geometry in this day and age, it's gonna change how IMO works

[barren iron]

Yes then they will create new ai to design new imo for ai then there will be competition to create best ai to conduct competition of ai

Then all unsolved problems will be solved

Then there will be new ai to create new problems

[gusty knoll]

Anyone know a way to solve this without actually adding up the cubes of 1 to 10?

[ocean narwhal]

Theres a formula for the sum of cubes

Nd that formula always gives a perfect square

Soo basically 2900 + the answer should be a perfect square

You could just do this for all the options

[gusty knoll]

I see

Thx

[midnight frigate]

Wait imma

Do and send u

[gusty verge]

Yeah it's gonna be crazy

Hopefully they can make AI create new questions

[soft vigil]

$\sum_{i=1}^n i^3=(\frac{n(n+1)}{2})^2$

[gilded halo]

The real Duck

[gilded halo]

Vanellope von Schmugz

[soft vigil]

Yep

[sick fable]

and inductive reasoning to prove this

[haughty sleet]

for logic training, is the best way to just do a ton of problems

[gusty verge]

Try the problem, study the solution and see what others thought about the problem, ie. how did they approach it, you can find this on forums like stack exchange

[waxen vapor]

hello guys how can i learn writing stuff as 0? what i mean to say lets suppose that i have to prove that a - b divides a^n - b^n, and i do that by induction.
how can i write something that by writing 0 prove the things im trying to do?

i saw my professor doing that once, it was like idk, awesome

$(a^n - b^n)(a + b) = a^{n+1} - b^{n + 1} + (a^n b - a b^n)$

[gilded halo]

Ruben

[waxen vapor]

i should prove that $\underbrace{a^n b - a b^n}_{ = (a - b)k}$

[gilded halo]

Ruben

[waxen vapor]

for some $a, b, k \in \mathbb{Z}$

[gilded halo]

Ruben

[near hill]

Notice that a^nb - ab^n = (a^(n-1)-b^(n-1))ab.

[waxen vapor]

$a^n b - a b^n = (a^{n-1} - b^{n-1})ab$

[gilded halo]

Ruben

[gusty verge]

There is no set approach you should just try things that have worked previously.

For instance the most obvious would be further factorising.

[waxen vapor]

what about $(a^{n-1}-b^{n-1})ab(a+b)$