competition-math

[swift imp]

just take amc 12

if u can do well in 10

its a lot easier to qualify

[hearty tendon]

idk last yr i was a soph

[ornate coyote]

hm

[hearty tendon]

so i took 10

[ornate coyote]

isnt usamo much harder than jmo

[swift imp]

They both hard

[ornate coyote]

im def gonna do jmo next year

but idk if doing amo is better during 10th

[swift imp]

well yea i was hinking just

its easier to get into aime with 12

[hearty tendon]

usamo 1 = jmo 2 roughly

[ornate coyote]

hm

sounds difficult

[ornate coyote]

well if you are planning to try to make amo why would you struggle with aime qual

[swift imp]

true

the cutoff for amo is less for 12 tho

[hearty tendon]

huh isnt jmo like

20 pts lower

w easier amc

[ornate coyote]

i thought

you had to do 12 for amo

and 10 is for jmo

[hearty tendon]

yea

[ornate coyote]

so jmo has different cutoffs for 10a and 10b right?

[swift imp]

yea

and amo same for 12a and 12b

amo values are lower than jmo cutoffs

oh i mean

lower score

[ornate coyote]

praying everyone sells on aime 1

i might be able to qualify for jmo

[hearty tendon]

its not tho??

[ornate coyote]

💀 180 is wild

[hearty tendon]

some yrs its similar

ig

[swift imp]

huh

[hearty tendon]

jmo is way easier to make

[swift imp]

This was last year

[hearty tendon]

huh

[ornate coyote]

😭 NAURR

[hearty tendon]

idk what happened

lol

[ornate coyote]

236

[swift imp]

I think someone was meming the amc 10 or something

to be that low 💀

[hearty tendon]

but jmo is way easier to make

yeah fr

230 index is crazy

idt thats right

i think it was like 218 last yr or sm

[swift imp]

ok tbh ur probably right

[ornate coyote]

werent there a lot of cheaters

[swift imp]

i don't even know anymore

[ornate coyote]

so maybe it is right

[hearty tendon]

theres always cheaters

lol

[swift imp]

You shouldn't be looking at scores anyways

Just do as well as u can!

[hearty tendon]

fr

[swift imp]

Me wasting time here

but idc cuz i cant even mop atm

[ornate coyote]

ive been losing sleep doing math in the night

[swift imp]

too old for mop

[hearty tendon]

fr

[swift imp]

ill just aime no study 🤓

[hearty tendon]

im not making blue

lmfao

[ornate coyote]

its way harder to make mop as a junior or senior iirc

[hearty tendon]

u cant first time senior

[ornate coyote]

i wonder how many middle schoolers qual jmo

[swift imp]

idk if i can second time

i actually dk

[hearty tendon]

egmo

[swift imp]

nah

what the freak was tststtststststst

[hearty tendon]

what main r u

[swift imp]

orz main

[hearty tendon]

🥲

is it like anti doxx

💀

[swift imp]

@hearty tendon im a

no main

or how about this

geo = combi = nt >>>>>>>>>>>>>>>>>>>>> alg

[hearty tendon]

g>>>>a=n>>>>>>c

[swift imp]

geo is goated

[hearty tendon]

😭

fr

[swift imp]

a is

uh

[ornate coyote]

algebra> geo>number>combinatronic

[hearty tendon]

combo sucks ass

[swift imp]

yea true

lemme rearrange

geo = nt > c >>>>>>>>>>>>>>>>>> a

[ornate coyote]

urgh

[hearty tendon]

based

[ornate coyote]

i should study

but like

i need a life

but like

[swift imp]

the only thing u need to study on is how to self study

[ornate coyote]

i need to qual

[hearty tendon]

grade and current index?

[ornate coyote]

huh

[hearty tendon]

like

how far away rae u

are u

[ornate coyote]

8th 133.5 a 139.5b

[swift imp]

orz

[hearty tendon]

lmfao u good

😭

[swift imp]

bro can probably make jmo with a 7 aime

[hearty tendon]

man wtf are these kids

[swift imp]

6 aime jmo qual?

[ornate coyote]

idk my aime scores are kind of ass

[swift imp]

same

i didnt get 15

sadge

[ornate coyote]

why do people say orz

[swift imp]

cuz its cute idk

juts say orz when someone is orz

AOPS WIKI FAQ

[ornate blade]

AOPS ppl are such the type to use that

for real

[swift imp]

orz

i heard at mop someones name was similar to like skibibi bop bop and everytime someone saw them ppl were liek
skibibi [name]

[ornate blade]

unhinged

[ornate coyote]

erm what

[swift imp]

Wait lemme find the blog post

[ornate coyote]

so like at the math club i be like tutoring these kids

and helping them prep for the amc8

why is the 1984 one harder than like the 2020 one

[swift imp]

@ornate blade

[ornate coyote]

???

[hearty tendon]

popopop 😭😭

[vague temple]

Do one index at a time

It’s convergent so you can factor out the independent terms

[lyric parrot]

look at the condition

it looks easy

till u see the condition

[ornate coyote]

hummm

cant you just use pie

or somethign

[lyric parrot]

😂

[ornate coyote]

probably wrong way of saying it

idk

[vague temple]

I don’t understand, don’t you just subtract then? Or am I confused

[ornate coyote]

wait is it not that

[vague temple]

Complementary

[ornate coyote]

i never really had a good learning of combinatronics names

i just did it

but like

[lyric parrot]

yes u subtract them

[vague temple]

Like you take 27/8 - 27/26

[lyric parrot]

and add 1 more

[vague temple]

So why does this approach not work?

Is there a problem I am not seeing

[lyric parrot]

this is the ans

[ornate coyote]

27/8-405/208?

[vague temple]

Oh true PIE

[lyric parrot]

OH

PRINCIPLE OF INCLUSION and exclusion u meant

@ornate coyote

u are right

[ornate coyote]

wait

[lyric parrot]

i thought u meant something else

[ornate coyote]

ok

[vague temple]

I forgot you can have i=j≠k

Why is combinatorics in algebra now I’m sad

[ornate coyote]

i wanna be able to coord bash for the solution in number theory

[vague temple]

Wait how do I know to use PIE here

[ornate coyote]

its like

you have conditions for the equalities of i j and k

[vague temple]

Because i≠j≠k is intractable directly so we use ( i≠j and j≠k and k≠i ) = not ( i = j or j = k or k = i ) = PIE…

I am so bad at recognizing PIE

I don’t have the intuition

Every time I have to be told about it, write out the formal logic statements and then I see it

Any cues to check PIE? Like several conditions with OR right

Union of events

I am stuck on this problem for a non trig-bash solution:
Prove that for any triangle, the intersection of all adjacent angle trisectors forms an equilateral triangle.
Is this possible using barycentric or trilinear coordinates or something?

[hexed oak]

On the surface of the planet lives one inhabitant, that can move with the speed not greater than u. A spaceship approaches to the planet with its speed v.
Prove that if v/u > 10 , the spaceship can find the inhabitant, even it is trying to hide.

Any ideas?

[ornate coyote]

???

i think we need more information

on the rules

on how it works

[hexed oak]

that is the question as given

I think by find it means that the line segment from the spaceship to the inhabitant doesnt cross the planet

[ornate coyote]

wouldnt it always cross the planet

if both are points on the surface of the sphere

[flint cipher]

In the land of Binary, the unit of currency is called Ben and currency notes are
available in denominations 1, 2, 2^2,2^3 . . . Bens. The rules of the Government of
Binary stipulate that one can not use more than two notes of any one denomination
in any transaction. For example, one can give a change for 2 Bens in two ways: 2
one Ben notes or 1 two Ben note. For 5 Ben one can give 1 one Ben note and 1
four Ben note or 1 one Ben note and 2 two Ben notes. Using 5 one Ben notes or 3
one Ben notes and 1 two Ben notes for a 5 Ben transaction is prohibited. Find the
number of ways in which one can give change for 100 Bens, following the rules of the
Government.

[hexed oak]

no

Cause the spaceship is on space

not on the planet

[ornate coyote]

then how would we know how far it could see

[hexed oak]

this

[jade widget]

idk what is a complex number, am I cooked

[prisma loom]

depends on what competition you are doing

Most high school competitions exclude complex numbers from explicitly appearing

Although of course they are often useful in solutions

[high goblet]

eww geo main wait nvm i can't read i just woke up

NT > alg > combi >>>>>>>> geo

[jade widget]

aime

I just look up the pass paper today

im cooked

[prisma loom]

There's still over a month

You can easily learn all the necessary material in that time

[swift imp]

There usually isn’t a lot of these problems

[hexed oak]

combi>nt>geo=alg

[leaden obsidian]

Can someone help me with this question?: "Decide, if it's possible to add one digit number to a number with sum of digits 2024 so resulting number will have sum of digits 74"

[hexed oak]

look at carry over

[leaden obsidian]

What's that? I don't speak English very well

[jade widget]

[hexed oak]

as in 999+3 has 1002

 11
 999
  +3
 ---
1002```

[jade widget]

good

[hexed oak]

the 1s u do are the carry overs

[leaden obsidian]

Oh I understand, thanks

[vernal axle]

take n=9999999899....9 where there are 217 counts of 9 in the group after 8. Then adding 3 gives the result.

[autumn cedar]

Hello guys. Do you know how I can prepare for competitive exams?

Like are there any resources

[deft wraith]

Alg is not better than combi hahaha

Maybe easier sometimes

[hexed oak]

combi is the best imo

funnest

[leaden obsidian]

Yes I already got the answer but thanks anyways

[ornate coyote]

aime is hard

[swift imp]

Yea

Fr

[hasty spindle]

sorry, this is a bit late but this just seems like a convoluted use of calculus

a+b=132, b=132-a

x+y=10, y=10-x

[hasty spindle]

using this, you can write f(x, y) simply as a function of x

call this g(x)

$g(x)=\sqrt{x^2+2x+a} + \sqrt{(10-x)^2 + 2(10-x) + b}$

[gilded halo]

vsninja19

[hasty spindle]

expand

$g(x)=\sqrt{x^2+2x+a} + \sqrt{(100-20x+x^2) + (20-2x) + b}$

[gilded halo]

vsninja19

[hasty spindle]

collect like terms

$g(x)=\sqrt{x^2+2x+a} + \sqrt{x^2-22x+120+b}$

[gilded halo]

vsninja19

[hasty spindle]

sub this

$g(x)=\sqrt{x^2+2x+a} + \sqrt{x^2-22x+120+(132-a)}$

[gilded halo]

vsninja19

[hasty spindle]

$g(x)=\sqrt{x^2+2x+a} + \sqrt{x^2-22x+252-a}$

[gilded halo]

vsninja19

[hasty spindle]

now differentiate g(x)

$g'(x)=\frac{2x+2}{2\sqrt{x^2+2x+a}} +\frac{2x-22}{2\sqrt{x^2-22x+252-a}}$

[gilded halo]

vsninja19

[hasty spindle]

$g'(x)=\frac{x+1}{\sqrt{x^2+2x+a}} +\frac{x-11}{\sqrt{x^2-22x+252-a}}$

[gilded halo]

vsninja19

[hasty spindle]

set g'(x)=0 to find extrema

$0=\frac{x+1}{\sqrt{x^2+2x+a}} +\frac{x-11}{\sqrt{x^2-22x+252-a}}$

[gilded halo]

vsninja19

[hasty spindle]

$-\frac{x-11}{\sqrt{x^2-22x+252-a}}=\frac{x+1}{\sqrt{x^2+2x+a}}$

[gilded halo]

vsninja19

[hasty spindle]

square both sides

$\frac{x^2-22x+121}{x^2-22x+252-a}=\frac{x^2+2x+1}{x^2+2x+a}$

[gilded halo]

vsninja19

[hasty spindle]

now you could try to solve it by cross multiplying then brute forcing it

but I'm gonna make it simpler

$\frac{x^2-22x+121+(131-a)-(131-a)}{x^2-22x+252-a}=\frac{x^2+2x+1+(a-1)-(a-1)}{x^2+2x+a}$

[gilded halo]

vsninja19

[hasty spindle]

$\frac{x^2-22x+252-a-(131-a)}{x^2-22x+252-a}=\frac{x^2+2x+a-(a-1)}{x^2+2x+a}$

[gilded halo]

vsninja19

[hasty spindle]

$1 - \frac{(131-a)}{x^2-22x+252-a}=1 - \frac{(a-1)}{x^2+2x+a}$

[gilded halo]

vsninja19

[hasty spindle]

$\frac{(131-a)}{x^2-22x+252-a}=\frac{(a-1)}{x^2+2x+a}$

[gilded halo]

vsninja19

[hasty spindle]

$(131-a)(x^2+2x+a)=(a-1)(x^2-22x+252-a)$

[gilded halo]

vsninja19

[hasty spindle]

$131x^2+262x+131a-ax^2+2ax-a^2 = ax^2-22ax+252a-a^2-x^2+22x-252+a$

[gilded halo]

vsninja19

[hasty spindle]

sorry I gtg now if you're reading this, I'll finish it later

[misty belfry]

\int _{-3}^6\int _{-17}^8\int _{-6}^{11}\left(4x+2x^{-\pi }:\left(\sqrt{18}\right)\right)+\left(7x-3x^{\pi }:\left(\sqrt{37}\right)\right)dxdxdydt

@gilded halo

[vague temple]

As Civil Service Program remarked, you can use distance formula and collinearity of the 2 points will maximize

[lilac niche]

Can anyone please explain telescopic series

I forgot how to do it

[radiant jasper]

include it in $$

also #latex-testing

[hasty spindle]

Alr, I could finish this now, but tbh I'm bored of this question, basically use quadratic formula to solve for x, you'll get 2 solutions, one is the minimum and the other is the maximum, use second derivative test to find which is which then, use the fact that the minimum of g is 10 to solve for a, then substitute other value from solving the quadratic to find the maximum

DM me if you want a more thorough explanation

[dapper remnant]

hello?

is anyone here?

[swift imp]

Hello

[dapper remnant]

does anyone have any tips for math olympiad?

[gusty verge]

Grind problems and study solutions and WHY they did what they did

[latent bough]

grind

if youre willing to read books they're quite useful too

because they provide a structured argument that also has the same style throughout the book versus online problems which are written by many authors with various proof styles

so you can learn from how they prove things and apply that to proof-based questions

[ornate blade]

Knowledge can be enhanced by simply studying and revising a lot, depending on your necessity and capacity. Understanding can be enhanced by asking yourself "do I really understand this?" and trying to explain a concept from a fundamental level, and then asking your teacher or watching a video (etc) to find an explanation. This is beyond only what is the textbook. A lot of times you may not cover things in class or in the TB that will be useful to you, so expand your knowledge beyond them when required.
Application requires you to 1) understand the topic, as then you will be able to know how to apply it, 2) enhance your problem solving, such as by devising techniques to solve the problems, and 3) practice.

Another important part is reflection. Reflect on where you're going wrong. What kind of questions are you going wrong in? Why are you going wrong in them? Is it because you're lacking knowledge? Because you didn't understand the concept? because you're unable to apply the concepts? Then, improve on that aspect by adopting a suitable strategy (as I mentioned above). I'd also suggest that you do a little bit of studying/practice everyday so you get into a habit of it, and will not have to grind in the last few months.

thanks Reddit guy

I know I've posted this message a lot recently

[gusty verge]

(I did read it just thought it was a great opportunity for this image, good message bro)

[ornate blade]

if you can read a 500 page book you can read 2 paragraphs on Discord

lmaooooooo

[gusty verge]

Who said I can read a 500 page book 🥺🥸

[ornate blade]

I actually disagree with a lot of people that tell you to grind many years worth of past papers. I used to see my friends spam past papers too ( and ofc so did I in the ending months before exams) but I think it is not always effective. The way I see it, you are a person with a tool box. Past papers help you use those tools and therefore get better at using them. However, sometimes you may not have all the sufficient tools required to solve a particular problem - in this case you have to attain them by improving your knowledge and understanding.

[latent bough]

my workflow is:
do past papers / problems
find weaknesses in subject
read books
solve more problems

you have to learn by doing, but you do need some basic theory to do so

but most problems AMC level can be solved without some random ahh theorem or another

even if it trivializes the problem

also dont be afraid of walls of text

read thru careful and try to simplify the problem down

[dapper remnant]

so grind?

[dapper remnant]

i wan a place where i get to have a feedback on my problem solving

[latent bough]

try MODS

its another discord server specifically for math olys

[dapper remnant]

ok?

thank you

can we be friends?

[prisma loom]

Reflection is really important

Every time I solve a problem I try to identify the "key move" and what led me to it

And every time I read a solution for a problem I didn't solve I reflect on why I didn't find the key move

[lilac niche]

<@&286206848099549185> can anyone please solve this the 74th question

[plain dirge]

you know general circle equation?

[lilac niche]

Yes

[plain dirge]

you have 3 points, put them in it.

[lilac niche]

The equation is x2 + y2 + 2gx+2fy+c =0

Where will u put them

[plain dirge]

x= 20, y =3 for the frist point, and so on. you'll get 3 equations with 3 unknowns.

[lilac niche]

And then solve for the unknowns thanks

[dapper remnant]

hello

[dapper remnant]

wdy by walls of text

[ornate coyote]

its the BMT today

[visual geyser]

see , you can also solve it in 2 variables

[high goblet]

and please don't make ur write-ups as bad as the ones i'm marking rn

also, if a question says that you need to show X and Y, that means that you actually need to prove X and Y and not just claim "X is trivial" 💀

[worthy current]

You can also find the centre through the intersections of the perpendicular bisectors of any two pairs of points then use distance formula

[prisma mulch]

thoughts on putnam?

[radiant jasper]

oh, is there no embargo?

[prisma loom]

The embargo ends when the problems are posted on aops

[burnt trail]

which embargo

[odd wharf]

@quasi lagoon putnam

[odd wharf]

I took it as well

[quasi lagoon]

thank you

[odd wharf]

Im actually pretty happy with how I did. definitely not up to the rigour I will need next year, but I think I got a few points

also @prisma mulch wait i already did that im so smart

[quasi lagoon]

you know given the fact that my uni does the putnam as a kind of intro to math finals and for fun. I think I got a lot more points then I thought it would.

[odd wharf]

someone in my room got a 16 last year

[quasi lagoon]

I was able to understand a good amount of the questions

[quasi lagoon]

damn nice

[odd wharf]

yeah! I loved B1

[quasi lagoon]

B1 was nice I agree

B2 confused me so much tho

[odd wharf]

I saw the paper of the guy who sat next to me, he just wrote "golden ratio"

[quasi lagoon]

so I tried B4, B5 and I got an answer for B4 that I couldn't find a way to say

[quasi lagoon]

LMAO

[prisma mulch]

mfw when everyone got a different answer than me 💀

[odd wharf]

B4 was apparently e^-2

[prisma mulch]

my dumbass said k=n-1 and let n be anything

[quasi lagoon]

I mean probably since it was a geometry problem the golden ratioo may have been somewhere in there

[prisma mulch]

bro is onto nothing

[quasi lagoon]

I retract my previous statement, I did not understand B4

my ass got 1/2

[odd wharf]

this made me laugh real

i was not ready for that 💀

[odd wharf]

a lot of the people near me for 1/2. I put 1

[prisma mulch]

for b2 what i basically said was that the line that creates the perpendicular bisection along ac is infinite in length so all u need to change is the length of AE and you have infinite quadrilaterals

[odd wharf]

i would have put 1/2 if i didnt fumble the question

[quasi lagoon]

nah I pulled fermat's last theorem out of no where on A1

[prisma mulch]

nobody in my uni taking it got past like problem 2 for both sections lol

[prisma mulch]

nah thats what i thought too

its apparently something to do with divisibility

[odd wharf]

yeah how in the world was FLT an A1 question

[quasi lagoon]

I think I will get if they are generous a 4

[odd wharf]

i havent seen a solution for it yet

[prisma mulch]

im getting a 0

[odd wharf]

I think im getting a score

maybe 1-4

[quasi lagoon]

as like I proofed something I think

on A1

[odd wharf]

A2 was a really weird one. Just divide by (p(x)-x)^2 and define p(x) as not x?

If its not that then I have no idea what it could possibly be asking

[quasi lagoon]

nah cause my uni is so funny how they do the putnam. As one of our professors is the director of the Putnam, but he just likes problems.

[odd wharf]

thats cool

[quasi lagoon]

he doesn't proctor the exam, he just says "oh y'all are taking the putnam? Oh yeah im the director of that, anyways onto real analysis"

[odd wharf]

thats cool

[quasi lagoon]

yeah

[odd wharf]

im a junior, im so ready to take the higher level math classes

real/complex analysis, graph theory, proofs, all the shit

[quasi lagoon]

nice nice

real analysis is fun

[odd wharf]

what did you do for A5

[quasi lagoon]

I didn't but I heard somepeople say the center and others say the edge

[odd wharf]

I came up with a pretty solid geometric argument for edge

[quasi lagoon]

one person described it to me as "imagine you are in the wild west, where would you want to be in a saloon when everyone is shooting"

and another person made an intergral they couldn't solve

[odd wharf]

the integral is what im interested in

i also came up with something i couldnt solve so i put it to the side and made a geometric argument

other people in my room that came up with an integral they also couldnt solve said that it would take way longer than the theoretical 30 minutes

[prisma loom]

You guys should take your discussion to DMs

[quasi lagoon]

A2 I made a very complex divisbility proof that really just came down to "if they divide each other, it works"

[prisma loom]

Embargo isn''t over

[quasi lagoon]

[odd wharf]

where in the world is the exam not over?

not rhetorical, where in the world

[prisma loom]

Not sure

But there's an embargo in the olympiad server

[quasi lagoon]

ooooh

yeah they haven't uploaded everything yet

[odd wharf]

olympiad server ⁉️

invite me

pls

[prisma loom]

Check the channel description

[odd wharf]

oh shit i didnt realise this was this channel

i thought this was #advanced-lounge

[quasi lagoon]

[odd wharf]

well

here we are

[quasi lagoon]

welp

[prisma loom]

Maybe it's still ongoing in hawaii or smth

[quasi lagoon]

I think hawaii is still going

or done

oh no they done

like they are on part B

[prisma mulch]

gg ur scores getting cancelled @quasi lagoon @odd wharf jk

[odd wharf]

GG

[quasi lagoon]

GG

[prisma mulch]

wait ur a girl? @odd wharf

[quasi lagoon]

[prisma mulch]

what the heck

are those even real

[quasi lagoon]

even better, I got my scores canceled by talking on discord

[odd wharf]

-# sigh

[prisma mulch]

STOP SKULL EMOJING ME GRRRRR

[quasi lagoon]

most wild statement

[prisma mulch]

brother

i havent even had a friend in uni i dont even know what a person is

anyways what did u guys think of a3

[quasi lagoon]

mans is a true math major rn

[odd wharf]

i saw my tablemate take a swing

ive got no idea

[prisma mulch]

i was like unironically happy to be surrounded by people at the putnam thing

thats how lonely i am i guess

[odd wharf]

me too actually

[quasi lagoon]

no thats fair tbh

[odd wharf]

i spend most of my nights in my dorm coding or solving my own math problems

[prisma mulch]

i think thats why im depressed cuz i dont have any interaction since i commute

tru

[quasi lagoon]

ahhhh I see

[prisma mulch]

how do u make ur own math problems

[odd wharf]

my own as in existing problems on my own time

[prisma mulch]

should we discuss this in a gc due to embargo

[quasi lagoon]

I can send you some of mine if you don't have enough

[quasi lagoon]

yeah prob

[odd wharf]

https://cdn.discordapp.com/attachments/1231378544240889996/1314177336412868670/attachment-8.gif

[prisma mulch]

i sent friend req

[quasi lagoon]

I should have showed up in this

[prisma mulch]

we had 2 girls at our putnam session

one of them i expected to come tho

[odd wharf]

it was me and one other girl

she was chinese and did her own thing. i was still friendly with her though

she sat next to me

[quasi lagoon]

it was me and the gay math majors I was able to convience to show up

[prisma mulch]

yo what does chinese gotta do w anything

[quasi lagoon]

so about 9 of us

[prisma mulch]

wdym by gay

[quasi lagoon]

lgbtqia+

[odd wharf]

"what is chinese" "what is gay" bro really is a math major

[quasi lagoon]

its almost the same venn-diagram at my uni

[prisma mulch]

speaking of putnam winners

and lgbtq+ members

[odd wharf]

i wish i had more drive to apply to schools

[prisma mulch]

is this a correlation or causation guys

[odd wharf]

im going to try MIT for my masters

[prisma mulch]

whats ur undergrad gpa

[odd wharf]

3.78

1450 SAT

[quasi lagoon]

derivative you ok if I send a friend request?

[odd wharf]

yeah sure

4.0 in math classes

[prisma mulch]

what math classes have u taken so far

[odd wharf]

just stupid shit weighing me down

[prisma mulch]

like ur hard stuff

[odd wharf]

discrete, calc 1/2/3, lin alg, diff eq

[prisma mulch]

not that baby calculus shit

ok cant say anything yet abt ur chances tbh

lot of hard classes left

[quasi lagoon]

me and my 3.0 gpa and 3.0 math gpa

[odd wharf]

on my own im working on real analysis rn

[quasi lagoon]

going into math education

[prisma mulch]

i got a C+ this sem in intro to proofs

[odd wharf]

and some graph theory

[prisma mulch]

hell nah

become an actuary

thats what im doing

[quasi lagoon]

cash scares me

hence math education

[odd wharf]

actuarial sciences seems weird

i dont want to be the person who has to put the price on shit that a price should no be on

[prisma mulch]

100k salary doesn't

[odd wharf]

100k is small money

[prisma mulch]

name one other good paying math major career out of undergrad

[odd wharf]

well now im going to seem hypocritical

government contract work ._.

[prisma mulch]

yo chat does this pic go hard

i was googling putnam winners and came across this masterpiece

[quasi lagoon]

middle guy has either to many friends or no friends

there is no inbetween

[odd wharf]

whats the base case for the induction one

[prisma mulch]

nah i wanna know red jackets story

[odd wharf]

B3

[prisma mulch]

THAT WAS INDUCTION???

HUH

[odd wharf]

I thought so

I couldnt figure it out though

[prisma mulch]

am i dumb or are you dumb

[odd wharf]

it smells like induction

[quasi lagoon]

girl, I didn't even know what $r_{n}$ was

[gilded halo]

Duck

[prisma mulch]

bro

[prisma mulch]

induction has to do with sequences

not bijections

[quasi lagoon]

so simple

[shadow spruce]

By parts?

[quasi lagoon]

my gutt tells me its 1

[prisma mulch]

yeah

[shadow spruce]

I just wonder how to get the latex code

[prisma mulch]

no its 0

[odd wharf]

B3 was the tan(x)=x

[prisma mulch]

oh

im sorry

i thought u meant a3

btw what is tan(x)=x

[shadow spruce]

$\int_0^1\frac{1}{x^2+2x}dx$

[odd wharf]

i meant B3 when I said B instead of A

[gilded halo]

Aestusy

[shadow spruce]

$\int_{\int_{0}^{1}x^{2}dx}^{\int_{0}^{1}x^{3}dx}xdx$

[gilded halo]

Aestusy

[odd wharf]

chat what is this

[shadow spruce]

$\int_{\int_{0}^{\int_{1}^{\infty}\frac{1}{x}dx}xdx}^{\int_{0}^{\infty}\sin(x^{2})dx}\frac{1}{\sqrt{1-x^{2}}}dx_{\sin xdx}$

[gilded halo]

Aestusy

[pale goblet]

Alguien que hable español?

[odd wharf]

yo

que pasa

[pale goblet]

Tengo una duda con el nombre de esta expresión

[shadow spruce]

Si

[odd wharf]

q es?

[prisma mulch]

@pale goblet @shadow spruce wrong channel stop spamming

[pale goblet]

No me deja mandarla

Pero es algo como

[shadow spruce]

We should have Chinese and ES chat

[pale goblet]

X-3

-2

[shadow spruce]

Channel

[pale goblet]

X-3
---- + -3
-2

[shadow spruce]

@pale gobletI don't understand the question you are asking here

[odd wharf]

como el nombre de (x-3)/(-2) - 3?

fracciones?

[pale goblet]

Es que no lo se xd

Pienso igual que es una fracción

Pero es primera vez que la veo

Creo que es

X-3/-2

Porque la ecuación completa es

X-3/-2=-3

[odd wharf]

necesitas x?

x = 9

[ornate coyote]

send help

[low fiber]

what happened?

[jade widget]

help

[glossy falcon]

$\int_{\int_{0}^{1}x^{2}dx}^{\int_{0}^{1}x^{3}dx}xdx$ = $\int_{\frac{1}{3}}^{\frac{1}{4}}xdx$

[gilded halo]

moonhalo

[glossy falcon]

$\int_{\int_{0}^{1}x^{2}dx}^{\int_{0}^{1}x^{3}dx}xdx$ = $\int_{\frac{1}{3}}^{\frac{1}{4}}xdx$ = $\frac{1]{32} - \frac{1}{18}

[gilded halo]

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

[glossy falcon]

$\int_{\int_{0}^{1}x^{2}dx}^{\int_{0}^{1}x^{3}dx}xdx$ = $\int_{\frac{1}{3}}^{\frac{1}{4}}xdx$ = $\frac{1]{32} - \frac{1}{18}$

[gilded halo]

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

[glossy falcon]

$\int_{\int_{0}^{1}x^{2}dx}^{\int_{0}^{1}x^{3}dx}xdx$ = $\int_{\frac{1}{3}}^{\frac{1}{4}}xdx = \frac{1]{32} - \frac{1}{18}$

[gilded halo]

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

[radiant jasper]

cool

[low fiber]

how do i start getting questions right on math comps

[reef condor]

Be come a sig Ma

[prisma loom]

shouldn't be that hard if you're the reincarnation of leonhard euler

[low fiber]

istg

[reef condor]

“How many solutions are there to x^n + y^n = z^n with n > 2?”

[prisma loom]

Infinitely many

[ornate coyote]

bro

[swift imp]

Do problems

[jade widget]

He didn’t say any of them have to be whole number

[radiant jasper]

"I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."

[torn gate]

I have a counter-example but the numbers themself doesn't fit within this discord message

[quasi lagoon]

I would tell you but the code that writes this message is not elegant enough to sustain my proof.

[high goblet]

actually probably like slightly higher than low 30s

ppl didn't find it as hard as what discord seemed to suggest

[snow tartan]

Ok

I’m hoping it’s sub 30 for y10 and below

So I have a chance

[digital hedge]

Find all n with the following property: we can choose n distinct lattice points in 2d Cartesian coordinate such that all of the points form a regular n-gon.

Can anyone help?

[meager sail]

C(np,n)-n is divisible by p can someone help me prove this

[ornate blade]

maybe try induction on p?

or n

[meager sail]

oh forgot to say

p is prime

[ornate blade]

oh that makes sense maybe it's like some weird application of Fermat's little theorem

[hexed oak]

isnt this trivally wrong?

take n = 1

@meager sail

[pallid ginkgo]

0 is divisible by p

[hexed oak]

p-1 is not divisible by p

[pallid ginkgo]

er wait

on right choose 1

[ornate blade]

oh yeah there must be conditions

[hexed oak]

yeh

[meager sail]

pCp-1=1-1=0

[hexed oak]

but here

it

says

npCn

not npCp

[ornate blade]

nah when n = 1, (p choose 1) - 1 = p - 1

[hexed oak]

pC1-1= p-1

[meager sail]

Ohhh

I mean

npCp

srysry

[hexed oak]

oh

that makes much more sense

[meager sail]

npCp - n

[hexed oak]

so combinatorically looking

you have nXp grid

[ornate blade]

there must be a combinatorical proofs yes but me smol brian

[hexed oak]

you choose p points on the grid, so that not all in the line

[hexed oak]

i cant do non combinatorial proofs

[hexed oak]

and you have to show that the number of ways of doing so

is divisible by p

got it

for each one

we can rotate it around

and get a new one

so it os divisible by p

ok lemme put it properly

first notice np = number of points in an nXp grid

and you basically choose p of those points

but you forget the n cases where all the p points are in the same line

[meager sail]

what is a nXp grid

[hexed oak]

aXb grid

you know

[meager sail]

?

[hexed oak]

like a 2x2 table

[meager sail]

um

[hexed oak]

this would be 6X10

[meager sail]

Ahh i see

yea i chose p of those points

[hexed oak]

now you remove the n cases where those p points fill a row

[meager sail]

but i forget n cases where all the p points are in the same line ok

[hexed oak]

now let us say the points are
(a1,b1)(a2,b2)(a3,b3)....(ap,bp)

[meager sail]

whats a and b

[hexed oak]

the x coordinate and y coordinate of the points

notice any rearragment of the indices gives the same result

[meager sail]

ok

[hexed oak]

we can also just have
(a1,b1)(a2,b2)(a3,b3).................(ap,bp)
(a1,b1+1)(a2,b2+1)(a3,b3+1)...(ap,bp+1)
(a1,b1+2)(a2,b2+2)................(ap,bp+2)
(a1,b1+3)(a2,b2+3)................(ap,bp+3)
...
(a1,b1+p-1)(a2,b2+p-1)......(ap,bp+p-1)

we can group these together

and there are p members in each group

so we are done

[meager sail]

so basically

in the n X p grid

[hexed oak]

we can just rotate the points

[meager sail]

hm...

[hexed oak]

we can only do this since p is prime

other wise we could have indistinguishable rotations

I have expained this very badly

i trust there is someone here who can understand what i have said and explain it to you better

[meager sail]

can u write it on paper with the grid?

[hexed oak]

sry, but no

[meager sail]

ok

[shadow spruce]

https://www.youtube.com/watch?v=O1yEdlVcUIg

[radiant jasper]

oh so im not alone tryna watch math stuff

this server so cool

[ornate blade]

indeed

[radiant jasper]

whoa

so easy

[hexed oak]

we can factorise any multionmial into linear fatcors right?

[ornate blade]

yes, if you allow complex numbers

that is correct

[hexed oak]

yes

[ornate blade]

more specifically any nth degree polynomial has n complex roots (including real roots)

FTA

[hexed oak]

yes

i said multinomial tho

[ornate blade]

oh shit

[hexed oak]

its not

hm

maybe it is

[ornate blade]

well a simple example would be like pq + qr + rp

that's not factorisable

[hexed oak]

yeh

[ornate blade]

not completely

[hexed oak]

what are the the multinomial primes?

if there are n varaibles

[ornate blade]

are you looking for elementary symmetric polynomials or nah

[hexed oak]

can i always factorise it into expressions of drgee n

[hexed oak]

nah

[ornate blade]

don't think this is possible

there are just too many possible multinomials

[hexed oak]

can you give me an example otherwise?

[hexed oak]

Prove that You can always pose a circle of radius S/P inside a convex polygon with the perimeter P and area S.

any ideas
i proved for triangle and quadrilateral
but inductive doesnt work
Ik that the diameter is less than the "least width" of the poylgon, but that is not enough

[hexed oak]

<@&286206848099549185>

[tough whale]

maybe you can find the most extreme case of those convex polygon

[hexed oak]

basically for the last point, i made two perpendicular lines which spanned the whole polygon,
lengths a and b
area <= ab
perimeter > 2a
so radius < b/2
so diameter < b

[hexed oak]

meaning?

[tough whale]

ive been thinking like making a really thin rectangle that satisfies the perimeter P and area S, and prove it is the most extreme case of such polygon, then just check if a circle of radius s/p is still constructible or not

basically try squeezing your polygon as narrow as you can

but of course, i havent done it myself

just my intuition

okay i have a better idea

you make a circle of radius S/P first

well thats it

or maybe, prove it is not possible with triangle, then proceed with squre

okay it is induction

[hexed oak]

induction doesnt work

i showed that induction doesnt work

because if i could do inductive argument, i could do infinite descent

and i showed that there is a polygon in which the cicle isnt in a triangle

[hexed oak]

that is what i did, but how do i prove

sry for sudden leave

<@&286206848099549185>

[slate scaffold]

if you would like help make a help channel dont ping here pls

!help

[scarlet root]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[thorny quail]

i got a mathletes thing in 2 days and i mad eit onto the team at the last practice i have 0 clue what im doing 🔥

[latent bough]

💀

you got this man

[radiant jasper]

I skipped all of those meetings bro 💀

I'm planning to go for once this week

[thorny quail]

😤

o do

[thorny quail]

😭

[hexed oak]

i am specifically not doing that, because i dont expect anyone to get an answer in a short amount of time, and i cant maintain a help channel for a long period of time

[shadow spruce]

Tedious and easy to make mistakes

[tough whale]

hold up... so you contradict the proof?

[tough whale]

😅

[tough whale]

its ok but i am going to sleep at that time

[hexed oak]

yep

[barren sparrow]

can someone explain the last step

[slate scaffold]

!noping

[scarlet root]

Please do not ping individual helpers unprompted.

[pallid tundra]

got absolutely shellacked on the Putnam 😭

[swift imp]

Aww

[thorny quail]

tourney tmr

what we thinking

😄

[radiant jasper]

💀💀💀😭😭😭😭

youre not helping anyone

you've been in this server for 4 days and you're bossing around someone who's been here for over a year

[ornate coyote]

is it weird to do high school comps in middle skool

[unkempt lodge]

no

[ornate coyote]

when are amc10 scores coming out

[swift imp]

They already have

[ornate coyote]

WHERE

[swift imp]

Idk

I got them emailed to me

[ornate coyote]

when did you get it?

im not seeing it in my email

[swift imp]

Like

A week after I took it

[ornate coyote]

i mean like the cutoffs

[swift imp]

Bruh score is not cutoff

It comes out when maa releases

[hexed oak]

I am not pinging?

[radiant jasper]

alrr

[hasty spindle]

Do you want me to finish it now or what?

[olive tulip]

We don't talk of such things anymore

💀

I did so bad

[hexed oak]

construct rectangles with height S/P inwards to the polygon, total area is S but the rectangles overlap, so some point inside the polygon is not covered. take that point as center of a circle with radius S/P, it will work

this is not my solution, i asked a sir, he solved in about 1/2 hr

[hexed oak]

it is so simple, agh

[radiant jasper]

yes finish it

take ur time

whenever u feel liek

u can ping me okay @hasty spindle

[reef saddle]

I made 63 on AMC 10A and 10B

[hasty spindle]

Alr, Ill finish it tmrw, I'll ping you when I do, if I forget (I probs will knowing myself), ping me

[radiant jasper]

alrr

or dm me

[junior wolf]

should i do it?

[cerulean path]

Wait how can math be competitive?

[prisma loom]

There is a problem set

Everyone tries to solve as many problems within some fixed time limit

The more problems you solve the higher your score

[gusty verge]

Who can count the fastest, who can add the biggest numbers correctly, reciting digits of pi contest

[prisma loom]

who can count the fastest 💀

[gusty verge]

😂

[slate scaffold]

no i help people but its ok youll see only what you want to see 🙂

[slate scaffold]

either what they said or like who can get the most right of difficult problems

[slate scaffold]

fr tho they use that chinese bead thing, Atticus, in their minds its wild

[slate scaffold]

you got it fr

[high goblet]

name the largest number

[latent bough]

you mean abacus? 💀

[slate scaffold]

yesss

atticus haha

[slate scaffold]

none

[latent bough]

1,099,551,473,989 is the largest number ever factored
2^136,279,841-1 is the largest prime ever found

grahams number is biggest with a name

[thorny quail]

we did ass

😭

well my team did bad

my school got 2/10 spots secured

so thats a good thing

but yeah

erm

the questions were NOT hard

but

yk what made it hard

and ik i sound like a sore loser

and salty

but i kinda am

was the speed of the response time of 2 individuals on my team

the other two, one of them being me, were visibly frustrated as we were alot faster than them and wasted too much time waiting

in the first round we only scored 5/18 possible points

8 questions, 2 on each page given to 4 people

so 2 per person

me and him finished our 2 questions

they combined took like 8 minutes doing multiple choice

and we missed the deadline to get the puzzle

and the puzzle is worth 10

idk i had fun meeting people tho

so in the end i gained an experience ig

this was one of the questions::

Below, the surface area of that rectangular prism was 16r^2, the value of t being 6, what is the value of the positive integer, r?

and the answer was

and another question

The starting term of a sequence is 24, the rules are: if the number is even, divide by two, if odd, multiply by 3 and add 1.

What is the 2024th term of this sequence?

i believe those rules are a specific problem from the internent that is unsolved, i forget the name of that problem though

It is extremely familiar

the answer to this was

||1||

||because after around the 10th term the sequence repeats, 4, 2, 1, infintely,||

[thorny quail]

||15||

but yeah guys those r the questions i found tricky if you want to try them

[latent bough]

collattz conjecture

my guess would be 1, 2 or 4

and ud have to hand calculate to find when it goes to loop

[latent bough]

i think r = ||3||

surface area is $4R^2 + 24R + 12R = 4R^2 + 36R = 16R^2$

[gilded halo]

reaver

[latent bough]

then just cancel shit

$36R = 12R^2$

[gilded halo]

reaver

[latent bough]

$12 = 4R$

[gilded halo]

reaver

[latent bough]

$R = 3$

[gilded halo]

reaver

[thorny quail]

YES I KNEW IT

I KNEW I HEARD OF IT BEFORE

[thorny quail]

yepp!!

and i had to substitute that intoa nother equation

i believe x^2 + x(t + 1) + 36 = 0?

and x^2 - 8x + 2 = 0

and t is the number from the previous qeustion

which is R = 3

so t = 3

[ornate coyote]

happy mathing

[glass pelican]

When are AIME cutoffs coming out?

[pallid tundra]

check back around january

maa tends to be hella slow with posting scores

[radiant jasper]

welp ur wish

[sturdy viper]

This week

Apparently

According to AOPS forums

[stone sky]

.

[junior wolf]

has someone already done it?

[radiant jasper]

maybe not

[radiant jasper]

have u done it mate

[hasty spindle]

Lmao sorry

Ill do it now

Alr where did I leave it

[hasty spindle]

$2ax^2 - 132x^2 - 24ax - 240x + 121a = 0$

[gilded halo]

vsninja19

[hasty spindle]

$(2a-132)x^2 + (-240-24a)x + 121a=0$

[gilded halo]

vsninja19

[hasty spindle]

This is gonna be disgusting

Quadratic formula

$x=\frac{240 + 24a \pm \sqrt{(-240-24a)^2 - 4(2a-132)(121a)}}{2(2a-132)}$

[gilded halo]

vsninja19

[hasty spindle]

I'm gonna use wolfram to simplify bcs I can't be bothered

Nvm that's still disgusting, I'll work with this for now

[hasty spindle]

These 2 values for x are the 2 extrema, one gives the minimum, one gives the maximum

Assume that the first case (where the plus minus sign gives a positive) is the minimum

So we have

$g(\frac{240 + 24a + \sqrt{(-240-24a)^2 - 4(2a-132)(121a)}}{2(2a-132)}) = 10$

[gilded halo]

vsninja19

[hasty spindle]

Substitute into this

$\sqrt{(\frac{240 + 24a + \sqrt{(-240-24a)^2 - 4(2a-132)(121a)}}{2(2a-132)})^2 + 2(\frac{240 + 24a + \sqrt{(-240-24a)^2 - 4(2a-132)(121a)}}{2(2a-132)}) + a} + \sqrt{(\frac{240 + 24a + \sqrt{(-240-24a)^2 - 4(2a-132)(121a)}}{2(2a-132)})^2 - 22(\frac{240 + 24a + \sqrt{(-240-24a)^2 - 4(2a-132)(121a)}}{2(2a-132)}) + 252 - a} = 10$

[gilded halo]

vsninja19

[hasty spindle]

Lmao it's too big

Disgusting equation

Anyway, solve this (I'm just gonna use wolfram bcs this is disgusting)

💀

Give me a sec, I'll type this out into desmos 😭

[hasty spindle]

I think I made an error in my working, getting no real solutions for both cases 😭

[ornate blade]

rewrite as $f(x) = \sqrt{\left(x+1\right)^{2}+\left(a-1\right)}+\sqrt{\left(11-x\right)^{2}+\left(b-1\right)}$

now observe this looks like the distance formula / Pythagoras

we want to minimise the total distance of the vectors $(x + 1, \sqrt{a-1})$ and $(11 - x, \sqrt{b-1})$

but the total distance is minimised when the two vectors are collinear, so they must have the same gradient

https://www.desmos.com/calculator/sux4evx7l7

[gilded halo]

south

[ornate blade]

https://math.stackexchange.com/questions/2400586/finding-minimum-value-of-sqrtx2-2x1-sqrtx2-6x13

[hasty spindle]

Should be -2ax

[hasty spindle]

Oh right, that's much smarter

[hasty spindle]

So -2a here

[ornate blade]

or that the shortest distance is when you just combine the horizontal and vertical displacement, since they lie on the same line

so $\sqrt{(x + 1 + 11 - x)^2 + (\sqrt{a - 1} + \sqrt{b - 1})^2} = 20$

[hasty spindle]

Still no solution, I give up

[gilded halo]

south

[ornate blade]

@radiant jasper

I get max value = ||sqrt(82) + sqrt(170)||

[gilded halo]

south

south

[ornate blade]

the turning point was the one where y = 20 and you can sign diagram it to check that it's a minimum

find f(0) and f(10) and then check they are both greater than 20

[vernal axle]

just check the Fourier series for |sin(x)|
https://math.stackexchange.com/questions/534794/fourier-series-of-sin-x

[barren sparrow]

try double differentiating it and adding it to orignal eqn

[gray heart]

hello everyone, im working on a problem of finding min(x^2+y^2+z^2) where x,y,z are reals and x^3+y^3+z^3-3xyz=1 , ive tried several things and i think the minimum is 1 but i cant get to an actual solution

[high goblet]

is this like BMO2 Q1 from some paper in like 2007 or smth?

anyway i don't fully remember the solution

but i think one step is to rewrite x^3 + y^3 + z^3 - 3xyz = 1 into something nicer

(there's a good factorisation to be aware of)

anyway then you can write everything in terms of p=x+y+z and q=xy+yz+zx

and then i seem to remember everything just works

[gray heart]

no idea tbh

[gray heart]

yeah, (x+y+z)(x^2+y^2+z^2-xy-yz-xz)

im well aware

[prisma loom]

It is trivial

Do the symmetric polynomial substitutions

[gray heart]

?

[prisma loom]

this

[vernal axle]

You can rewrite it as (3s-t^2)t=2, where s=x^2+y^2+z^2 and t=x+y+z.
Then t>=0 as t^2<=3s. So, 3s=2/t+t^2>=3. Thus s>=1. Equality is with t=1.

[gray heart]

omg how i didnt think of that

thanks

[radiant jasper]

alrr

[gleaming field]

Hello, any number theory expert, which would help me pls with #help-35 ?

[warped wedge]

Has MAA released the official AIME cutoff yet?

Are the ones on AOPS historical results official

[radiant jasper]

Another year, another fail.

At this rate, I will never make AIME

I am so done

[prisma loom]

So you should up the rate

[radiant jasper]

Too late to up it

[prisma loom]

Was this your last year

[radiant jasper]

????

No but

Another kid in my grade made it

so like

college waise

im screwed

[prisma loom]

bro

AIME qual is not gonna be the end all be all of your college application

that is just a dumb mindset

[radiant jasper]

it kinda is if its like your only extra curricular

[prisma loom]

yeah but if this isn't your last year you at least one year left to do other stuff

[radiant jasper]

4

[prisma loom]

you hvae 4 years left?

[radiant jasper]

Yeah

I'm an 8th grader

[prisma loom]

Dude

You should not be worried about not making AIME

The fact that you even know it exists means you're ahead

Just keep training and improving

[radiant jasper]

But like

Ivies are cutthorat

And literally kids I beat in AMC 10 last year

Made AIME

and I didn't

[prisma loom]

you could've just had a bad day

I missed IMO this year because of a bad TST

[radiant jasper]

2 bad days??

[radiant jasper]

ORZ

[prisma loom]

Yes

[radiant jasper]

WHAT

[prisma loom]

(I live in a country with a few million people, so IMO isn't that hard to get into)

[radiant jasper]

It's still IMO though

And I can't even make AIME despite this being my 3rd year trying

And I missed it by 4.5 points

[prisma loom]

How much did you miss it by last year

[radiant jasper]

10-15 maybe?

[prisma loom]

so that's improvement

[radiant jasper]

No but like

There are kids who were way behind me last year

And this year

They qualified