competition-math

[magic skiff]

because like bash doesn't need like much thinking

js a lot of computation

[keen lake]

I will not succumb to bashing

bashing is bad

[half mulch]

this is perfect

maybe add vandermondes identity to cp

yoo I'm doing egmo rn

or at least attempting

gonna finish it by amc hopefully

[kindred wraith]

why use chatgpt when you have so many resources available?

https://brilliant.org/wiki/amc-1012-math-contest-preparation/

https://artofproblemsolving.com/wiki/index.php/AMC_10_Problems_and_Solutions

like this took 2 seconds with a google search and you dont need to then go to someone else to verify

learn to use search engines, LLMs are not reliable

[undone sonnet]

Any ioqm aspirants?

[tropic ridge]

Whats 67 x 41 x 69 😔

[half mulch]

41 is so niche

[amber briar]

Does anyone have good sites for bitsat level maths qs? Or even bitsat mock tests on the maths part

[neon moss]

I have the AOPS books and practice problems, just don’t know which chapters or concepts are most important

[neon moss]

Alr tysm 🙏

[kindred wraith]

in general its hard to tell because youre not supposed to be able to prepare exactly for the test

if you just post the chapters in the books you haven't gone over, i can give you a rough idea of how to prioritize them

otherwise just prioritize core skills over the niche things

[half mulch]

yeah this especially

niche tricks come second

[kindred wraith]

the problem with the summary chatgpt gave you is that it words things weirdly

[half mulch]

cuz amc problems are designed to be able to be solved through intuitive solutions

[kindred wraith]

which, the concern is if you follow, you might have a weird perspective on things?

[half mulch]

although knowing the tricks can be an option

[neon moss]

I just want to learn some tricks so some parts of the question might be easier compared to if I didn’t know them

[kindred wraith]

for example, the screenshot you posted with combinatorics, it lists a "key skill", but its not a key skill in the way the other skills are "key skills"

in the other screenshots, those "key skills" are actually general intuition and problem solving strategies

however, in the combi case, thats a "core skill", you cant properly do combi at all if you cant check your work

also it says those things are "tested" but its not quite that they are explicitly tested

those are general techniques that you should have in your toolkit, and every problem is going to not only use a combination of these techniques, but which techniques to use are not obvious, and each problem also has many different valid solutions that use different combinations of techniques

the way chatgpt explains it, if you follow it as if it was a study guide, will likely be very inadequate unless youre just a very good self study

thats why i say to avoid using chatgpt

and this is just some of the problems with combi, which are the most egregious

@neon moss if you have questions, feel free to ask, but use non-LLM resources whenever possible

[neon moss]

Yeah I completely agree, but I don’t have most of these skills in my “toolkit”, so I’m trying to just see which are applicable to different competition questions, also combining practice questions and other material

[neon moss]

I asked it for the topics, then I’m going to use AOPS books and chapters to learn

[kindred wraith]

ok just checking

[neon moss]

But are the overall topics it listed useful?

[neon moss]

I mean I could study all the topics but I definitely wouldn’t have a deeper understanding compared to if I just studied a few core concepts or most important strategies

There’s like 130 chapters across all 4 intro books

[kindred wraith]

you know what

i have the books, let me just give you a rundown

hold on

[neon moss]

Thanks 🙏

[kindred wraith]

@neon moss how much do you already know/what are you comfortable with? what is your goal and when are you taking the test?

[neon moss]

Im from Canada, upcoming grade 9 and already took some Canadian tests such as the gauss, pascal, and Cayley, and got top 25 percent for all, but I feel like im not well prepared for AMC and for all other comps I just used my intuition and no actual concepts, which is why I wish to learn some helpful strategies or concepts to boost my overall performance. I’m decently comfortable with AOPS books but I definitely don’t have time to learn everything in the books by mid November (AMC 10 test date), so I’m trying to learn and understand the most important/helpful topics.

I’m also getting the intermediate books but a lot of people said the intro books are “good enough” for AMC 8 and 10

[kindred wraith]

ok unfortunately not too familiar with the canadian tests, so im doing a quick search of a sample test to get a rough gist

[kindred wraith]

this is true

and it sounds like you're getting into crunch time so you really just want to hit the big stuff

[neon moss]

Yeah I discovered the material too late, so now I’m kinda panicking 😅

[kindred wraith]

so a few tips to keep in mind

[neon moss]

They are much easier than the AMC, and to get top 25 percent is relatively easier since Canadian students are less competitive and also less concept based

[kindred wraith]

before even going crazy studying and cramming

AMC is a very particular test, it isn't a indicator of one's math potential or anything

there definitely is a "style" this test has, and those that prepare well can do better than those that don't prepare at all, even if they aren't as mathematically talented

these competitions should be viewed more as recreation than anything else

don't beat yourself up over a bad effort and don't put too much stress on yourself

i also got into this stuff really late, around grade 12, the last year i could really double down to study and prepare, and only reached AIME

and yet, without even majoring in math, i managed to find lots of opportunities doing math professionally in adult life

we all have our own paths, don't take it too seriously

[neon moss]

It’s mostly to prep for future math contests, and also maybe if I want to study in the US in the future this might be helpful, so I’m taking this pretty serious but I’m not gonna be super mad if I don’t do too well, since I’m still going to do plenty of other math contests

[kindred wraith]

ok that seems fine then, still good to take it seriously as long as you won't have regrets doing your best

that's what's most important

ok i'm gonna do algebra first

chapters 1-8 should mostly be stuff you find some familiarity with, though you might find these useful to review:
3.4 linear equations in disguise / 5.5 more linear equations in disguise - just so you're aware of it
6.3 conversion factors - very powerful and useful way to make these kinds of problems simpler and less prone to error

chapter 9 is probably familiar, but there's a lot of weird trickiness with inequalities if you're not careful, so review if you find necessary

max priority: 10.4 sums and products of roots of a quadratic, this is very common in AMC 10/12, also look up Vieta's formulas for a generalization which is also useful

very high priority if you don't know these: chapter 11 get comfortable with special factorizations, particularly knowing where to apply them

high priority: chapter 12 it's moderately important to have fundamentals with complex numbers

chapter 16 (functions) is great practice, not too many novel concepts, but the problem solving here gets very challenging

high priority: chapter 19 (exp and logs), 20 (special functions), 21 (sequences and series) are all pretty important to know the basics and defintiions

chapter 22 (special manipulations) gives good high level strategies

[neon moss]

Omg thank you so much

🔥

[kindred wraith]

geometry next:

ch2 (angles) is foundational, even though it's very basic, make sure this is super comfortable
ch3 (congruent triangles) and ch5 (similar triangles) very high priority if you don't know the congruence and similarity theorems

ch4 (perimeter area) and ch6 (right triangles) are not new topics but excellent practice of problem solving techniques

ch7 (special parts of a triangle) medium-low priority: definitions help, and sometimes they can make a tricky problem much simpler

ch11-13 (anything circles) max priority: circles are core to geometry

ch14 very useful to check out if you don't have comfort dealing with 3D geometry

ch15 (curved surfaces) if you already know all the formulas, medium-low priority

ch16 (transformations) unclear how important this is, but probably good to know
ch17 (analytic geo) good to get a baseline idea of what this is

ch18 (trig) basic trig is probably medium-low priority for AMC 10, probably should at least know the definitions of sin/cos/tan, anything else meh

ch19 problem solving strategies again are just useful

[neon moss]

Geometry is my weak point so il be sure to focus and do all of these

[kindred wraith]

number theory:

ch1-2 (divisors, primes) are core, this must be comfortable
ch3.7 you should know the euclidean algorithm, medium-high priority
ch4 (prime factorization) is absolutely critical and core if it's not comfortable already

ch5 (divisor problems) medium priority: you want some familiarity with this, might be a problem or two

ch6 (special numbers) this chapter is useless except for maybe low priority involving factorial numbers

ch8-10 (base numbers) is high priority if you haven't done any problems whatsoever, no comfort in them, medium-low otherwise

ch12 (modular arithmetic) very high priority
ch13 (divisibility rules) high priority

ch15 (number sense) once again, it's the problem solving strategies chapter

[neon moss]

So the other chapters are not that necessary right now?

[kindred wraith]

combi and probability:

this area is a little special, because knowing what concepts to use on a problem is just as or even harder than actually applying the technique, what is more important is:

• knowing how to experiment and try different methods of attack
• knowing how to check your work
  the rest is experience and intuition

for this reason, foundations are important, so I will label the concepts that are of high priority, but the combi problems really should be practiced almost religiously

ch1-3 are all core, concepts and general ideas that are used as foundation in almost everything else, must be very well understood before proceeding

ch4 knowing combinations is max priority
ch5 you want to review high priority 5.2 (paths on a grid) and max priority 5.4 (distinguishability)

ch7 is basic of probability, review if need be, and then everything in ch8 is max priority (except maybe shooting stars, a little niche)

ch10 (geometric probability) low priority
ch11 (expected value) low priority

ch12 (pascal's triangle) it's not that you need this per se, but it will help your intuition with combinatorics so much that it may as well be very high/max priority

ch13 (hockey stick identity) it helps when you're bashing I guess, medium-low

ch14 (binomial theorem) high priority, helps with algebra at times too, can be useful when bashing

ch15 problem solving strategy chapter

[kindred wraith]

correct

if i didn't mention the chapter, assume minimal priority

the only exception is the counting and probability book

which you want to practice more in general holistic terms, but in very structured ways

[neon moss]

So basically do all the chapters?

[kindred wraith]

as in you want to rigorously practice problems, make sure you understand each problem thoroughly, in particular understanding not just how the problem is solved, but why you can justify that it is correct

holistically, you just want to make sure that you're paying attention to the thing i mentioned before which is that

with combi problems, knowing what techniques to apply is sometimes trickier than actually applying the tricks

so a "holistic" practice simply means to practice combi more generally, so you can figure out how to handle the curveballs and unexpected problem types through experimentation and checking your work

https://www.youtube.com/watch?v=uxjAHkn4VFI

this video and some other lower-difficulty videos on this channel may help explain this in a bit more detail

ok that should cover most everything, plenty for you to work on by nov

[neon moss]

Ah I see, so for probability it is difficult to master all the tricks, so I should just generally understand everything to be able to apply them through practice

[neon moss]

For sure, I really appreciate you for dedicating all your time 🙏 ❤️

[kindred wraith]

it's sort of the inverse, it's very easy to master all the individual tricks, it's hard to know how to combine them to attack a wide range of problems

identifying the right tricks is harder than actually applying them

you might notice the aops combi book is the thinnest of all

and yet it's one of the harder ones

[versed bobcat]

good evening everyone

[kindred wraith]

np, come here if you have questions, i gotta sleep now

[neon moss]

Alright have a good night

[radiant jasper]

🧐

[keen lake]

bulko orz

[subtle sundial]

a mystery

there are some geometry people here

[pure yarrow]

Hello, I have my first international mathematics competition after 3 days , yet I feel frustrated cause I decided to take a break for the week before, I only do one hour or two maximum , am I ok or I should've done more, and if anyone did well in any maths competition, please tell me how was your schedule the last 3 days

[golden oak]

Honestly, when I competed in internationals comps, including subject other than math, the last few days aren’t really for consuming new knowledge nor cramping and doing so much new practice problems. But, if you unsure, it’s okay to 1-2 hours reviewing key ideas just don’t burn yourself out. So don’t stress too much, I’m sure you’ll do great!

[vague summit]

Actually, what's ur current math level and most importantly which competition? There is lot.

[subtle sundial]

^^^

it depends on the competition and what level it is at

[severe eagle]

indeed

[tiny grove]

Hey

I dont know if this is more a rant or quetsion anymore

I GENUINELY am struggling at like basic questions on alcumus alegbra

Like just algebra not the intermidiete

I mean i took a algebra 1 final and passed really well and i know algebra 2 well so i dunno why this is so difficult

Im just tryn practice for amc 10, aime

[neon moss]

Wait same

Where r u struggling

[neon moss]

I think it’s cuz a school math is really different from comp math

You have to apply different techniques in unique ways

[tiny grove]

I think i think abstract

But just not abstract in the amc way

I mean amc still has a hierarchy

Just different from hs

Which is why normally sumplr stuff throws me off for both

But i also may just br greked its 5am

[radiant jasper]

Like Aiden

[summer whale]

hey guys

is this channel about solving equations as fast as possible

or something else

[radiant jasper]

thats the worst thing ever

[summer whale]

what is it about then

[radiant jasper]

skibidi

[slender canyon]

bruh , do not say it here ok , it is just for math competitions

[radiant jasper]

skibidi!!!!

what is this skibidi hate

[summer whale]

yea when i get to some good level of math ill come back here

[slender canyon]

do not spam here bro

read the rules again

[radiant jasper]

i add more info if i say skibidi than if i say math competitions

[radiant jasper]

if i never read them, how can i read them again

[slender canyon]

I beg your pardon , Please do not say it here it's not a random channel

[radiant jasper]

brainrotphobia is real

i think this is the most appropriate channel to say this because math competitions are very similar to that

[slender canyon]

solid man , go listen thick of it and drink prime , bet?

[radiant jasper]

thats kind of offensive

brainrot is like genders you cant assume i am a thick of it fan

[polar patio]

guff is reserved for #discussion and stuff, not #competition-math , please don't message here unless you want to engage in related topics

[radiant jasper]

i was being serious

[fleet yoke]

has anyone participate in this IMC yet, I need a few Qs to ask huhu https://www.imc-math.org.uk/

[radiant jasper]

lol i saw you in a screenshot from a chat in mods today lol

the guy with geometry as nickname was there

i mean at imc, but also in the screenshot lol

[tiny grove]

is the amc and or aime genuinely hard

😭

[subtle sundial]

depends what you define as hard haha

[half mulch]

yes

[tiny grove]

😭

[strange yacht]

its completely different from school math

amc first 10 questions pretty easy

and its not abt proof

[tiny grove]

Yeah

At least no proofs🌹

[strange yacht]

YES

NO PROOFS

THATS THE ONLY GOOD THING

[calm raptor]

can any1 link me to the general chat :/

[subtle sundial]

#discussion

[neon moss]

Hi, does anyone here recommend the AOPS courses they offer? I’m thinking about taking the AMC prep course, as well as the AIME prep courses 1/2, have anyone taken them and are they worth it?

[faint nymph]

Proofs make mathematics lovable.

[prisma python]

https://www.scribd.com/document/599550964/seamo-Paper-F-2021?v=0.259
what are yall's thoughts on this olympiad?

it's a small olympiad for south east asian students and this paper is for grade 11-12

[faint nymph]

Ez

[bleak jasper]

Idk where this would go, so here I am :
Let there be a sequence of n terms and some c such that c belongs to natural numbers
You start from the first term and count up to c terms
Then you remove the cth term u ended up with
Then u start counting c terms from the next term
If u ever reach the end before c counts are over, let's say at v<c, then u start with v+1 from the start and till c
This continues until u are left with 1 term
Now, find the general formula of c to end up with the rth term

eg n=5 and c=6
note:each line represents he next step and black circles are removed terms
IGNORE THE 4TH LINE PLS IT IS A MISTAKE

[lusty plaza]

Hi

Can anyone please give me pathway

For MATH

[agile gazelle]

are you sure with the 4thline

[bleak jasper]

oh sorry lel

[agile gazelle]

ill give it a try

[strange yacht]

take think academy, they're comp math is way better than aops

[river valley]

i know this might seem like a stupid question (going into alg 2 competiton) but what are aime amc and all of these mean?

[neon moss]

American math competition, and then AIME is if you qualify from AMC

The next stage is USAJMO or USAMO

[lusty plaza]

Can anyone please give me pathway for learning CALCULUS

[half mulch]

khan academy

[versed bobcat]

https://tenor.com/view/maxwell-floating-gif-10118186011343519400

[wide sinew]

u ii a i o iii a i

[olive lichen]

based

[radiant jasper]

am a student grade 10, I am very interested in learning math, my goal is to get to IMO level as fast as possible, (side note) there is zero to none competition for IMO Selection in my country, my math knowledge is not good, i just started learning functions, ......
Now, my questions :
if i want to get to IMO level how many years shall i dedicate?
With what subject shall i start?
any other recomandations?

[pallid ginkgo]

for the first one it completely depends on how good you are, like how much you are willing to spend each day, how fast can you improve

[radiant jasper]

rn i can spend more than 8 horus per day until the 16 september

i can do my best i can learn things quickly

[pallid ginkgo]

for subjects, since your starting out (?) i reccomend just getting a feel of all of the questions equally, like maybe drill amc10 or amc12 maybe

[radiant jasper]

ok

i will look into that

[agile gazelle]

ye to be exact you need to solve problems without feeling tired like enjoying them really

[radiant jasper]

telling to. guy who plays 10 hours chess daily

-_-

[radiant jasper]

no problemi n that

in fact i would be happy

[agile gazelle]

what elo are you rn

[radiant jasper]

2600 in chess.com

[agile gazelle]

lets play

rn

im 2500 international master

lol

[radiant jasper]

nice

https://lichess.org/H0jNgvEv

[agile gazelle]

not lichess

i dont have

ok lets play im in

[late quiver]

hey

any one here who had tried imo

[radiant jasper]

hi

[dire aurora]

Hi

[radiant jasper]

ggs

i was playing pugb

while playing chess sorry for the delay

well played tho

[dire aurora]

Why didn't you play with your account

[agile gazelle]

breh

[radiant jasper]

why should i

[dire aurora]

We want to see the IM

[radiant jasper]

i am trying to be as ananoymous as possible

[dire aurora]

I got you but no need to be THAT strict

[radiant jasper]

i generally hate to show my acc to other people

btw do you guys use mechanical keyboard?

[dire aurora]

Its a flex though

[radiant jasper]

its not

trust

maybe for 10 sec but then its not flex

[dire aurora]

Alright up to you

[radiant jasper]

whats your rrating?

[dire aurora]

Nothing much around a 1000 but stopped playing like a year ago

[radiant jasper]

yh its ok

[agile gazelle]

ye but for real i think you re around 1500

[radiant jasper]

plus 1100

[agile gazelle]

nah dont think so

[agile gazelle]

show ur name

[radiant jasper]

hell nah

[agile gazelle]

:)))

so ig you didnt play serious against me

a 2000 could beat me easly i did a lot of wrong moves

[radiant jasper]

i still won with like 95%

accuratey what is you talking xD

[agile gazelle]

if your oppenents accuracy is low its normal to have high accuracy

:(( you should know that

[radiant jasper]

do you nkow what this diagram means?

[dire aurora]

Blitz?

[radiant jasper]

this is the game i played

ryne

he never got advantage i just over played him

[agile gazelle]

yep thats what i said a normal 2000 would have taken advantage of that

[dire aurora]

@radiant jasper you are rated by fide right?

[wide tendon]

Isnt 2600 like really high?

[wanton ridge]

welcome to the mathcord, yall! but remember to keep discussion on topic this is the competition math channel, you might want to check out #chess-go-shogi

[subtle sundial]

starting to aim for imo at 10th and without prior experience is pretty hard

how much years you spend depends on how math intuitive you are

i recommend starting out with elem and adv number theory, and branch out from there

also be really comfortable with proofs

[blissful echo]

please help me to solve this

[subtle sundial]

whatd you try out first?

[blissful echo]

i tried

[ornate blade]

PFD clearly first

[kind pulsar]

factorize the denominator fully then use fraction decomposition

[slate hatch]

Question number 10

[pallid tundra]

,rotate

[pallid tundra]

which one are you specifically having trouble with

9 and 10 i would just differentiate the answer choices and see which matches

[hot zodiac]

What does the " . " . In the sin(2017x).sin^2015 . Exercise 10

[pallid tundra]

prob just a multiplication sign

[scenic kestrel]

is alcumus on aops a good tool for mathcounts

[cerulean drum]

Use reduction formula

3-4 step solution

[cerulean drum]

Use identity (a+b)(a-b) in denominator

[slate hatch]

Question number 10 i said

[half mulch]

for 10 you write it as sin(2016x + x) then expand

then from there u get a reverse product rule integral

[slate hatch]

Yeah i got by this method
Thanks

[half mulch]

no problem

[slate hatch]

I wonder how we think like this

[half mulch]

whats the source of the problem

[half mulch]

I saw an mit integral that's pretty similar

I just happened to remember that solution development

[slate hatch]

It’s my school book

12 grade

[half mulch]

that's pretty crazy for a classroom integral

[slate hatch]

Yeah

[half mulch]

what are they feeding these kids

[slate hatch]

I am preparing for the world’s toughest exam

So it’s not a big deal for them

[slate hatch]

After all we have to deal with these crazy integrals everyday

[half mulch]

the jee?

[slate hatch]

Yeah

[half mulch]

nice good luck bro

[slate hatch]

Thanks

[half mulch]

jee math is the equivalent of competition math in America lol

[blissful echo]

not working

[slate hatch]

Maybe

[slate hatch]

I saw the SAT questions and they are pretty easy

[half mulch]

lol funny

I took the sat just now

sat is really easy yeau

well the English is challenging

[slate hatch]

Yeah

[agile gazelle]

guys can anyone help with this problem

[minor moth]

whats jee math

[bronze smelt]

can someone give me guidance on this question?

i dont know what im doing wrong

[near hill]

Neither do we, since you haven't shown either the question or your attempts at solving it so far.

[subtle sundial]

i think its a test in india

[pure mauve]

It's a famous engineering entrance examination in India, yes

[suffice it to say, not exactly competition mathematics]

[bleak jasper]

just search up josephus proble

problem

[prisma python]

what's a good resource to learn combinatorics theorems? like (2n-1)Cn=(1/2)(2nCn)?

[keen lake]

like bulko

[pallid tundra]

that’s not a “combinatorics theorem” that’s a “binomial coefficient identity” which any introductory combo text should cover

[subtle sundial]

just give the man a book 😭

[prisma python]

yeah lol I need to lock in this year

[half mulch]

aops intro to cp

and intermediate cp

[prisma python]

thanks

[gritty stag]

lmao

[lusty plaza]

What is the fastest way?

[ivory ember]

Observe that the exppression is zero whenever two of the variables are equal

Further hint: ||This implies the factorisation is of the form (a-b)(b-c)(c-a)Q(a,b,c) for some polynomial Q in a,b,c||

[lusty plaza]

Oh

Ok

Got it

[ivory ember]

[lusty plaza]

Yep working getting the same ans

As the longer method

Thanx

[pallid void]

Yo

Gurt

Anyone here do high school math competitions?

[near hill]

If I'm keeping the binomial expansions right in my head, abc should also be a factor.

And then there’s no room for any more factors within the degree of 6.

[analog phoenix]

probably a lot of us here

[pallid void]

What competitions do you do?

[analog phoenix]

the normal one's that everyone does

[pallid void]

Which one

[analog phoenix]

amcs, aime, jmo

[pallid void]

I only do state level competitions

[pallid void]

What grade are u in

[scenic sun]

Was the longer method the following? Let x = a(b-c), y = b(c-a) and z = c(a-b). Then the expression you want to factorise is x^3+y^3+z^3. Pull out the identity || x^3+y^3+z^3 - 3xyz = (x+y+z)(x^2+y^2+z^2-xy-yz-zx) || and recognise that || x+y+z = 0 || to conclude that || x^3+y^3+z^3 = 3xyz || which after substituting back in you arrive at the factorisation

[lusty plaza]

Yeah exactly

I did it like that

But that became soo much messier

[scenic sun]

Yeah true

[half mulch]

wh8cy

which

[pallid void]

UIL Academics

[pallid void]

It’s in Texas

Theres Mathemathics, Number sense and calculator applications

[half mulch]

interesting

[pallid void]

Mathemathics goes from Algebra to Calculus

And you have 40 minutes for 60 questions

[half mulch]

nice

send some calc questions

[pallid void]

It’s really basic calculus

It’s just integrating or differentiating something

44. Consider the graph of 2xy²-3y+4x² = 13. The y-intercept of the line tangent to the curve at the point where y = 3 and x>0 is (nearest tenth)

[half mulch]

oh pretty light

[pallid void]

40 seconds per question

[half mulch]

well the algebra u can probably do in like 10 seconds

so u stockpile time for the bashier questions

[bronze smelt]

has anyone down math counts

[pallid void]

F

[radiant jasper]

looks disgusting

[honest torrent]

Heyy guyss
Is there anyone here obsessed with maths challenges (imos...)?

[lusty plaza]

Yesir

[radiant jasper]

go to #competition-math

[radiant jasper]

def me

but i am asss ( as level, i luv math) in math so it sucks

[honest torrent]

https://discord.gg/aXyvBqY6

the plan is to share internationnal olympiads and explain them simply

cose most of the solutions are written in a complex way which scares students

[radiant jasper]

i joined

but i have no permission?

[honest torrent]

i sent u a mesg

[lusty plaza]

Me joined but no permission 😭

🥀 🥀

[frail geyser]

I have been trying this problem for like 20 mins but im still stuck, could anyone give me a hint on how to proceed in this Q?

[radiant jasper]

i think i can solve this

look there is a 1/4 chance of solving this correctly

wait this is really ez

[prisma python]

using pick's theorem?

or use coordinate geometry and use the shoelace theorem

[radiant jasper]

i think you can use piythagores teorem

[frail geyser]

i havent heard of that, gimme a sec to look it up

[radiant jasper]

wow

[frail geyser]

i tried to make triangles to try and isolate the area but i kept getting a number which wasntone of the answer

[radiant jasper]

i was just trying it myself

i just realized

[frail geyser]

just looked it up and this is so useful

[radiant jasper]

marvin W

[frail geyser]

fr

[radiant jasper]

dayum

shoelace therom works so fine

igh

[peak kestrel]

This one is easy tho

you can just use similarity

To directly get 4 * (5/4)²

[kind pulsar]

the blue triangle and green triangle are similar

1/2 = h/2.5 -> h = 1.25

the overlapping area is a rhombus which area can be calculated by (d1 × d2) / 2

here d1 = 5 (the horizontal red line in the middle)

and d2 = 2h = 2×1.25 = 2.5 = 5/2

[frail geyser]

thanks this helped a lot, wasnt able to see those similar triangles till u drew it

[prisma python]

oh wait yeah nvm i was wrong, pick's theorem needs integer coordinates

it's probably still possible with adding more points though

[kind pulsar]

so area is (5 × (5/2)) / 2 = 25/4 = 6¼

[frail geyser]

does this mean u can only use it when every point is an integer?

[prisma python]

yes

in other words when the points are on a dot

shoelace theorem works though

[peak kestrel]

You can just subdivide all linear lengths by 4

[frail geyser]

but if each point on the diagram is 1 distance away, why cant u just set the bottom left as origin and then each point on the rectangle and the shape in the middle then is an integer? Am i missing something?

[frail geyser]

for picks theorem

[peak kestrel]

and in fact technically generalizes to all rationals, and then by extension reals (but not very practical at that point)

[prisma python]

you can but you need to find the area of the intersection, and 2 of its vertices aren't on the grid

[prisma python]

you would need to count an infinite number of points for rationals though lol

[peak kestrel]

for rationals no

[frail geyser]

mb if im being dumb but could u explain what u mean

[peak kestrel]

for reals yes, but then you can take a limit

[prisma python]

irrationals i mean

[peak kestrel]

Check this out

red is 4 square units

it also has long diagonal 4, whilst big one has long diagonal 5

[radiant jasper]

can you not use shoalce formula

man

[peak kestrel]

so area is scaled by (5/4)²

You get the result directly

[peak kestrel]

You can

[radiant jasper]

isnt that easier?

[peak kestrel]

not for me

[frail geyser]

yh that makes sense

thanks

[radiant jasper]

hawklo

maybe you can try this out aswell

[frail geyser]

yh ill try

[peak kestrel]

But you have to find the coordinates for the vertices

which is definitely possible, but that just seems like too much computation in this case

[prisma python]

basically add 3 dots between each of the dots, so each point is 0.25 units apart, but it's not very practical

[frail geyser]

i thnk cyclictree's method is quicker but i doubt i would spot that while doing the Q so probs more likely to use shoelace

[radiant jasper]

thats the ez part

i thought you can start with ( 1, 1 ) for the point in bottom left

[radiant jasper]

that works aswell

[frail geyser]

I got another Q, why isnt the area 24? i keep getting 24 as an answer but the answer is E

This is the graph i got

[ornate blade]

that's not right, because if you replace $x \mapsto -x$ or $y \mapsto -y$, you get exactly the same expression on the left-hand side

[gilded halo]

south

[ornate blade]

so the region is indeed symmetric around the origin

by symmetry we can consider the portion in the 1st quadrant

then you can consider the boundaries of the region and figure out which points are in/out through testing

[radiant jasper]

lines and lines .......

nice

[ornate blade]

do you know about the triangle inequality?

[radiant jasper]

hell no

[ornate blade]

you should learn it then

you have that |u + v| <= |u| + |v| <= 4

(the <=4 is specific to this question)

[ornate blade]

also, there is symmetry where if you swap x, y in one equation, you get another equation

[ornate blade]

so then |u + (-v)| <= |u| + |-v| <= 4 and so on

[coarse patrol]

I am stuck pls help
Not stuck
I cant even start
How to start?

[radiant jasper]

yea but i dont have time

a lot of time

just use __

xD

it starts with A and ends with I

[coarse patrol]

Probably AI
but i am not sure
I will use lifeline

[peak kestrel]

There's probably some combinatorial identity

[prisma python]

my first thought is a^2016=1mod2017 with fermats little theorem

[coarse patrol]

This is a question that wants to take you there
But you dont have to go there

[prisma python]

yeah

the expression is kind of similar to the binomial expansion of (a-1)^2015 but i don't know how to progress

[peak kestrel]

i don't think fermat's ever works because it can't prove that it's smallest?

[prisma python]

smallest?

oh yeah thats true

[radiant jasper]

guyhs

how many years would it take a normal joe to get to IMO level?

[summer roost]

It can take somewhere from a year to 6

But considering you are an IM

You might be able to improve quickly

[radiant jasper]

yh

[summer roost]

But that totally depends

[radiant jasper]

i have 4 years until i cannot participate in IMO

[summer roost]

Since they are completely different skills

[radiant jasper]

i wish to finish everything in 2 years

[summer roost]

Plenty of time

If you are dedicated

I assume you are in grade 8th or 9th

And in most countries school studies shouldn't affect your olympiad preparation

For some time

[radiant jasper]

no

10 i will be 11

[summer roost]

Uh

[radiant jasper]

its until 20 years

[summer roost]

Then how do you have 4 yeats

Years

[radiant jasper]

i checked

[summer roost]

It also depends on the regional exams

Did you check thise

[radiant jasper]

my country exams are so ez

compaared to other countrys

[summer roost]

The age limit is 20 but you cannot participate if you have entered college

In my country I cannot give the exam after 17

[radiant jasper]

USA?

[summer roost]

No

But here after 12th grade we cannot participate

[radiant jasper]

i think i will dedicate a lot of time

as you said being a IM wasnt as ez aswell

so i kinda know how to handle big chucks of stuff at the same time

[summer roost]

Also I would recommend to check a few competitions especially aime and amc to see if you like to solve such questions

After all it is of no use to prepare for competition math if you don't find interest in it

[radiant jasper]

i am watching videos like that

[radiant jasper]

ik

[radiant jasper]

ofc

[summer roost]

Well best of luck for your preparation

[radiant jasper]

can i ask you a q

if you were me what would you do like? as learning subjects and lockin in? ( if you were a average joe)

[peak kestrel]

e.g. this question just looks annoying to me

[peak kestrel]

This one is more interesting

[summer roost]

Uhh I don't know

I stopped preparing for competition math

So I am not the best person to answer the question

[radiant jasper]

what was routine maybe its easier to answer?

like at the times you prepared

[summer roost]

I used to solve problems that was it

But I didn't prepare for more than 3 months

Since I was a bit late to thsi

[radiant jasper]

what kind of problems have you maybe have them still?

can you maybe dm me ss of those maybe?

[summer roost]

I used to do amc 12 ot mid aime

Nothing beyond that

[summer roost]

You will find plenty of problems on this server

[radiant jasper]

i saw

jjust now

amc 12

[summer roost]

Initial problems are easy

The last ones are good

[radiant jasper]

nice

do you have other websites like that?

i gtg cya time to play basketball

[dense rivet]

If radius is x, then shouldn't we integrate y, and not x?????
So it should be y²dm?
Helppppppppppp

[mild bay]

Nah

Take small unit of that ring

Moment of inertia of that pt is the mass of the pt . x^2

And x is constant

So we get dm x^2

Got it?

[ivory ember]

Cute - I like it. \ \

This essentially reduces to finding $\sum^{2015}{k=2} (-1)^k \binom{2015}{k} k^{2015}$ and $\sum^{2015}{k=2} (-1)^k \binom{2015}{k}$ modulo $2017$. \ \

I'll talk about the second sum first since it's significantly easier. Using the binomial theorem on $(1-x)^{2015}$ yields $$(1-x)^{2015}=\sum^{2015}_{k=0} (-1)^k \binom{2015}{k} x^k$$ Setting $x=1$ and chopping off the terms for $k=0$ and $k=1$ takes care of the second sum. \ \

For the first sum, recall that for a polynomial $P$ with leading coefficient $d$ and leading coefficient $c$, we have $$\sum^{d}_{k=0} (-1)^{n-k} \binom{d}{k} P(k) =c \cdot d!.$$ This is straightforward to prove by finite differences.

[gilded halo]

Civil Service Pigeon

[ivory ember]

https://math.stackexchange.com/questions/2117460/show-that-sum-k-0n-1nkn-choose-kakb-n-nan?noredirect=1

Proof for the finite differences result ^

[coarse patrol]

What is finite diferences?

[coarse patrol]

You are my type of guy
Something horrific comes and we say Cute 😍

[glossy tinsel]

Could someone help me with this? I’m thinking it can be solved using number theory/modular arithmetic but im not quite sure

[coarse patrol]

I guess take the worst case scenario and PHP

[ivory ember]

https://brilliant.org/wiki/method-of-differences/

[hushed charm]

Needing help here. I know that $\frac{a^2b^2 + b^2c^2 + c^2a^2}{abc} \ge 3\sqrt[3]{abc} \text{ and } \frac{1}{3} \ge abc$

[gilded halo]

samuel

[hushed charm]

I'd say that the answer is $\sqrt[3]{9}$, but that doesn't seems to be right.

[gilded halo]

samuel

[half mulch]

cauchy Schwarz maybe

[outer mural]

is this meant to be done without calculus?

[pallid tundra]

yes

[zinc grail]

I don't know if it helps, but imagine a, b and c being coordinates of a point on a sphere (because the equation of a sphere of radius 1 is $ x^2 + y^2 + z^2 = 1 $). Then you can express them using spherical coordinates
a = sinθcosφ
b = sinθsinφ
c = cosθ

θ is the angle between the Oz axis and the radius
φ is the angle between the projection of the radius on the Oxy plane and the Ox axis.

You can copy paste them in the expressions (assuming the necessary conditions are met) and then check to see how it goes.

If you want to learn more about spherical coordinates, see
https://en.wikipedia.org/wiki/Spherical_coordinate_system

Sorry for not using latex everywhere, I'm typing this on my phone.

[radiant jasper]

woaw those formulas look cool, ...

[scenic sun]

A hint is to consider || a King’s moves on the chessboard || and assume || FTSOC (for the sake of contradiction) ||

[lusty plaza]

Hi

[radiant jasper]

hi

[outer mural]

i can get || sqrt(3) || with lagrange multipliers. i can get the same answer using rnicol's approach. it's pretty messy either way.

[green lotus]

x = 6, y = 5 and x = -5, y = -6

[mild bay]

I got it in the help page, ty tho

[green lotus]

Oh ok

[prisma python]

factorize by difference of cubics then divide xy to the (x^2+xy+y^2) term then since 61 is a prime, either (x-y)=1 and (x/y+y/x+1) is 61 or vice versa

wait nvm i read the question wrongly

[mild bay]

Dw, I alr got it. I have to use a^3+b^3+c^3 -3abc

=1646

A=3x, b=-3y, c=-1

[outer mural]

how does that help?

[green lotus]

(x-y)(x^2+xy+y^2)=xy+61=(+/-6)^2+xy+(+/-5)^2

And go from there

[outer mural]

is that a different approach from what yoda said?

[dense rivet]

It's moment of inertia (rotational mechanics)

[prisma python]

what's the easiest way to solve this?

I got like sum of n=0 to infinity of (-1/12)^n(2n-1)!/(n-1)!n! or something

[ivory ember]

$\sum^{\infty}_{n=0} \binom{2n}{n} x^n=\frac{1}{\sqrt{1-4x}}$

[gilded halo]

Civil Service Pigeon

[prisma python]

thanks

are there any other results similar to this that I should memorize?

[ivory ember]

idk

[radiant jasper]

russian way right?

[mild bay]

Wdym

[radiant jasper]

its a russian olympiad test

[vernal axle]

You can put x+y=a and x-y=b.
Then you have a²=(244-b²(b+1))/(3b-1) which means 0<b<6 (otherwise RHS is negative), so you just have to check b=1,...,5.

[mild bay]

Hmm

[thick falcon]

why are half the questions here c&p

[outer mural]

be the change you want to see in the world

[subtle sundial]

true

!

[near hill]

What is "c&p"?

[half mulch]

counting and probability

[ornate blade]

should be p&c lmao

[opaque hearth]

Whats 2+2 💀

[cloud dagger]

its a very difficult question

[noble crest]

perplexing indeed

[radiant jasper]

1

[fast atlas]

Anyone has experience with IGO? What should I study to prepare for that?

[radiant jasper]

do geo lol

[radiant jasper]

what's your level on geo?

roughly

[fast atlas]

Eh...

I have no idea

[radiant jasper]

bruh

have you ever done geo lol

[fast atlas]

Well yes, I know the basic things and like Ceva's, Ptolemy's, Menalaus' theorems and stuff

[radiant jasper]

did you read egmo

I recommend doing basically everything except the bash chapters

(imagine bashing)

[fast atlas]

Euclidean geometry in mathematical olympiads?

[radiant jasper]

Yes

[fast atlas]

Nope

[radiant jasper]

It's the geo bible

[fast atlas]

Does it have a learning curve?

I'm no good

I have like more than a yeah to prepare though

Or around that

[radiant jasper]

I don't think the level is too high

but you don't need to do all problems from all chapters, it's ok to leave some of them

but if you already know stuff like Ceva and Menelaus, I don't think you'll have too much trouble

[fast atlas]

I'm probably skipping all the barycentric and imaginary stuff

[radiant jasper]

yeah bashing is for losers

also if you want you can join mods, there are a lot of problems you can use to train, and for all levels

[fast atlas]

Mods?

What's that

[radiant jasper]

the server linked in the description of this channel

[fast atlas]

Thanks, just did, hopefully the material there won't be too advanced for me

[radiant jasper]

if no one helps you just type "-t tutorial" in like botspam and it'll say everything you need to know

[radiant jasper]

you can also use your country's national olympiad first rounds problems

or other rounds depending on where you live lol

[fast atlas]

Those are definitely way too advanced

My country seems to like geometry it seems like

All the IMO problems that were proposed by my country are all geometry problems too

[radiant jasper]

Hm

Vietnam?

[fast atlas]

Yes

[radiant jasper]

Lol

Ok Vietnam geo is cooked

Well just see how you do with what I gave you and if not then I'll see what else there is

[fast atlas]

Okay i'll check out the book

[radiant jasper]

then ofc try past igo problems sometimes to get an idea of what they look like and how hard they actually are

[fast atlas]

I found the IGO problems from 2017-2023 but for some reason couldn't find 2024 and 2025

Do you have them?

[radiant jasper]

2025 igo hasn't happened yet

[fast atlas]

Oh

[radiant jasper]

2024 should be on aops

[fast atlas]

It's in October right?

[radiant jasper]

iirc yeah

[fast atlas]

I might try it this year even, though I probably won't do well

But then i still have next year

Couldn't hurt

[viral rain]

no it will

they give you a public execution if you take too long

[night kettle]

Hey guys

Anyone speak spanish here?

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/

[rugged prairie]

Yoo

So i think im pretty bad in math personally, im grade 9 or 3rd year highschool..

But i wanna study well and do well in the competition upcoming

May i ask for some advice..

[warped folio]

Bro I am also in grade 9 a advice is that you have to practice as many questions you can, u have to understand the concepts and practice 5-15 question on one topic, revise formula regularly and practice 5 question on one formula so you can grab the concept and btw which chapters are u studying

[rugged prairie]

thank you so much bro..
im not sure which chapters im gonna study, the competition entry just released

are you in philippines perchance

you mightve been invited to the same competition

im gonna take that note advice to the heart so tysm

[warped folio]

No I am actually from India but which competition is it

[rugged prairie]

this hongkong heatround thing

[warped folio]

Np like which chapters are in ur syllabus

[warped folio]

Seems like a advance level competition

[rugged prairie]

HKISO i think

[rugged prairie]

Right now its Quadratic equations in the first quarter,

things like extracting square roots, completing the square, quadratic formula

[warped folio]

In competition or in school

[rugged prairie]

factoring

[rugged prairie]

school

i dont know the competition yet

Ill ask next week, but i wish i could ask rn but im unable to

[warped folio]

Oh wow in India quadratic equations is in grade 10

[rugged prairie]

Yeah our education systems are different

[warped folio]

Ye I know about polynomials, identity, factor and remainder theorem

[warped folio]

Ye

[warped folio]

I am also giving a good level olympiad

IMO

[rugged prairie]

ohhh

whats remainder theorem

never learnt about that

nvm i searched it up

we did learn it

but not the name funnily enough

[warped folio]

It's when we are given that eg. (x-1) Is factor of the polynomial p(x) x3+2x²+1 (any) so we put x-1=0
So x=1 and put value in the given polynomial

[warped folio]

@rugged prairie

[subtle sundial]

focus on geometry

nt and algebra should be easy pickings

[carmine sundial]

Hai guys, I have 2 months till an Olympiad competition (bmo round 1) and I don't have any experience w/ math competitions since I spent most of my time learning mv/vector calculus and diff eq/lin alg(and they don't help w/ math comps smh). I'm in s3 or 9th grade, any tips are welcome, and I feel kinda cooked...

[soft vigil]

which bmo

[carmine sundial]

the british math olympiad

round1

[carmine sundial]

why?

[soft vigil]

theres two

balkan and british

[carmine sundial]

oh ok, do you have any tips for me:3

[soft vigil]

aops has a lot of good intro stuff

[carmine sundial]

is it free?

[soft vigil]

no

[carmine sundial]

https://tenor.com/view/bro-is-finished-cooked-finished-dog-closing-eyes-dog-with-eyes-closed-gif-8933440936102921947

[gleaming aurora]

guys i got 18 on amc 8 last year can i get 120+ on amc 10 this year?

the year before i got 4 on amc

[half mulch]

what

isn't a blank test like

more than that

[outer mural]

it took me like 4 hours to solve this, how do i get faster?

[half mulch]

u get faster as you understand more and more solutions

because u develop an intuition for creating your own solutions or recognizing patterns which can lead you down paths you're familiar with

[pallid tundra]

amc8 is 1 point per correct answer

different scoring scale

[silent cliff]

Repeating my question here since I was told I have a better shot at finding out -- but does anyone know what the Gauss contests in Canada are for? My friend's sister keeps talking about it but it's new to me. is it to search for gifted school candidates or something?

[ornate blade]

no, all students are welcome, not just gifted students

it's a way for students to be able to practice maths, problem-solve, and think creatively about maths in a way that is different to the regular school curriculum

in fact here's what the CEMC (the contest organiser) has to say:

The Gauss Contests introduce students in Grades 7 and 8 to a broader perspective of mathematics than their school curriculum can typically provide in a fun, accessible way. Intriguing problems and a multiple-choice format make the Gauss contests a wonderful opportunity for all participants to grow their interest in and curiosity about the power of math.

[silent cliff]

Ah I see. So the point is to inspire children and challenge them in a way? That's pretty sweet. Thank you for the explanation

[ornate blade]

yeah, that's right! no worries!

[silent cliff]

Are students selected to take the test? or is it a whole-school thing?

[ornate blade]

no, students can join if they're interested

but the school has to sign up to administer the contest, so if their school doesn't offer it, they're out of luck

[silent cliff]

Ah I see. Thank you for explaining this to me! I was confused :)

[ornate blade]

no worries again!

[summer tide]

thanks for answering after I redirected OP, south

I was worried there'd be no response

[ornate blade]

wait, you redirected OP??

wow

[stark swallow]

\textbf{Problem.} A $2\times3$ rectangle and a $3\times4$ rectangle are contained within a square without overlapping at any interior point, and the sides of the square are parallel to the sides of the two given rectangles. What is the smallest possible area of the square?

can someone draw this figure for it

[gilded halo]

BlackidoZΣ

[stark swallow]

can someone show the figure for it

[ornate blade]

there's also another configuration actually, where the 3 * 4 rectangle is rotated 90 degrees

[stark swallow]

one side is 5 then

and since it is a square other has to be 5 and the area is 25 then

another problem What is the greatest possible perimeter of a right-angled triangle with integer side lengths if
one of the sides has length 12 ?

let one side be x
other side = 12
and let hyp be y
y^2=x^2 + 144 now in the picture what is logic of rejceting two cases?

[ornate blade]

ah, so 144 is even

but then if y - x is odd, what parity must y + x be then?

given that (y - x) + 2x = y + x

[stark swallow]

then shouldn't both factors be of same parity

[ornate blade]

exactly

that's your answer

[stark swallow]

then only 12x12 is possible

ig

is it?

how to reach to final answer bro @ornate blade

[ornate blade]

no, so if you try y - x = 2 and y + x = 72

see what happens

[stark swallow]

x = 37

y = 39

+12

but question want greatest

and greastest in x is 72 and greatest in y is 12

give me logic what to do

perimeter is (x + y + 12)max

[ornate blade]

indeed so you need to maximise x + y

and the x, y you found were integers

[stark swallow]

yes

[ornate blade]

so there's no other larger y + x that works, from the list

[stark swallow]

out of 5 (72,2) is maximum ig

[ornate blade]

exactly!

[stark swallow]

=> 72+2+12 = 86?

[stark swallow]

how do i fit (72,2) here?

to get correct answer

@ornate blade what to do bro

i get correct answer if i do 72+12

84

how x+y can be treated as 72 if x = 72 and y = 2?

@ornate blade

[ornate blade]

no

you should get x = 35 and y = 37 actually

[ornate blade]

you solved for x, y wrong here

[summer roost]

It will be easier to check all Pythagorean triples with 12 in this case

[ornate blade]

it doesn't matter what x, y are

you already found that x + y = 72, so perimeter = x + y + 12 = 72 + 12

[stark swallow]

okay

[bleak jasper]

not comp. math but am i cooked if i dont even understand the proof?

[near hill]

The last step is perhaps a bit tersely stated, but the point is that you can rearrange the left-hand side of the equation from the second-to-last line to make it a^phi(n) times the same product as the RHS. Now each of the a_i factors are all invertible (since they are coprime to n), so you can cancel all of them and just get a^phi(n) = 1, which was to be proved.

(The topic channel this belongs in is #elementary-number-theory).

[bleak jasper]

i couldnt see that channel

thx

[near hill]

You may need to check the "Show All Channels" checkbox in the context menu of the server name (above the channel list). Discord thinks it's being helpful by hiding those channels by default when you've just declared your level as "Pre-University Math".

[bleak jasper]

oo i think i get it
lets take the product of coprimes as S
u get S(a^phi(n)) ≡ S (mod n)
divide both sides by S
a^phi(n) ≡ 1 (mod n)
but i need to prove that n is divisible by S?

[near hill]

but i need to prove that n is divisible by S?
No, just that S has a multiplicative inverse modulo n. Multiplying by that inverse cancels the S's.
S is invertible because it is the product of factors that each has an inverse modulo n (which they do because of Bezout's identity).

[bleak jasper]

ahhh ok makes sense

i think i saw bezout's identity somewhere

lemme find it lel

i saw it in a practice ppr ig

idk

i am cooked

[near hill]

It's more important to remember "everything that's coprime to n has an inverse modulo n" than to know the fancy name of Bezout's identity.

[gilded halo]

azart

[weary vortex]

gcd(49^(p-1) + 49^(p-2) * 5^1 + ... + 5^(p-1), p) = 1

is this true? (for prime p btw, forgot to mention)

[radiant jasper]

its fake

it should only be true for p≠2,11

[weary vortex]

so, for p=2,11

p | {that whole expression}?

shit, guess i messed up in the solution

[radiant jasper]

no p doesn't divide

you're saying p is corpime to that

[weary vortex]

accidentally wrote ≠, you're right

[radiant jasper]

oh

yeah when p=2 or 11 that thing is divisible by p

that expression is (49^p-4^p)/44

you can use lte to find the vp of the numerator

Its 1 when (44,p)=1 and 2 when p=2 or 11

oh wait 44 is divisible by 4

no wait nvm what I said is correct

Because you also get a 44 on the numerator lol

[weary vortex]

in the problem I'm solving, I'm dealing with 22

so no worries

[bleak jasper]

oooooo ok

[outer mural]

is this a vieta jumping problem?

[radiant jasper]

No

[outer mural]

ok

i'm working on it

16 is also 13-eautiful

i just have || (x+y)^2=bx+y for digits x and y. so i guess this is a diophantine equation that i have to solve? what do i do from here? ||

|| i think it's a conic section ||

[magic hatch]

hi guys!

im from a community called mustang math and i wanted to share this with you

i htought htis would be a really good opportunity for students in this server

Register Now for the Annual Mustang Math Mania (M^3)Team Tournament!!!

Hey all!

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Participants may compete in any one of 3 divisions:
Foal: Teams with all students in 6th grade and below
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Teams may choose to compete in any division above the one to which they are assigned, but they cannot compete in a lower division.

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If you have any questions or concerns, please don't hesitate to reach out to [e-mail].

thank you!!!!

also if you have any additonal questions feel free to dm me

[wide tendon]

26 problems in 45 minutes is crazy 😭

but cool, i've never seen an olympiad like that

[outer mural]

does anyone have a hint for this?

[outer mural]

nevermind someone explained it to me

[ornate blade]

Discord doesn't allow users under the age of 13

I'm not going to bother you but Discord very well might do something since you're breaking ToS by hosting this competition on Discord

Also <@&268886789983436800> this is selfpromo

[rancid horizon]

26 problems in 45 minutes? Wow 😭

Those who can easily manage that many competition problems in only like 40 minutes or less have my respect

[radiant jasper]

Sorry I went to sleep right after I replied to you the first time

[radiant jasper]

Was their solution kinda like ||rewrite (x+y)²=bx+y as s²-s=(b-1)x where s=x+y, then the number of b-eautiful numbers is the number of integers 2≤s≤b-1 such that b-1|s(s-1). Clearly (s,s-1)=1 so there exist p,q coprime such that p|s, q|s-1 and pq=b-1. If b-1 has d distinct prime divisors, then there are 2^d ways to split b-1 into p*q like this and each has exactly one solution 1≤s≤b-1 by CRT. The only one that doesn't work is s=1 so in total there are 2^d-1 b-eautiful numbers||

I didn't care too much about the solutions to delete so maybe the actual number is ±1 that but anyway 2^4 = 16 so I doubt there are as many as 7 fake solutions

[tawny matrix]

anyone help me in this question

pls

[half mulch]

since the bounds add up to 0, you can use u=-x

make sure u right it as cos + sin

then u can add the two integrals

and use trig identities to simplify

lmk if u need help after that

[regal tree]

Hi!

[half mulch]

hello

[outer mural]

yeah exactly

[outer mural]

i'm still trying to wrap my mind around it

[maiden bane]

Does anyone know how much undergrad math I'd have to know in order to do decently well on the Putnam? I've studied real analysis, lin alg, multivariable calculus, and basic group/ring theory. Would it be worth going further with stuff like fields/analysis in generalised metric spaces, or should I start focusing more on competition math specific techniques/ideas now, like from Putnam and Beyond?

[half mulch]

definitely start learning competition math

your foundation is really good

[maiden bane]

cool, tysm!

and should I formally learn analysis for multivariable calc?

for stuff like justifying interchanging of limits/integrals/summations/derivatives

bc that may be really useful

or just learn the statements

[half mulch]

I think it's useful conceptually

but not really necessary for putnam

it might help u with understanding the intuition behind certain techniques

[outer mural]

it seems tricky to find the bounds 2≤s≤b-1

[radiant jasper]

s^2 = (x+y)^2 = bx+y <= b(b-1)+b-1 = b^2-1 so s<b

x>0 and x=(s^2-s)/(b-1) so we must have s^2-s>0, so s>1

i found the first bound immediately by noticing that a number with 2 digits is at most b^2-1, the second bound comes from trying to delete the variable x but also trying to keep all the information you had. And so you realise that as long as s>1, you have x>0

[outer mural]

do we need both directions? i.e. 2≤s≤b-1 implies x,y are in the proper ranges?

[radiant jasper]

i just deleted y by putting y=s-x, and you need y>=0 but this is always true because you can get x<=s

[radiant jasper]

yeah

if youre counting the exact number of solutions

otherwise youre just giving an upper bound

[outer mural]

right

thanks

[outer mural]

CRT doesn't guarantee that the solutions are distinct

@radiant jasper

[radiant jasper]

why?

[outer mural]

it says nothing about that

using different moduli

[radiant jasper]

yeah but it's trivial

if you have two distinct ways of splitting it b-1=p1q1 and p2q2
Suppose that the corresponding s is the same for both.
Since the two ways are distinct you'll have something like
There's a prime that in you put in s in one way and in s-1 in the other way. So you would have a prime dividing s and s-1

or like just notice that a given s has only one corresponding way of splitting b-1 into two coprime factors

[outer mural]

i see

this problem is beyond me, i'll need more practice
there are four other problems on the exam that i got wrong. once i took a second look at them, i was able to come to the right answer. but it's so easy to overlook something.

[torpid igloo]

hey!

does anyone here go to any in-person contest math learning centers

[pure hull]

putnam and beyond is a nice book

fr

but don’t be fooled cuz some of the chapters look simple but take some thinking

[pallid tundra]

the Putnam is also pretty explicitly written to screw over people who only study from those books

[half mulch]

lolll

[pallid tundra]

I think they said as much in some interview with the problem writers or smth

(I took an intro combo class with one of them)

[ornate blade]

the IMO windmill problem...

everyone who prepped typical IMO topics would have been tilting at windmills

[pure hull]

wait wot

i mean they consistently come up with harder and weirder questions

but these books r still good right

[ornate blade]

yes, but that shouldn't be your only source of study material

[pure hull]

of course

past putnam problems good source too

[pure hull]

do u have any good resources?

[ornate blade]

no, sadly

[pure hull]

:(

[pure hull]

did u take putnam 2024

[ornate blade]

no I have no experience with Putnam nor IMO

[pallid tundra]

the top scorers (all usually at MIT) are largely just coasting off their HS Olympiad training

nobody actually seriously studies for this contest at the top level

[maiden bane]

yep, check pc

[pure hull]

ok ok

[pure hull]

fair

but they do have a really good putnam seminar i think

[round echo]

Hi

[frank hornet]

Hi

[ornate blade]

that's like AMC10 q15 difficulty

[glossy tinsel]

are u sure

[ornate blade]

well hmm, okay so that case isn't possible

[glossy tinsel]

lol

think more like distance formula

[ornate blade]

yeah that makes sense then, probably like q20 to q25 AMC10 even still

which would be like q15 to q20 AMC12

[glossy tinsel]

Alr that’s fine thank u

[ornate blade]

no worries!

[glossy tinsel]

https://tenor.com/view/please7tv-please-beg-pray-hope-gif-3860103425950934673

i have to improve by 1st december

[ornate blade]

oh I finally figured it out using your hint

should be $(\sqrt{272} - 1)^2$

[gilded halo]

south

[ornate blade]

||it's the minimum distance between two curves, one of which is the upper half of a circle||

[glossy tinsel]

yes its a very nice problem

[outer mural]

how do you calculate the minimum distance?
did you have to factor a cubic?

[radiant jasper]

maybe identity?

[outer mural]

|| i spent a lot of time looking at the boundaries (x1 = -1, x1 = 0, x2=0) but if you look at the two curves you can kinda rule those out ||

|| i guess you can make it a 1-dimensional optimization problem since the line of shortest distance must pass through the center of the circle ||

|| then i guess the hardest part is factoring 4x^3+4x^2+x-324 ||

[vernal axle]

||yes, you should minimize the distance between the parabola (x,x^2) and the point (18,0). So,
f(x)=(x-18)^2+x^4->min
f'=2(x-18)+4x^3=0.
Thus, x=2 and min(f)=256+16=272. Then the answer is (sqrt(272)-1)^2.||

[outer mural]

|| you made the factoring easier by changing coordinates ||

[radiant jasper]

i made a couple small mistakes which cost me a lot of points

i wanna aime qualify really badly and 2 months isnt a lot of time

[fluid marsh]

Hey what is that website you’re using I’m also studying for the amc and that’d be really nice to have

[radiant jasper]

https://artofproblemsolving.com/contests/practice

here

if you scroll down you’ll see a few

don’t use them up that quickly

practice in between them

[fluid marsh]

Thanks

[outer mural]

is there a good way to pick four distinct integers from {1, ... , 8} that sum to 18?

i found eight ways but it was tedious

i want to make sure to find them all

[pallid tundra]

in addition AoPS has basically every past AMC in their contest collections for further practice

[torpid condor]

I dont know why they didnt mentain this

ALso they have every AIME and USAMO stuff and proably a lot others I'd assume

[pallid tundra]

me neither tbh

[neon narwhal]

anyone free, i want create a model for coordinate geometry and could use some peer discussion

[gleaming timber]

Hi! I'm looking for my co-worker. If you are interested , please contact me.

[pallid tundra]

<@&268886789983436800> user with no message history and account freshly created today posts suspicious off topic message

[tight gazelle]

the ans key says 120 but idk how they got it

[ornate blade]

the area of the hexagon is 120?

[tight gazelle]

yes

apparently

[pallid tundra]

what answer are you getting

i was gonna go to sleep rn but i suppose i can stay up a bit longer to work on this lol

[tight gazelle]

i don’t have an answer but i thought it would be more than 120 coz i think bcef is isosceles

[pallid tundra]

my first thought is try drawing an equilateral triangle around all this but idk how much that'll help

[tight gazelle]

i also tried making 2 trapezoid by dividing AD

im lost

[pallid tundra]

looks like you labeled the wrong area as 60 in the diagram but yea 120 seems like it'd be a bit small

lemme try it

[tight gazelle]

oh i labeled it 60 there and also like the tri as 60 lol im just pulling numbers

[pallid tundra]

can we necessarily say angle BFC is 60 deg?

[tight gazelle]

that im not sure

[pallid tundra]

from iso BCEF i think we can say taht angle FBE is 60 deg as well

[tight gazelle]

what supports it

[pallid tundra]

should just follow from definition

(BCEF cyclic thus FBE = FCE)

[tight gazelle]

but FC doesn’t cut the iso trap in half right? i just realized

[pallid tundra]

unfortunately nope