competition-math

[hidden rose]

yea im thinking of doing that next year

[radiant jasper]

This for the first time or you have give nmtc and IMO earlier

[ashen pond]

hi

i am new to this channel

[eternal hollow]

hi

[ripe slate]

Was #10 on aime 2 907

[soft vigil]

Yes

I put 8! times that tho

[ripe slate]

Oh

So 907 is correct?

[soft vigil]

ye

[ashen pond]

give me any question

[jade widget]

find positive integer solution

[warm ore]

whats the ans? ive been trying for like 20 mins, very complex

[pallid dragon]

we have a bot command with the answer

but it's hard to remember

!elliptic curve meme

[scarlet root]

🍎 = 154476802108746166441951315019919837485664325669565431700026634898253202035277999
🍌 = 36875131794129999827197811565225474825492979968971970996283137471637224634055579
🍍 = 4373612677928697257861252602371390152816537558161613618621437993378423467772036

[pallid dragon]

got it

[warm ore]

thats the ans-

oml

[jade widget]

[radiant jasper]

Omg my friend gave this exact same photo to me like years ago and I took it personally that I couldnt solve it hahaha

[sullen blaze]

I am more interested how other solved it.

this is not possible even with the most efficient algorithms available with computer.

[hazy ibex]

$Solve I : I = \int_0^\infty \frac{\ln(x)}{1+x^2} , dx$

[gilded halo]

mouad_o_

[acoustic nova]

the smallest possible one yeah

[warm ore]

wow-

[kindred wraith]

its actually worse than that

suppose that 4 was replaced with N

it turns out there are always positive integer solutions for any even N

let the smallest solution of a+b+c for a given N be defined as f(N)

f(N) is not only not strictly increasing

but it is uncomputable and will dominate the growth of any computable function

source: https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4/answer/Alon-Amit

[kindred wraith]

oh whoops not all even N have solutions

[deft marsh]

find all primes (q,r) where q<r such that $$ q! + r! = 2qr^2 - 24$$

[gilded halo]

saintyzy

[warm ore]

only one pair is possible

(3,5)

[deft marsh]

Yeah cause q divides 24 and then assumed r>=7 which is impossible by mod 7

[warm ore]

that works too ig

i just did trial and error

till it got to (5,7)

[deft marsh]

Nicee

[warm ore]

where the lhs is 5160

nd rhs was no where close

and since q<r

there wont be anymore pairs fs

[deft marsh]

I just needed the solution becaue i made aharder poblem

[warm ore]

ahh

[deft marsh]

And needed to solve this to complete the solution

[warm ore]

wheres the qs from?

[deft marsh]

I made it

[warm ore]

ahh

got it

do share the complete one

[deft marsh]

Yee

[warm ore]

would love to see

[deft marsh]

Its not much harder tbh but here

Find all triplets of primes (p,q,r) where p<q<r such that p! + q! + r! = pqr^2 - 22

It is for junior olykpiads tbh

[warm ore]

oo nice

[warm ore]

i see

ye it would have more solutions only if the < condition is changed

[deft marsh]

Yeah

[radiant jasper]

yoo

anyone here take this years mathcounts yet

I got a questions cuz idk what the right answer was for number 7 and 8 on target

[soft vigil]

why is bro discussing

[radiant jasper]

hello

anyone take mathcounts chapter

[radiant jasper]

just replace the symbles like x or y and solve it

[kindred wraith]

ok do it

try and see if you can

[daring patio]

Yall know when Putnam scores come out?

[pallid tundra]

I don’t think we’re supposed to discuss that yet

since not everyone has finished them

[warm ore]

this is so hilarious after i already tried it

[jade widget]

I didn’t enter the leading zero in online AIME…

cooked

cooked

I hate myself

[radiant jasper]

d.x Is (>* 1 + In

[worldly lynx]

ibp cuz integral 1/1+x2 is just arctan

[ocean narwhal]

it isnt that tough

[ocean narwhal]

sub x = tanx
and then use int f(x) from a to b = int f(a+b-x) from a to b

and then add the two integrals

[vague temple]

Easiest way, let x = 1/t. Then I=-I.

[radiant jasper]

ok

[dry quartz]

Interesting problem, give it a try

[stark warren]

i jus took mc chapter

[cerulean torrent]

hello does anyone have good resources for mathcounts

like books or anything

[stark warren]

yea

u can search any aops book

like intro to geometry

on internet archive

[cerulean torrent]

l

k

thx

but i dont have too much time

is volume 1 good

[swift imp]

Any book should be fine

You know urself better

[pallid tundra]

in addition to the books

do lots of problems.

once you’ve learned enough theory

drill problems under contest conditions

so for sprint rounds for example

just set a timer to 40 minutes and work through as many of the 30 problems as you can

etc

[barren sparrow]

in this question i know the first eqn is of circle and the 2nd one is of ellipse but how do i find the number of common points bw the two

[ornate blade]

You can convert both into standard form first

Simultaneous equations in x^2 and y^2

Solving will tell you

[barren sparrow]

i mean thats one way but this paper(from where the question is from) was suppose to be an easy one so is there any other shorther way

[ornate blade]

Graphing which isn't allowed

Cramers rule with determinants may be easier

At the end of the day you need to know which quadrant the solution is in

You can't have x^2 or y^2 to be negatives

[barren sparrow]

fair enough

[ornate blade]

Ah I think you can test two values for x^2 and y^2

Check if the rhs is more or less which will tell you which side of the line the solution is

It has some chance of working but not guaranteed

[barren sparrow]

what do u mean by thus

[kindred wraith]

i think he meant like if you were to graph

f(x,y) = 1

if you plug in an arbitrary x and y, you might either get

f(x,y) > 1 or f(x,y) < 1

and each of these cases gives you one side of the graph boundary

[digital hedge]

Help pls

[soft vigil]

Did anyone else go to HMMT yesterday

[vernal axle]

Construct an equilateral triangle with side AC and a center K inside OCA). Then CKOD is a parallelogram (as CK=DO, CD || KO, and KCD, ODB are both acute angles). Then 80-alpha+30=90, so alpha = 20.

[digital hedge]

How do you know ck=do and cd||ko?

[vernal axle]

Suppose, you have a triangle with angles 30,30,120 and its largest side AC is x*sqrt(3). What is its smallest side?

[stark warren]

whats that?

[deft marsh]

find all triplets of non negative integers (a,b,p) where p is prime such that$$ a! + b! + 7ab = p^2 $$

[gilded halo]

saintyzy

[soft vigil]

Surely you just know that when b!=0 we have that LHS is divisible by b

So b=1 or p

[vagrant musk]

What do you guys think is a sufficient Putnam score to get into at least 1 REU program?

[latent bough]

100%

get all correct

i beliee in you

[stark warren]

if u took mc chapter yesterday

pls dm

[maiden relic]

mine is on feb 22

[stark warren]

nice

[soft vigil]

discussing is not allowed

[stark warren]

all chapters are over

but ig

ur right

[deft marsh]

Wlog a>=b so b divides LHS so b divides p² so b = 0,1,p,p²,a

[burnt trail]

,w (0,1,0,1) * (-1,1,0,0)

[gilded halo]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[mortal matrix]

was the AIME II harder than last year's

[sterile stirrup]

Does anyone have international cometition recommended?

[deft marsh]

wdym

[hasty jay]

Given the sequence (an):
Find out integers a and b,such that a1+a2+…+a4047=a*sin(pi/b)
Justify your answer

[vague temple]

a=-4, b=675

1. Telescope the sum
2. Use sin(x)+sin(2pi-x)=0
3. Simplify fraction

[tame wyvern]

Does anybody have advice for getting started with competition math? For reference, I;m in high school taking AP precalc. I'm no math whiz but I do great at school math.

[soft vigil]

Aops books probably

[acoustic nova]

look at a past AMC. how many of those questions do u feel confident in?

[pallid tundra]

standard school curriculum is insufficient by itself to do well on contests

start by looking through some contest problems to get a feel for what kinds of stuff they ask about

[ember heron]

Hi guys, would be greatly appreciated if someone would be able to help me solve this problem. Thanks

[hidden cloak]

i feel like W can literally be anything (any real number) here no?

is there any other data?

ohhhh

yea i should've noticed what that weird notation meant 🤦‍♂️

[marble kernel]

It is 11 bc if W x A x S x P = 1331^1/15, M x N = (W x A x S x P)^5 = (1331)^(1/15 x5) = 1331^1/3 = 11

[winter token]

and no using rayo's number

[jade widget]

there’s no W😭 😭

[rotund musk]

nice

[radiant jasper]

where is this problem from?

[winter sable]

ok so check ts question up guys : can photons vibrate by sound waves? i m thinking about ts for a month

[acoustic nova]

wrong server

[fallen palm]

probably but they travel at a wayyy bigger speed

so it isnt noticeable would be my guess

[teal mountain]

the left side is a multiple of a and b, so p must also be a multiple of a and b, which means a and b are either p or 1 and from there you can try each case and the left side will grow faster than the right side so you will find your solutions

[graceful plover]

so probably not

[novel karma]

anyone doing mao state?

[sleek slate]

Famat?

[novel karma]

not in florida but same thing

[lusty salmon]

Did anyone of you participate in SMO?

Singapore Mathematical Olympiad

[fallen palm]

no senator im not singaporean

[sleek ravine]

he is singaporean

[cerulean torrent]

im in middle school i cant do mao states but i competed in algebra and got 3rd in my region

bro u know american heritage and bucholz is insane in florida @sleek slate darkglory101

[sleek slate]

Yea ik em

What school do u go to

[shadow spruce]

😭

[soft vigil]

did any of you do hmmt

[gusty verge]

Surely this is wrong:

Let $y=-1$ then $(-1)^{-1}+(-1)=-2<0$

[gilded halo]

Max

[gusty verge]

(it's for a GMAT lol, but feel gaslighted by this)

I put d, the correct answer is c... apparently

[vagrant torrent]

What is GMAT

You could actually prove that option C is wrong

[gusty verge]

Yeah really easily too

[vagrant torrent]

Weird that the answer is C

[gusty verge]

It's for business schools but this job im going for has it as one of the tests as a GMAT

[vagrant torrent]

I see

But I do notice something

Try sketching out the graph of f(y)= y^y + y

[gusty verge]

but for $y<0$ it cannot be plotted

[gilded halo]

Max

[gusty verge]

it's discontinuous everywhere

[vagrant torrent]

Strange cuz it cant continue

[vagrant torrent]

Yeah

Ok but C is def wrong

[gusty verge]

yeah like it's not even defined for all $y<0$ but apparently is more than just defined but in fact positive lmao

[gilded halo]

Max

[gusty verge]

I wouldve got 100% on this section otherwise... so annoying haha

[vagrant torrent]

Haha i see

Interesting exam

[trail tusk]

did any1 attept INMO 2025 (india)

like casually

cuz i had a few doubts

[fallow prairie]

what are the basics of AP Stats

[ornate saffron]

waht even is stats

also sry for sounding this stupid

my grade didn't even start learning anything about trig other than the cosine

[royal estuary]

Only was able to solve p1

[tepid surge]

Study of interpreting data and drawing probable conclusions

[ornate saffron]

oh ok thanks

[civic gorge]

Can someone explain to me how to write a proof for this kind of problem. Like when we prove properties of a sequences

[midnight idol]

Centroid of semi cardioid of the arc r=a(1+costheta)

[kindred wraith]

"this kind of problem" is pretty vague, but for this particular problem it looks like you'd want to use AM-GM probably

not sure how to answer that question without more context or specifics

[vagrant torrent]

AG MG inequality

[trail tusk]

ok

in p1 is it alr if we like use the observation and prove it by induction?

cuz in like the earlier stages i did tht for a qn and they gave 0 though im pretty sure it was correct

[tiny saffron]

Let $a$, $b$ $\in \mathbb{R}$ such that $a \geq b > 0.$

First we prove the 1st inequality:

[gilded halo]

Tyrese Haliburton

Tyrese Haliburton

[tiny saffron]

Scratch that ^

Here's a better way to solve it:

We are gonna make the following substitutions $a = x^2$ and $b = y^2$. Then the first inequality rewrites as

$\frac{(x^2 - y^2)^2}{8x^2} \leq \frac{x^2 + y^2}{2} - xy $ (since $a, b > 0$, we don't worry about absolute value)

[gilded halo]

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

[tiny saffron]

$$ \implies \frac{(x - y)^2(x+y)^2}{8x^2} \leq \frac{(x^2 - 2xy + y^2)}{2} $$

[gilded halo]

Tyrese Haliburton

[tiny saffron]

$$ \implies \frac{(x + y)^2}{8x^2} \leq \frac{1}{2} $$

[gilded halo]

Tyrese Haliburton

[tiny saffron]

$$ 2(x + y)^2 \leq 8x^2 \implies 4xy + 2y^2 \leq 6x^2 $$

[gilded halo]

Tyrese Haliburton

[tiny saffron]

which is true since $$ x \geq y \implies xy + y^2 \leq x^2 + x^2 $$

[gilded halo]

Tyrese Haliburton

[sleek ivy]

i mean the middle thing can be written as (sqrta - sqrtb)^2/2 if that helps

[winter sable]

kinda me

guys i topped the state maths

[royal estuary]

Every claim needs to be proved, just writing the observation won't fetch marks, unless it's too obvious

[pallid girder]

hey, can anyone recommend any good resources for becoming better at IMO math problems?

[placid lion]

https://www.reddit.com/r/math/comments/cdy7mn/does_anyone_have_resources_to_study_for_the_imo/

@pallid girder Someone provided a list in this comment section.

[pallid girder]

thanks 🙏

[placid lion]

Np

[austere lark]

national math olympiads usually dont allow calculators right

[ornate blade]

usually they don't

that's correct

[austere lark]

ok ty

[vagrant torrent]

At that level, likely to be a small number of proof questions

[ornate blade]

even for computational questions

the style is such that all the calculations can be reasonably done by hand

of course the time is an issue but you shouldn't face any horrendous computations, maybe just a lot of smaller hand calculations

there's always a way such that you never need a calculator, even if it takes some ingenuity to discover it

[reef condor]

Ngl if calc was allowed

Ppl would calc bash algebra

And find new ways to do it

Like given a decimal, getting to (a+root b)/c would have whole handouts on it

Or maybe not like that
But also stuff like a + b cbrt c + d cbrt e answer extraction

[kindred wraith]

i always found calc bash to be useful but very clumsy

not really in the spirit of math olympiads except for small steps/lemmas

i enjoy giving my students problems that look like they could be calc bashed in theory but are actually disgustingly awful if they actually tried that

Find the global minimum of the function
$$
f(x,y) = \sqrt{x^2 + 4} + \sqrt{(x-y)^2 + 9} + \sqrt{(8-y)^2 + 16}
$$
where $x$ and $y$ can be any real numbers.

[gilded halo]

Cozmogrgdfschkipkhrshtensi

[kindred wraith]

credits to aops for this one, this one is cute

[rapid kettle]

If (3.4)^x = (0.34)^y = (10)^z the show that 1/x - 1/z = 1/y. Try this.

[deft wraith]

i thought u were talking about calculus for a while

but yeah

[reef condor]

Calc
As in calculator

[kindred wraith]

aaaaaaaaaaaaaaaaa

embarrassing

yes

i shouldnt respond on autopilot

[sleek ravine]

i hoenstly couldn't tell which they were talking about 💀

[deft wraith]

yeah calculus is allowed anyway

[radiant jasper]

My teacher solved this question quite nicely a while back using geometry

You can almost spot the right angled triabgle and pythagoras here

Blew my mind away lol

[versed prism]

fornite

[acoustic nova]

^

[vague temple]

Actually calc bash is not that bad here, there is a lot of symmetry and cancellation. It can be much worse

The function is convex, such that its critical point will be its global minimum. Note that the middle term will be common to both partial derivatives when set equal to 0, so equating common term and squaring:

$$
\frac{x^2}{x^2+4} = \frac{(8-y)^2}{(8-y)^2+16}
$$

Clearing denominators cancels the cross term, such that $16x^2=4(8-y)^2$, or $4x^2=(8-y)^2$.

The objective becomes, with $u=3x$:

$$
f(u) = \sqrt{u^2+4}+\sqrt{(8-u)^2+9}
$$

Once again, if you differentiate and cancel the cross term, you get

$$
u^2=4(8-u)^2
$$

Take square root of both sides:

$$
\pm u = 2(8-u)
$$

Either $u=\frac{16}{3}$ or $u=16$. But since the minimizer lies between $0$ and $8$, we must have $u=\frac{16}{3}$. Then substituting back into $f(u)$, we get:

$$\min_{u} f(u) = f(\frac{16}{3}) = \frac{1}{3}[\sqrt{256+324}+\sqrt{64+81}=\boxed{\sqrt{145}}.$$

[gilded halo]

victor

[kindred wraith]

unfortunate

i actually want that to be way worse

maybe i need to add two more terms and make it a 4 variable function

[shell surge]

Anybody good at very basic STATS ?

im missing the easiest error, and I'm yet to find it.

[pallid tundra]

!da2a

[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/

[shell surge]

No disrespect but I've been at this for 30 minutes. FINDING THE MEDIAN?!

im beyond confused

but I respect your choice to ignore

(I may have misunderstood; I'm trying to seek the median in a seemingly simple stats data set)

[pallid tundra]

send the full question

[tepid surge]

list the set of values in order

count how many elements are in the set

then find the middle one

[shell surge]

PROBLEM IN SOLVING I APOLOGIZE FOR MY INCONVIENCE (you may witness history in 11)

It was seeming a wording issue

no my math

thank you kind soul

[tepid surge]

so youve solved it?

[shell surge]

I appreciate your time

1/3 of my issues

yes.

[stiff mirage]

here seems doesn’t have a probabilistic channel

Idk I should ask my question on which channel 🥹I’m new here

[tepid surge]

#probability-statistics

[stiff mirage]

Thank you!!

[sleek ravine]

<@&268886789983436800> ?

[unreal beacon]

Can someone send some competitive problem idk what to do

[kindred wraith]

what are your goals? what level of math are you comfortable with?

there are problems of all kinds and all difficulty levels and giving you problems that dont fit your needs wont help you

[unreal beacon]

you can send everything expect geometry and trigonometry

i like to spend quite some time on some problems

i do pretty much everything

[kindred wraith]

that doesnt narrow it down

[unreal beacon]

i'm first year of high school

[kindred wraith]

artofproblemsolving.com

[ornate niche]

Hello friends. Can someone please suggest what to study for IMO? And which book is best for it?

[pallid tundra]

if you’re having to ask that question I don’t think you should be studying for IMO yet

[radiant jasper]

Anyone taking cemc tmrw

[lusty salmon]

Does anyone of you have notes for SMO Senior?

[vague temple]

Yes

[ancient sphinx]

anyone know any good resources/books to get better at competition style math? i plan to start doing competitions next year

[radiant jasper]

Cayley?

[torn gate]

Uhh AoPS

[torn gate]

https://discord.gg/3sbwZdh

[acoustic nova]

yeah

why?

[ancient sphinx]

thank you!

[radiant jasper]

How r u preparing

[unreal beacon]

Is cemc hard?

[vague temple]

Fermat

[radiant jasper]

How r u preparing for it

Just mock exams?

[acoustic nova]

just do a mock or two

what country r u in? just curious

[radiant jasper]

Does it help a lot if u do more

Im in xanada rn

Canada*

[vague temple]

Yeah mocked past 6 years

Also AMC 12

[radiant jasper]

Does it help if u do those

[vague temple]

For sure

[radiant jasper]

I can’t solve 24 and 25

I guess im just not at that lvl

[vague temple]

Well what level are you at

[radiant jasper]

Cuz my tutors say these contests are where u test talent

Not smth u can study for

[vague temple]

That’s expected, I also cannot solve one or two of B and 1,2 of C in time in Fermat

[radiant jasper]

Well ive never made it to the honor role

[vague temple]

No you definitely can study for

[radiant jasper]

I just need to reduce mistakes

Getting a question wrong in a or b in cayley is stupid

[vague temple]

If you can score like 110 on AMC 12 you can easily ace those tests for sure

[radiant jasper]

110 on amc12?

Never

[vague temple]

Then practice past contests timed for speed, precisely for that reason

[vague temple]

Maybe you should switch tutors

[radiant jasper]

Lol

I mean i think he’s right but at the same time i disagree

[vague temple]

Every Olympiad tutor and participant will tell you that practice is a crucial role

[radiant jasper]

Like imo idt its achievable by practice mainly talent

[radiant jasper]

Oh

[vague temple]

Anything before IMO requires basically no talent with sufficient drilling

[radiant jasper]

Oh rlly

[vague temple]

Just how dedicated you are, if you spend like 5 hours a day grinding

For sure you can easily do it

[radiant jasper]

Oh

Um

I guess i didnt study hard enough

[vague temple]

Depends on your goals, it is not worthwhile for everyone to go through this, but if you love it sufficiently it is certainly possible

[radiant jasper]

I rlly hope i make it to the honor roll this year

Next year i wont do much competitions bc of ap

Bc i think ap > contests for uni applications

[vague temple]

Well it’s the day before, I saved 2024 as a mock for final warmup before tomorrow

[radiant jasper]

Oh

[vague temple]

Yeah well if your goal is uni then Cayley is essentially useless, Waterloo does care about Euclid though (max 12th grade)

[radiant jasper]

Yeah

Just want to be on the honor roll

[vague temple]

Good luck 👍

[radiant jasper]

Ty gl to u too

[vague temple]

I didn’t prepare as much for Fermat so I am not expecting much, mostly as an exercise under proper test conditions for upcoming Euclid

Though the nature of questions are fairly different but it’s a good speed drill for sure

[radiant jasper]

I dont want to look down but waterloo contests are like rlly easy compared to other exams

Like amc and kmo are nowhere close to cemc lvl

Thats why im trying to get onto honor roll bc i think its doable

[vague temple]

Yeah

[vague temple]

They make it easy so everyone can participate, but it is also why they have Euclid, which is quite difficult for the last 2 questions

[radiant jasper]

Wait what do u do when u cant solve a question do u look for a solution after a certain amt of time

[radiant jasper]

Oh

[vague temple]

Like 1-8 is usually doable fairly easily, but then 9-10 is like high AMC 12 to mid AIME depending on the year

[radiant jasper]

Not many ppl take it tho

[radiant jasper]

Oh

[vague temple]

Skip

[radiant jasper]

Ive never tried euclid actually

[radiant jasper]

Oh

[vague temple]

Especially for PCF contests if you do not immediately think within like 30 secs of a path then skip

And come back

[radiant jasper]

No like when ur practicing

[vague temple]

(Scaling according to difficulty)

[radiant jasper]

Like sometimes part b question puzzles me

Usually cuz im not a native english speaker

Like the words and all that

[vague temple]

After like 1h30 I will usually look at solution, probably 40mins-1h is better tho (I am just stubborn against it sometimes and do manage to solve it but it’s less efficient)

[radiant jasper]

Ok

[vague temple]

Our school is providing it in French

[radiant jasper]

💀

What

[vague temple]

And it’s sometimes hard to read I agree

[radiant jasper]

French is crazy

I would never

[vague temple]

Usually Waterloo does a good job in problem formulation though

The reading comprehension questions are more of a troll, usually I leave them for later

For those long questions diagrams are often very helpful

[radiant jasper]

Yeah

24 and 25 i dont even understand the questions sometimes dont know where to bein

But im not shooting for those, ill get to 23 and leave the last 2 blank

[vague temple]

That’s probably due to lack of experience

[radiant jasper]

Oh

[vague temple]

24 and 25 is usually more theory reliant

At least in Fermat, I haven’t done the Pascal/Cayley

[radiant jasper]

Yeah i never like “studied” comp math with aops textbooks

[radiant jasper]

Oh

My friends do that too just take fermat

[vague temple]

Are you in grade 10?

[radiant jasper]

Yes

[vague temple]

The theory is not very deep usually

So if you studied for AMC 10/12 it is plenty sufficient

[radiant jasper]

Amc 10 i studied those basic theories

But none of them seem to come out

Like not many combination questions ive seen in cayley

[vague temple]

Usually like Pythagoras, basic trig relations and the sin/cos law are enough for geometry

[radiant jasper]

Trig doesnt come out in cayley

Lol

[vague temple]

For algebra there is like no theory

Just plug and chug algebra

[radiant jasper]

Yes

[vague temple]

Which, other than combinatorics

[radiant jasper]

Geometry?

But im confident in geometry

Like those formulas i went thru

And the angles

But most i learned them in korea so

[vague temple]

Ok

Actually I haven’t checked past honor rolls

I wonder the score for Fermat

[radiant jasper]

Isnt it like 132

But its inflated to 136 recently

132 i can assuming i dont make mistakes

136 idk

[vague temple]

That’s interesting, means there is more competition since questions are getting harder

[radiant jasper]

Yeah

[vague temple]

Where did you find honor rolls I don’t see it anywhere

[radiant jasper]

Go results

Cayley results fermat results

[vague temple]

Oh ok I found it

Damn, I just mocked 2024 Fermat and I managed to find the correct path for each problem, but I made 5 unfortunate careless mistakes and ended up with 116/150

(2 were incorrect reading)

[reef condor]

Rip

[radiant jasper]

Oh cutoff is lower

[sleek ivy]

Is that for a distinction?

[jovial sundial]

im doing cayley tomorrow

i ended up with 118/150 i wasnt able to figure out the part c's apart from one

[sleek ivy]

wb the extra pts you get for not answering

[soft vigil]

o

ive done one of those contests before

i took the pascal 4 years ago and got like 150 or smth

[ancient heath]

I did the fermet today

I think I should get a 100 (maybe)

I only did q23 in Part C.

[jovial sundial]

got the rest wrong, didnt leave one unanswered since it was a mock n js went for it

110 from a n b then that one c for 8

[sleek ivy]

its like a 1 in 100 chance thats crazy

[jovial sundial]

educated guess right💔

[smoky lintel]

what did you guys get for the part C questions?

[smoky lintel]

what did you get?

[fallen magnet]

bro what is that group

im talking about the name of it that ur in

[blazing salmon]

WHO CAN GIVE ME A HARD MATH PROBLEM

[smoky lintel]

damn i think mine is wrong then

anyone else did any c part problems?

[smoky lintel]

What question did you do?

[twilit peak]

Rori

want a hard math question

who wants to solve hard math questions ?

[vague temple]

That’s the correct answer, unfortunately I made an algebra mistake

[smoky lintel]

did you solve any other part c questions?

[vague temple]

I got 21,22,25 right

[smoky lintel]

25???

what did you get dude

[vague temple]

24 was tricky, it was easy if you knew the trick but I failed to come up with it

[smoky lintel]

i couldnt do 24 and 25

what was the trick?

[ancient heath]

How'd you get 23 wrong if you were able to do 25 😭

Definitely 23 was the easiest in the part c section

Careless mistakes are quite the annoyance

I know a very talented guy who got 4 on the AP Calculus and then went ahead and got question 1 part A wrong ☠️

[smoky lintel]

what was the ans for 24

21 was easy

[vague temple]

Because I wasn’t sure if I correctly remembered the formula for the combined time, so I did algebra by hand but I was tired or something and replaced time for the faster one by t instead of t-14

[ancient heath]

How much time did you guys take finishing the test?

[vague temple]

Also 25 wasn’t hard just slightly long, I burned too much time probably

[ancient heath]

I took around 35 minutes.

[vague temple]

Ran out of steam for 20 and 23,24 which made me make mistakes

[ancient heath]

Strategically chose which questions not to answer.

[smoky lintel]

i think i got 20 wrong

[vague temple]

Bro I did not finish

20 I just forgot cases, had the right logic too

[smoky lintel]

what did you get for 21

[vague temple]

So I need to practice for improvement: speed and accuracy

[ancient heath]

You're in uni and you did the fermet this year? @vague temple

[vague temple]

No I’m in 11th, otherwise you can’t participate

[smoky lintel]

i need to improve everywhere

[ancient heath]

Oh okay, you have undergraduate role so I guess you really enjoy mathematics

[vague temple]

Yeah

[ancient heath]

Honestly, I'm doing pre calculus till 12th and then business school.

[vague temple]

If I didn’t put the role I couldn’t access the channels

[ancient heath]

I don't need calculus or anything beyond.

[ancient heath]

You can still view all channels.

[smoky lintel]

what was the logic for question 25

[vague temple]

I forgot the question what was it

Like

[smoky lintel]

yeah

what was the ans

i think i did something like that

[vague temple]

If you send me the question in DMs I’ll answer

To prove you took the test

[smoky lintel]

yeah ok

can i not send it here directly

[vague temple]

Uh I think we are not supposed to officially discuss within 48h

Because other countries take it a day later

[smoky lintel]

ohk

[vague temple]

I can discuss in DMs

[ancient heath]

Yes, but who is actually following that.

[vague temple]

If you want

@smoky lintel do you want to discuss in DMs

[smoky lintel]

wait let me remember the question my brother

im texting my friend

[vague temple]

For some reason they let us keep our copies of the questionnaire this year

[smoky lintel]

not us

[ancient heath]

I have the copy if you guys need it.

[vague temple]

Well if you can vaguely remember any few questions other questions on the test that’s enough proof, and I can provide the solution

[smoky lintel]

is 134/150 enough for an honour roll?

[radiant oyster]

when will the answer key for cayley be out

[devout crater]

combinatorics

[twilit peak]

hi ?

[sleek ivy]

Was fermat hard?

Im giving it on tuesday

[wise cloak]

hiii

i really need help

I have a contest and I need help understanding geometry

[pallid tundra]

start by showing us a problem you’re having trouble with

[radiant jasper]

fermat wasnt that hard

[sand swift]

i'm studying for an olympiad rn and i don't know where to startor what books to do

anyhelp would be very very thanked

[quaint oyster]

https://www.rotupitti.it/materiali/Santos_Jiunior problem seminar_2008.pdf
https://drive.google.com/file/d/1iYEcw3jbQoWerkgrZzIrffaRmdCyPDmV/view

[quaint oyster]

both are free online

[sand swift]

tysm

[quaint oyster]

yw

[hard crag]

Someone help

I noticed that the tens number increases by 1

And for the ones digit

-2, -1, +1, +2, +3?

[ornate blade]

yes, the pattern should be that 61 - 53 = 8, 36 - 27 = 9
76 - 65 = 11 and 87 - 75 = 12

[hard crag]

So what's x?

+13?

[ornate blade]

since 10 is skipped

[hard crag]

Oh

[ornate blade]

I think it's 58 + 10 = 68??

it's hard to know

[hard crag]

There's no answer key unfortunately

So uh

Maybe

[ornate blade]

it could be 58 + 13 too

why did they skip 10 though, idk

[kindred wraith]

in general though, any questions of this kind, like "whats the pattern" or "whats the rule", are all pretty "useless" as math problems in the sense that they never have a true correct answer, they only have intended answers

you can justify any answer so long as you find a rule, and for any pattern you can always make up a rule that forces your answer to work

the goal of these problems pedagogically is to train pattern recognition in the broad sense

if these questions dont come with an answer at the ready in case i can't figure out the intended solution, its not worth my time

unless its motivated explicitly by a math problem, in which case you just give that math problem in the first place

[vagrant torrent]

71

Number + Digit sum

but again, thats just one solution, it could be any rule but thats just what seems to work for the others so I guess it should be the intended answer

[ornate blade]

ah wait that's clever

nice

[hard crag]

OHHH

Thanks

[vagrant torrent]

np

[deft wraith]

shouldnt ask this if u havent sat the exam

[sleek ivy]

What difference would it make

[deft wraith]

if you hear it’s hard, change your approach i.e less afraid to skip a q, more likely to check answers - otherwise if you hear it’s easy trusting your gut more etc

the point is that it’s information about the test which may give you an advantage, even if it’s just in strategy

[rough ether]

I was gonna assume it was x = 72 by the adding pattern: 8, 9, 11, 12…wouldn’t 14 be the next in line if we follow that pattern?

[strong thunder]

Hi

I'm new here

I'm looking for a team to participate in a math competition

if anyone is interested dm me

[ornate blade]

that's the problem with these pattern questions

any pattern is valid as long as you can justify it

[rough ether]

Goddamn. 😭

The more you know.

[gusty verge]

There are infinitely many 5th order polynomials that fit this data

And hence infinite possible answers

[kindred wraith]

i was about to say there is actually only one but remembered that 5th deg polynomials have 6 coefficients, its the 4th deg polynomial that only has one

[gusty verge]

My bad, 4th degree would do, 5 coefficients arent fixed by 4 equations

[cold python]

this opened a new spectrum for me 🫢

[radiant jasper]

"The test is to purely test your intelligence"
The provisional answer key:

[cinder harbor]

help me

left side is first pg

lol i need help

[vague temple]

The goal was to show x~y on page 2 eq (1) since you already have a~a

Since ~ is transitive then b ~ x ~ y implies b ~ y, so if b in X then b in Y, such that X is a subset of Y. Repeating this argument with x and y swapped by symmetry of ~ yields Y is a subset of X, overall X = Y contradicting X ≠ Y.

[cinder harbor]

ok thx

[quick frost]

Lagrange interpolation my beloved

[cinder harbor]

can someone pls help me

[quick frost]

In fairness, I think that if you have a well-defined problem, being able to make good guesses about the general answer after computing it up to some small n is very valuable.

[quick frost]

I think you should ask this in #proofs-and-logic.

[radiant jasper]

https://mathcontest.trubox.ca/wp-content/uploads/sites/2596/2024/06/2024_Junior_Prelim-solutions.pdf

what would the difficulty of this math contest be? Compared to the ones such as AMC or Waterloo math competitions?

I found them to be more difficult than the Waterloo math questions

[edgy vapor]

Below EMIC I guess….

[vague temple]

How much time do you get? It looks much, much easier than Waterloo contests like CEMC Fermat, COMC or Euclid

Looks easier than AMC 8 from what I can tell

[radiant jasper]

45 minutes

I never took euclid or fermat i took cayley this year

[vague temple]

Yeah I think it’s easier

[radiant jasper]

Eaiser than cayley?

[vague temple]

Idk about Cayley, I’ve never taken it, but I assume perfect scoring on this is easier than in Cayley if it’s not much easier than Fermat

[radiant jasper]

Oh

I should try them actually never went thru

Like anything until 23 in cayley is

Rlly easy

Just time is the only issue

[vague temple]

Yeah that’s what I’m evaluating, it seems like every question on this is easy as opposed to CEMC the last few can be time-consuming or more challenging

[radiant jasper]

Oh rlly

Ok thats good to hear

What do u think the overall gradenlevel is?

Its a junior exam

[vague temple]

If you compare to AMC 8 then probably grade 7-8

[radiant jasper]

Rlly

[vague temple]

Yeah AMC 8 is significantly harder than this I would say

Especially some recent years

[radiant jasper]

Okok thats good

[vague temple]

It depends though I am assuming we talk about perfect score

Because like CEMC the first few on AMC 8 are trivial

But if you take the hardest difficulty and overall time to fully complete then for sure AMC 8, CEMC are harder

[radiant jasper]

Oh i see

[radiant jasper]

I dont expect a perfect score maybe one or two wrong

I jist need to get top 3 in school to compete in the next round

[vague temple]

Then you should be good as long as you maintain consistency in easy questions

[radiant jasper]

Theres this one crazy kid who was off 2 marks from a perfect score on cemc

So um yeah

[radiant jasper]

Okok

[vague temple]

2 marks? Like did he not answer a question on A or what

[radiant jasper]

No it was like one of those that were out of 40

[vague temple]

Ok

[radiant jasper]

And he got like one of those smaller questions wrong

3. c) or smth

[vague temple]

I mean yeah if you are serious about math contests there will be these crazy kids in Texas getting 150 on AMC 12 in grade 7

[radiant jasper]

Yeah bro

Im not that level

[vague temple]

Me neither

But you’ll do good 👍

[radiant jasper]

Ty🤞

[jovial sundial]

seems harder than cayley apart from the part c, not sure about fermat though

[sleek ivy]

Young Sheldon type shit

[mental pivot]

10 people are to be divided into 3 committees, in such a way that every committee
must have at least one member, and no person can serve on all three committees. In
how many ways can this be done?

[balmy hound]

do anyone work on the goldbach conjecture?

[pallid dragon]

it's not clear, we should assume a person can serve in 2 commitees at once

but can they serve on 0?

[lament frigate]

does anyone know when u of t is gonna release the solutions to the 2025 fermat contest

[high goblet]

lol that is a wild question

uhh why do you ask?

i think in general, mathematicians aren't currently working on the goldbach conjecture rn bcus we think we're lacking the tools to tackle such a question

sieve theory gives results but it has issues turning that into a proof

i think something like twin prime conjecture would be more plausible bcus i think ppl think we're just a few clever ideas away from solving it

anyway i'm not up to date with the latest methods/progress/approaches on goldbach conjecture, so ur better off asking in like #advanced-lounge or #advanced-number-theory

[torn gate]

PROMYS 2025 P3

DO NOT HELP HIM

[pallid tundra]

Most importantly, we ask that you tackle these problems by yourself. Using external resources like the internet will make it much harder for you to demonstrate your insight to us.

[deft wraith]

why cheat…?

[novel karma]

hey i'm js curious but r u korean

[radiant jasper]

Yeah

[novel karma]

oh same

[surreal willow]

I know a guy who knows a guy who got into jmo in 7th grade

He’s currently taking university classes and he’s in 8th grade I think

Some of these kids are insane

[swift imp]

Sorry about Texas (ik some of these )

[deft wraith]

Cali math kids are insane

[waxen olive]

yea frong

[radiant jasper]

Oh rlly

Hi

[pallid tundra]

not entirely sure if this is warranted but <@&268886789983436800> attempted cheating

[ornate blade]

absolutely

you could also ModMail next time

[sleek ravine]

when you modping report yourself
jkjk 💀

[pallid spear]

getting caught cheating in discord is crazywork

[shy saddle]

Guys im learning functional equations rn

Anyone have good rescources that I could use to further expedite my learning?

[pallid spear]

there was a small book by Andresscru, it was well structured as i recall

[shy saddle]

Yes I found it

Thank you!!!

[pallid spear]

eeeeh maybe you shouldn't post it, it violates the discord tos

[shy saddle]

Thanks for letting me know

I wasn't aware

[robust stream]

Hey, anyone here preparing for Indian competitive exams?

[wise ferry]

Someone solve this

[woven jungle]

a+b=30/7 ?

I think?

[pallid tundra]

this an old MATHCOUNTS problem?

I feel like I’ve seen it before

[woven jungle]

The volume of a regular dodecahedron is ((15+7sqrt5)/3))*s^3 where s is the side length.

I think there might've been a mistake in the question

[radiant jasper]

sigma sigma boy

[woven jungle]

Can anyone confirm my answer?

[surreal willow]

Yea it’s I think a state sprint round

Maybe 2023 or 22

[deft wraith]

Evan Chen’s handouts or Titu’s book

[visual sonnet]

.

[opaque coyote]

yeah am preparing for JEE mains and advanced

[warm cave]

ok

[tranquil loom]

How did session one go?

[opaque coyote]

not good
did u give session 1??

[opaque coyote]

whats maybe??

[sullen blaze]

you can ask me if you have any doubts.

[dry rune]

Yo guys

I have a math olympiad problem

That stayed for 2 days till now in help 8

And didn t solved it

And like 8 people tried it

Maybe you take a look

[mellow summit]

Could some help me with this

My answer ends up not being one of the answer choices

[obtuse temple]

hum

For a number to be divisible by 5 it has to end in 0 or 5 and for a number to be divisible by 3 the sum of the algorithms has to be multiple of 3
so

[magic oxide]

900+255

E

[obtuse temple]

yeah

[fallen magnet]

case b=0:

• the number is a00
• the sum of digits is a
• a must be 3, 6, or 9
• possible numbers: 300, 600, 900

case b=5:

• the number is a55
• the sum of digits is a+10
• a+10 must be divisible by 3, so a must be 2, 5, or 8
• possible numbers: 255, 555, 855

smallest number is 255, and the largest is 900.
255+900=1155

answer is E.

[mellow summit]

Kk tysm 😁

[fallen magnet]

np

[wise ferry]

😲

[fallen magnet]

i just realised that my school never gave out the gold certificates for ukmt senior challenge

:(

[jade widget]

251.5💀

[soft vigil]

its so cooked

[hearty tendon]

lmao

[deft wraith]

Same

I haven’t got my BMO stuff back either

Don’t they just print it off?

@high goblet school can just print BMO certificates from portal or does ukmt need to send them pdfs?

[high goblet]

i have no idea i don't remember

[sleek ivy]

sure

which ones did u solvw

[radiant jasper]

I took cayley

Did u take cayley?

[sleek ivy]

oh no

i took fermat

[radiant jasper]

Oh

[radiant jasper]

I hate that competition math is only rly in highschool

Like i started doing this in my senior year but now its just too late

[kindred wraith]

not true?

there's competition math in college too, the most famous one i think is the putnam

don't think of it as being too late, because like

the accolades you get from competing only matter if you get really far

[radiant jasper]

Yeah no im doing it just for fun

[kindred wraith]

so really what matters more is the spirit of competition, having fun, being inspired and developing passion

yeah so don't worry

[radiant jasper]

Idc about the accolades

[kindred wraith]

you'll find plenty of opportunities in college

[radiant jasper]

Alr

[kindred wraith]

and you'll find plenty of like minded people everywhere

this discord, and everywhere else on the internet

artofproblemsolving.com also has a nice community iirc

it's never too late to start liking math

[radiant jasper]

Alrr

tyty

Unrelated but im so sad bro one of my irls missed the usamo cutoff by 2 points

We were so sure he was gonna qualify

Then they had like crazy high cutoffs

[kindred wraith]

happens

[deft wraith]

Yeah usamo qual was super high

Like 250 from aime ii and amc12b

[pallid tundra]

250???

jfc 😭

[blazing elk]

@everyone please dm if anyone can open password protected pdf without password

[civic gorge]

Anyone doing mathcounts. They're holding the state competitions soon

[torn gate]

*251

[low fiber]

Is 166 good on mathcon for a new freshman

[kindred wraith]

i feel like good is relative

liking math enough to even enter a math competition and earnestly trying to get a good score is already good imo

[low fiber]

like good like i can feel proud about it

[kindred wraith]

you should feel proud about liking math enough to enter a math competition and actually trying

i can at least say that much

[deft wraith]

Agreed

[tepid surge]

Doing good on a math competition is awesome and all

But its a lot different from doing math research or smth like that

So as cozmo said, be proud that u gave it ur best shot

[soft vigil]

do you want the sugar coated answer

[languid ledge]

im currently 16yo and ive been intrested in the math olympiad, how would i go about doing it

[deft wraith]

https://web.evanchen.cc/faq-contest.html#C-0

[low fiber]

i want the real answer

does anyone know a good schedule for amc prep

[radiant jasper]

There's not really any fixed schedule you can follow. Some people are quick to grasp concepts and can do well in AMC by just a few hours of daily prep. Others may need more devotion. Of course, the more the better. Depending on your level, as well as your schedule, you will have to fix your own time.

[soft vigil]

166 is bad

[low fiber]

I like skimmed aops and im in geometry + algebra 2 rn

[radiant jasper]

That doesn't mean much, try solving questions

"Skimmed" is really vague

[hard crag]

Anyone knows how to find the number of square factors of a factorial

n!

Context

[pallid tundra]

!status

[scarlet root]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[hard crag]

Uh

I've tried

Matching factord

But it's too tedious

I think it's a diff method

[pallid tundra]

prime factorizing is the intended first step

what do you get when you do that?

[regal tinsel]

i only know the basics of factorial like 5! which is 120

[light fossil]

Is that a public server?

[hearty tendon]

idk but im the legend

😎

[light fossil]

elaborate?

[hearty tendon]

nah i was kidding read the msg above ur tagged one

😭

[light fossil]

hah

did you compete in ICTM?

[hearty tendon]

i did

[light fossil]

this year?

[hearty tendon]

yeah

[light fossil]

how did you do?

[hearty tendon]

state is in a month?

or so

[light fossil]

2 months i think

[hearty tendon]

idk i did decent i forgot

[light fossil]

i got 1st alg 1

nvm your right its just 1 month away

[hearty tendon]

oh W

are u a soph now

[light fossil]

no

it is the same year

i meant at regionals

[hearty tendon]

ah regionals

gl at state

[light fossil]

thanks

i think im cooked tho cuz the highest team's average in my division was 18.25/20

and i got 17/20

[hearty tendon]

lol

my region is not that competitive

thankfully

[light fossil]

yeah

[soft vigil]

if ur in IL i can invite you

[light fossil]

Yeah I am

[slow root]

hi i need help on this problem ive been working on: Consider the first 30 terms of the following integer sequence:

1,4,7,12,20,32,44,60,81,108,135,168,208,256,304,360,425,500,575,660,756,864,972,1092,1225,1372,1519,1680,1856,2048
I need to determine a pattern or formula for the
n-th term. I have already checked the OEIS database and attempted polynomial interpolation, but I was unsuccessful.

I found the pattern lies in the second difference, but its a polynomial sequence of 4thdegree or higher of somesort

[pallid tundra]

if it's a polynomial you could try lagrange interpolation

(on 30 points it's extremely tedious but it will give a polynomial fit)

actually i tried plugging this into a lagrange interpolation calculator and the result is super nasty

💀

[kindred wraith]

always very funny to me when people use high powered lagrange interpolation on sequences to determine if theyre polynomial

just use finite differences

yeah so taking forward difference twice you get

[0, 2, 3, 4, 0, 4, 5, 6, 0, 6, 7, 8, 0, 8, 9, 10, 0, 10, 11, 12, 0, 12, 13, 14, 0, 14, 15, 16]

clearly the pattern is 0, 2n, 2n+1, 2n+2, looping for each n from 1 onwards

so if you take the first differences

[3, 3, 5, 8, 12, 12, 16, 21, 27, 27, 33, 40, 48, 48, 56, 65, 75, 75, 85, 96, 108, 108, 120, 133, 147, 147, 161, 176, 192]

you can see that from the first 3, every 4 terms its going to go up by 3 * 3, then 5 * 3, then 7 * 3, etc

so suppose this sequence is f0

the first difference we call f1, second difference f2, and so on

f1(0) = 3, f1(1) = 3, etc

then f1(4k) = f(4k+1) = 3k^2

you can probably from here similarly find a formula for f1(4k+2) and f1(4k+3)

and then use these together to find a formula for f0(4k)

which should also allow you to then find the other 3 cases for f0 with input mod 4

and you at least get a piecewise function that gives an explicit formula for f0

this is pretty obviously not polynomial

[slow root]

thanks, but is there no way to get a full function which is not piecewise?

i have come to a piece wise function conclusion. But i think maybe there is a full function too. Is there any ideas of how i could achieve it. Because the piece wise was too tideous

[kindred wraith]

nothing comes to mind atm, and theres no general method to do this either

[slow root]

thanks for the help thou!

[radiant jasper]

Hello does anyone wana help me with a math competition?

I had a question i couldnt understand in an 8th grade competition

Basicly the question is 1+3+5+7....+k=40000 what is k

Thanks to anyone who answers

[radiant jasper]

Do 1 + 3, then 1 + 3 + 5, then 1 + 3 + 5 + 7.
Do you notice a pattern?

Yes its every od number

nono, compute the sum

But the way that you get k is very complicated and idk how to do that

Wait ill send the answer

1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16

What can you notice about 4, 9, 16?

[radiant jasper]

(Its in croatian but youll get the numbers)

[radiant jasper]

All different by 5?

[radiant jasper]

Think, squares.

Ohhh0

2^2 = 4
3^2 = 9
4^2 = 16

So it seems the sum of first n odd numbers in n^2

First 4 odd numbers = 1 + 3 + 5 + 7 = 4^2 = 16

if you've studied Arithmetic Progressions, this is an AP. find the sum of n terms to confirm this.

Here

Question 5

How is 1+3+5...+k=1+2+3+...k-(2+4+6..+(k-1))

[radiant jasper]

we tkae the sum of EVERY (natural) number, then we simply remove the even numbers to get the sum of odd numbers

[soft vigil]

k^2 is the sum

🔥

There’s a really nice no words proof of it

[radiant jasper]

Still thanks for the help

Honestly im half-good at math

Physics is more of my strong point

[hexed violet]

Are you from Romania and is this a math homework and if not, then what is it?

[honest creek]

yes finnally your doing math

oh no that was 1:32

[radiant jasper]

the penguins are more important

[gloomy kite]

is anyone here preparing for mathcounts states?

[honest creek]

ACK

[honest creek]

reminding me of my hopes and dreams

I wish I can join mathcounts

but stricts parents

lol

[gloomy kite]

oh dang thats sad

[honest creek]

I have a friend who moved onto states by scoring 1st place on mathcounts

[gloomy kite]

im just rly cooked

i need to last minute prepare lol

[honest creek]

wow good luck

I do want to know how this goes

you would do fine trust me

if you friend me I might be able to put you in a dm with someone who is doing the mathcounts states

[soft vigil]

no but i was last year

[languid ledge]

does anybody have a place with good modulo word problems for beginners, ive recently been getting into comp. math and have been seeing them used alot in solutions, so i learned how to use them but i dont know how to translate word problems into their use.

[radiant jasper]

Modular arithmetic essentially deals with remainders. If you're looking at word problems explicitly, usually problems that talk of dividing things or things that overlap. But many times, there is no general method of seeing where or why congruent modulo is being used. Most competition problems have multiple solutions. Whilst one may use mod, other may design a clever solution using algebra or geometry. One example I can think of is some problems of invariance where the usage of modulo seems to come out of nowhere ("a giant has 100 heads. One can add or remove 9, 21, or 15 heads at one turn. may the giant ever have 23 heads?").
Having that said maybe try https://youtu.be/I8b-kKiEo24 ?

[languid ledge]

Thank you!

[radiant jasper]

np

[radiant jasper]

BTW if you're wondering the soln "a giant has 100 heads. One can add or remove 9, 21, or 15 heads at one turn. may the giant ever have 23 heads?":
Notice the amount of heads we can add/remove are all multiples of 3. Thus the remainder when we divide the number of heads on the giant after any number of turns by 3 never changes.
100 leaves a remainder of 1. 23 leaves a remainder of 2. Thus 23 may never be achieved!

[sleek ravine]

what kind of giant has 100 heads and adds/removes them by...turning...

[pallid tundra]

i think “turn” means “an instance of slicing off heads” in this case (hi viper lol how have you been)

[soft vigil]

yeah i think thats it

an instance of adding or removing 9, 21, or 15 heads

[weary edge]

$$ \sum_{k = 1}^n (2k - 1) = n^2 = 40,000 $$

[gilded halo]

Flamango

[weary edge]

You might have learned in class that the sum of the first n odd numbers is n^2

[radiant jasper]

Yeah i found out the problem we havent learned all of that becouse what im working on is for a competition

Thats why i couldnt figure it out

[weary edge]

Ok

[radiant jasper]

I only did the basics of the concept like 1+2+3+4+5+6=2×6+3 becouse 1+5=6 and 2+4=6 but i sadly havent learned ony of these formulas
Thanks for the help tho

[soft vigil]

@radiant jasper geometric proof of it

[slate loom]

Any body wants to participate with me in the Standford Math Tournament?

[acoustic nova]

that’s not very rigorous

[soft vigil]

i know but

its a nice picture

[silent lance]

Does anyone know if there are any good mit opencourseware classes for someone in the 8-10 range on the aime hoping to make jmo next year? Also, I could use some ocw classes for f=ma/usapho, if anyone here does physics

[novel karma]

should i start learning computer science if i'm decent at math?
i think it's too late because i'm a total beginner and 14 yro, but i would like to get started on it for an available internship
pls list some ways to get started on it, i would appreciate it

[hidden rose]

Can anyone suggest good books for IOQM and RMO [INDIA]?

[summer roost]

I also want some recommendations

Can someone please provide some suggestions

For self study

For rmo

[quaint hearth]

pathfinder for olympiad maths

[acoustic nova]

whats funny? yes squares = squares
but it gives no reason why the pattern should continue

if u try to make some reasoning it just turns into the algebraic argument

definitely not

but in this case that picture on its own doesnt do anything

no. that picture proof on its own is insufficient

i dont like it anyways. as i said its just sqaures = squares

this is i think an actually useful picture proof

demonstrating why 1 + 2 + 3 + ... + n = (n + 1) choose 2

i know. i like picture proofs very much. but i think that picture doesnt help rlly with anything

[tepid surge]

tbh i think the square one is pretty good

[acoustic nova]

why? it doesnt rlly make the theorem more obvious, as squares = squares, and doesnt give intuition to why its true

[acoustic nova]

this is a nice one though do u see what it shows

[tepid surge]

yes it totally does

if you have an n by n square, and you want to increase it to an n+1 by n+1 square, you have to add 1 block in the corner and n blocks on the top and the right, so n^2 + 2n + 1 = (n+1)^2

[acoustic nova]

this is exactly my point that u just reverted to an algebraic argument

either is completely fine if u r careful

[tepid surge]

yeah but the algebra is visually represented at each level

i mean its a geometric visualization of an algebraic claim