competition-math

[ornate coyote]

me during mathcounts

[tame burrow]

Scratch paper exists for a reason lil bro

[latent bough]

this is why i hate numbers

but i hate letters even more

[tame burrow]

safhnaks;jdfghaopsihfalsidghl;ksafhpoadhnsgipsdufh'ansdfpik;asdhfo;asjdgf;/jsado;ghf;a

hehehehaw

[ornate coyote]

whats crazy is i got 139.5 on B and 133.5 on A but got a B on my geometry test (basic school geo)

[tame burrow]

Bro I cannot relate cuz I sleep through all my math and science classes

i straight up dissing the teachers

[latent bough]

i hate chinese characters ngl they all look the same (the chars)

[tame burrow]

erm actually

[ornate coyote]

i got a whole lot of snitches in my class

not letting me sleep

[latent bough]

oml my teacher just throws packets at us

[tame burrow]

I sleep even though people snitch on me

[latent bough]

i have a b+ somehow in my class

[tame burrow]

cuz me half dead and starving is still better than 99% of my school

[latent bough]

the tests are harder than amc 12 ngl

it just doesnt make sense

im in precalc + ab mashup

[ornate coyote]

my algebra teacher used to just throw me on desmos classroom and not teach anything

so i just like spent 30 out of 50 minutes of the class doing my own math homework

[tame burrow]

Bro the teachers let me sleep cuz they have no right to stop me; I'm literally better than them at their job 💀

[latent bough]

oh the teachers at ur school not at uni right?

[tame burrow]

Bro the uni I alt at is literally MIT

how tf am I supposed to compete

[ornate coyote]

in my coding class some kid just took a few spinny chairs and started sleeping on them

even took his crocs off

[latent bough]

valid

[tame burrow]

That's me

except im in math

[ornate coyote]

my math teacher is such a weird person

she makes us parade through the hallways

[tame burrow]

and I don't wear crocs

[latent bough]

💀

[ornate coyote]

blasting side angle side congruency

music

and walks into random normal LA classes

[latent bough]

i like soh-cah-toa

[tame burrow]

do you have one of those happy-go-lucky math teachers?

[ornate coyote]

and forces us to dance

yes

[tame burrow]

bro I can relate

that's my english teacher tho

and that makes it so much worse

[ornate coyote]

the students yell special ed class while we do it

its so

awkward

[tame burrow]

lwk I kinda want to see that, I need a good laugh

[ornate blade]

typical coding class

[tame burrow]

Yes bro

[ornate blade]

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

cancer

[ornate coyote]

LITERAL CANCER

[tame burrow]

WOMP WOMP MOMENTS

[ornate blade]

they even performed in front of the whole school

at assembly

watch the end of the video

[ornate coyote]

they are doing it at the jazz concert

in front of the whole schooll

and my teacher is making us dance up there

[ornate blade]

what kind of school............

[tame burrow]

Why

just why

[ornate coyote]

a weird school

[tame burrow]

Bro the weirdest thing my school has is electing an orchestral val

which is just stupid

[ornate coyote]

there has been weirder

[tame burrow]

and then making said val play a 40-minute concerto in front of the entire school district with a youth orchestra 💀

My embouchure hasn't healed yet, and it's been a year 💀 RIP

And I wasn't even the guy playing the concerto

i was just there for support

[latent bough]

what happeneed to your embouchoure bruh

[ornate coyote]

tbh i should just study throughout the school

[latent bough]

how does that even work

[ornate coyote]

40 free minutes during my coding class

[tame burrow]

I couldn't bubble my mouth for a day and a half afterwards

[ornate coyote]

💀

[tame burrow]

Bro and the guy was a trumpet player

[latent bough]

💀

trumpet

i played trumpet for half a year

i quit

im a quitter

https://tenor.com/view/pepe-walking-away-leaving-bye-pepe-the-frog-gif-6463915606758186278

[ornate coyote]

i was forced to do either orchestra or band

[tame burrow]

I play bassoon; carrying that shit is literally an entire arm workout

[latent bough]

band is goofy bruh 12 percussionists and half of us just sit around

on our phoens

[ornate coyote]

all my teachers are so strict

they dont let us do that

smh

[tame burrow]

Wait

let me show you what my section each had to play for a contest
https://www.youtube.com/watch?v=PYOPQuhdoQM (skip to 1 mintue marker)

I almost quit right there

[ornate coyote]

yall play mozart?

my class just plays star wars and stuff

for the 5th graders apparently

[tame burrow]

Bro the arpeggios and fast runs killed my tongue

[tame burrow]

No, my youth orchestra

[ornate blade]

I feel choir can be more chill than orchestra though

[ornate coyote]

why does that guys hair look like an M

[latent bough]

💀

[tame burrow]

Hey don't disrespect my goat Voltan

[ornate coyote]

i get sick way too often for choir

and also the choir sounds interesting...

too few voices

[tame burrow]

💀

[ornate coyote]

im gonna go do some woot

[tame burrow]

yes bro

I wish I was able to do woot

but I'm broke af

[latent bough]

i wanna do woot but im too stupid even for amc

so no point

is woot hard

[tame burrow]

you'll get there eventually

[latent bough]

what do. you do in woot ?

[tame burrow]

Olympiad prep

[latent bough]

yh ik

but like what do you do tho?

[ornate coyote]

i wouldnt say woot 1 is too hard

[latent bough]

not for u

[ornate coyote]

its like aime level mostly

[tame burrow]

Yea it is

[latent bough]

also why tf am i watching a video about group theory

im tweaking i havent even done calclus yet

[ornate coyote]

once i looked at my brothers woot 2

[tame burrow]

you don't need calc for gt

[ornate coyote]

or just like normal woot before they added woot1

[latent bough]

yah but i should prolly just study calc so i can skip

and i also i keep failing my precalc tests so 🤷

[tame burrow]

Yea you should do that

[latent bough]

what book u rec

stewart?

[ornate coyote]

aops

[latent bough]

bruh for calc?

[ornate coyote]

aops da goat

aops has a calculus book

[latent bough]

is it good tho?

[ornate coyote]

idk

[latent bough]

💀

[ornate coyote]

i havent done a lot of calculus

[latent bough]

ive heard of stewart and apostol

[soft vigil]

ye

[swift imp]

What’s woot

[latent bough]

wolrrdwide online olympiad training

aops

[radiant jasper]

Apostol is good but lengthy

If you're willing to really grind through it, then definitely do apostol

[latent bough]

ok

[swift imp]

Oh

Never heard of it

[latent bough]

huh

[vague temple]

Is group theory useful for AIME? Should one learn it, and if so, where to start?

[shadow spruce]

aops?

[shadow spruce]

yeah k330-332

[shadow spruce]

+1 just read over analysis

[vague temple]

Does anyone know how to bulk download past contests from AoPS

[lyric parrot]

nice q here

jee level

for trigonometry enthusiasts

[barren sparrow]

Do u know the formula sinxsin60+xsin60-x

[lyric parrot]

yes

sin x sin (60-x) sin (60+x) = sin 3x /4

[barren sparrow]

Yes use that and the multiplication formula for sin

[lyric parrot]

alright

[vague temple]

80?

[haughty portal]

sin (a+b)* Sin (a-b)

can also be used?

[shadow spruce]

Anyone needs LaTex OCR API? I just purchased one, I can send you API Key if you want.

use double angle identity you get 80

Or you can solve for \alpha and subsitute

$\sin^210^\circ\times\left(\frac12\sin40^\circ\right)\times\left(\frac12\sin80^\circ\right)=\frac14\sin^210sin40sin80$

?

[gilded halo]

Aestusy

[shadow spruce]

and sin80 and sin10 together

and expand sin40 to 2sin20cos20 solve for a

[barren sparrow]

that identity is used to derive sin x sin (60-x) sin (60+x) = sin 3x /4

so yea same thing

[drifting oak]

Have you solved it yet?

[velvet aurora]

does anyone know if reading napkin by evan chen will help w comp math

specifically pre-oly (like aime)

[high goblet]

uh no lol

very very very maybe for olympiad maths

definitely not for pre-oly lmao

napkin by evan chen is meant as an exposition to university mathematics

[velvet aurora]

fair enough

[high goblet]

unless the maths competition syllabus has dramatically changed, knowing topology or galois theory is not gonna help on AIME lol

[velvet aurora]

i heard group theory could help for the qs in 14-15

[high goblet]

i'm not american so i've never done AIME

potentially some group theory could be helpful for some later qs

[velvet aurora]

ah ic

[high goblet]

but you almost certainly won't need anything more complicated than that

(sometimes some harder olympiad questions are immediately killed by advanced theory, i.e. 2003 IMO P6, but like those are quite rare)

(and will often involve lots and lots of theory)

[velvet aurora]

interesting

[high goblet]

basically read napkin if ur interested in uni mathematics, but don't read it specifically for maths competitions

[velvet aurora]

ill take a look at 2003 p6

[velvet aurora]

thanks for the response :)

r there any texts that helped u

a lot

[high goblet]

nw!

[high goblet]

ok so i'd like to preface by saying that i'm british

personally i didn't use that many theory books, i mostly did problems

https://bmos.ukmt.org.uk/home/bmo.shtml

i grinded all of the british maths olympiads R1 from like 1995 onwards and then also did a lot of BMO2

[velvet aurora]

damnn i see

[high goblet]

then i started grinding some IMO problems

[velvet aurora]

to grind these problems

dont u need a base lvl of theory

or did u js pick it up

as u solved

[high goblet]

there's like a few books that contain like a collection of just BMO1/2 problems & their solutions that i worked through

it's like "a mathematical olympiad primer" or smth like that

[high goblet]

again, not american but like certainly for the UK

you don't need theory for the very start

u'll have to learn more theory as u get into like harder olympiads

but it's best to just start doing problems

sometimes there'll be a question that requires a tiny amount of i.e. modular arithmetic theory

but often ur meant to just pick it up as u solve it if u don't know the theory already

cus also if u do that it'll stick with u a lot better

[velvet aurora]

thanks for the good advice :)

[high goblet]

nw!

[radiant jasper]

I have major ops on BMO 1 😂 Its next week

[tame burrow]

Sorry, I was busy doing smth else, stilll wiorking on it

[vague temple]

Does anyone know where I can find combinatorics problems/handouts for AMC 12/AIME

[tame burrow]

I mean, just AoPS has like an absurd amount of problems, and youcould just search up like combo problems

[barren sparrow]

Can someone explain why the red part is wrong

I know it causes arrangements of object as well but how

[sturdy viper]

Sohil Rathi predicted a 105 aime qual

😭

[jade widget]

For which

I’m not B taker

[vestal yacht]

probably meant b

i think a will be like 99

[soft vigil]

tf

[ornate coyote]

OH i just realized

i think te order of amc10 in china is different than in usa

[ivory ember]

I think it was scrambled in the us too - I took the 12 and my question 11 was question 13, question 22 was question 20, etc.

my answers were scrambled too

I think they're just scrambling it for everyone to try to fight cheating ngl

[acoustic nova]

does anyone have any recommendations for AoPS-style books that go beyond the AoPS curriculum?

[ornate coyote]

yeah i saw some guy selling answer keys before amc10b in this server

to fight the people who just memorize the answers

[iron terrace]

does anyone here have any advice for the amc8

[tame burrow]

Don't stress (too much)

[ornate coyote]

practice to fast

[vague temple]

Only online I think, my physical copy for 12B has the exact same order as AoPS

[ivory ember]

Well tbf the physical copy is the “unscrambled/reference” version

Everything else is compared to that

Because the physical paper copy is what they release

[ornate coyote]

i think its scrambled in china

because they take it earlier

and some people end up cheating

[haughty umbra]

How do u apply for math competitions in middle school? I’m trying to get into some competitions because it sounds like it would really make my application to high schools sound good and I wanna be ahead the competition

I’m in the USA btw and im studying algebra 1

[tame burrow]

You don't need math comps to apply for high school; you don't apply for public high schools

[latent bough]

maybe try local hs

[tame burrow]

Uh

[latent bough]

some places do

[tame burrow]

Well, if your school supports it, you could try MATHCOUNTS or the AMC series

Normally, they'll tell you if they have it

[swift imp]

check local university of email high schools near you

[tame burrow]

Some middle schools also give hs competitions

[swift imp]

these are like goated ms tho

[tame burrow]

Like mine?

[swift imp]

like top ms only really do that

[tame burrow]

fair enough

does lexington ma count?

[swift imp]

hell yea

smart ah place

[tame burrow]

I go there

wait

why'd I just say that

[haughty umbra]

Mine has absolutely no competitions am I cooked💔

[tame burrow]

Just email ur high school you'll be fine

[swift imp]

lexington ma got 5 usamo awardees last year so

i think

thats pretty good

[haughty umbra]

Wym email ur highschool

like any highschool

[tame burrow]

I see those kids on a regular basis 😭

[haughty umbra]

Or the one ur going to

[swift imp]

any hs works but like start with the one that ur zoned to

[tame burrow]

email the school district highschool(s)

[haughty umbra]

oh

[swift imp]

some other districts hs might let u

but

urs is most likely to

[tame burrow]

probly not

[haughty umbra]

brooo im so cooked for my highschool applications

[tame burrow]

What high school are you applying to?

[haughty umbra]

my only thing going for me is me being in the gnt and having good grades

[tame burrow]

whats gnt?

[haughty umbra]

Coltsneck highschool in New Jersey

[swift imp]

bros trying to get into exeter 💀

[haughty umbra]

Gifted nd talented

[swift imp]

or somethign

[haughty umbra]

What’s that

[swift imp]

those who know

[haughty umbra]

phonk plays

[swift imp]

@tame burrow usmao awardees on a map

[tame burrow]

Nah... Exeter's overrated

[tame burrow]

💀 I can't do math so I get grilled on a regular basis; al I can do is physics

[haughty umbra]

But seriously I’m stressing bc I’m in no clubs, my only thing going for me is straight A’s and taking advanced classes (gifted n talented)

am I cooked?

No competitions either

😞

[tame burrow]

Nah

[haughty umbra]

[tame burrow]

It's literally a public school

I don't think u have to apply

[haughty umbra]

maybe

it’s not the only school I’m applying to

[tame burrow]

if they're all public, why'd u have to apply?

[haughty umbra]

I’m applying for like 3

[tame burrow]

You don't usually apply for a public high school

[haughty umbra]

rlly

I swear all my classmates told me u had to

nvm

u do have to apply here

[tame burrow]

Oh then that's different

[haughty umbra]

mhm

but u can’t just say “hi, I wanna join” in a top school

I’m also trying to apply for high technology high school which is top 10 highschool

[tame burrow]

Oh is it?

[haughty umbra]

mhm

[tame burrow]

Then that's a totally different monster

[haughty umbra]

coltsneck is like my happy school

like if I don’t make it huge then I can settle at coltsneck and Il be happy wit what I did

[tame burrow]

When you make Andover but can't pay the tuition

[haughty umbra]

my parents make 200k+

I’m fine

I also got 2 dollars in the bank so I can pay for it 🤑

[tame burrow]

👍

[haughty umbra]

[latent bough]

💀

[haughty umbra]

I’m delusional

[tame burrow]

rich ass kid

[haughty umbra]

Yeah

I’m not tryna flex

[tame burrow]

I'm literally in debt

to my parents

💀

[haughty umbra]

🥱

quick flex

took this yesterday

[tame burrow]

Yes bero

☠️

[latent bough]

💀

[latent bough]

💀 not the ☠️ emoji

[tame burrow]

heheheha

[ornate coyote]

1434

[jade widget]

ok

[ornate coyote]

WHAT'S andover

[novel karma]

where did you find this?

[swift imp]

Made it

[soft vigil]

yo

my aops post count is 1434

[vague temple]

I thought you were about to pull a Ramanujan

[soft vigil]

pull a what

[vague temple]

https://en.m.wikipedia.org/wiki/1729_(number)

[soft vigil]

oh lol

[sturdy viper]

Bro i got a 99 on 10b

im actually so sad

😭

I expected 102

[iron terrace]

bro

a 99 is good wdym

i'll take a 99 any day of the week

[sturdy viper]

Bro

I woke up at 5 am

I knew I could have done better

which is the most painful part

if I capped out at 99 I would be fine

[iron terrace]

What is the maximum score?

[sturdy viper]

But the fact that I could have done better is sad

[sturdy viper]

150

[iron terrace]

oh

i thought it was 99/100

it's not that bad at the end of the day

[sturdy viper]

Have u taken amc10 before

[ornate coyote]

how do you expect 102 if you already know how many questions you didnt answer

[soft vigil]

tf

there is no difference

[sturdy viper]

i thuoght i guessed them

[sturdy viper]

there is

102 has a higher chance

[soft vigil]

i think that 0-0=0

[ornate coyote]

hm'

[sturdy viper]

Are u JMO

that probably explains why u think 102 is bad

😂

[soft vigil]

yes

[soft vigil]

no

[sturdy viper]

Well well well

[soft vigil]

but im saying

[sturdy viper]

Another jmo

[soft vigil]

3 point difference isnt much

[sturdy viper]

there are too many

[sturdy viper]

Oh

[soft vigil]

i got 12 point difference on 10a

[sturdy viper]

Nah look

[soft vigil]

some people got like 30 point

[sturdy viper]

if u got a 103.5 last year on the 10b

THEN a 3 point difference would have

donnnnnnnneeeeea lot

[soft vigil]

ye

ok

[sturdy viper]

I pray cutoff 99

what u think

50/50 chance?

[soft vigil]

I have no clue

[hearty tendon]

i dropped a 24 diff once

lol

[jade widget]

What does the colour of pointer mean

[round jackal]

how do you do sigma notation

[jade widget]

Idk

[ornate blade]

do you have a specific question

https://www.youtube.com/watch?v=XJkIaw2e1Pw

or are you happy with watching this org chem tutor video?

[round jackal]

i learned it on tiktok but thx

[ornate blade]

RIP TikTok, but appreciate the thanks

[round jackal]

ye

[shadow spruce]

mathematicas puras

[ornate blade]

do a and b have to be integers?

or can they be real numbers

either way note that you must have $a^2 + b^2 = 13^2$ which is a circle

[gilded halo]

south, just south

[ornate blade]

ah it doesn't matter what a, b are then

[pulsar terrace]

real

the answer is ||26||

[ornate blade]

cool

[pulsar terrace]

but how so

[ornate blade]

hopefully you see how this happened
||sub in a = x and b = y||

[pulsar terrace]

oh accha

[ornate blade]

||cause (x, y) = (a, b)||

[pulsar terrace]

you just pick two points on opposite side of circle

alright

[ornate blade]

exactly

once you come up with the equation yes the maximum distance has to be the diameter

[radiant jasper]

Yeah

26 is right

[vague temple]

For chicken McNugget problems of 3 and more container sizes does applying pairwise always work?

This person did it and it worked (luckuso in solution #4, on 2023 AMC 12B #16)
Say 6, 10, 15. So 6a + 10b + 15c.
First apply to 6 and 10, reduce to 3 and 5, so you can represent all combinations beyond (3-1)(5-1) + t for nonnegative integer t = 8 + t.
Then substitute into the original expression:
2(8 + t) + 15 c = 16 + 2t + 15c
Apply pairwise to 2t + 15c: you can form any (2-1)(15-1) + u = 14 + u
So you can form 16 + 14 + u hence 30 and above hence 29 is max

Or are there additional restrictions in some cases

[ornate coyote]

cihcken

chimken

[acoustic nova]

dont memorize those though

[jade widget]

chicken

[ornate coyote]

math. is hard

[pallid tundra]

chicken chicken chicken

[ornate blade]

Exactly

I like the video cause it tells you that working with summations is literally just working with addition

Good examples

[radiant jasper]

wtf

there was a chicken nugget problem in amc 12?

[ornate blade]

The best strategy is to not assume
Check that 30, 31, 32, 33, 34, 35 are all possible
Then check 29 is impossible

[vague temple]

Bro I can’t escape combinatorics, I went to watch a chess video and got hit with “how many possible configurations exist that allow a doubly disambiguated bishop move (i.e. 2 bishops lie within the same row and 2 bishops like within the same column and all of them can move to the same square, so they form an isosceles right triangle like in the picture)

Reasoning: consider the symmetries. First, light vs dark so x2. Now we see each square generates 4 choose 3 = 4 rotations of isosceles right triangles. Each square can only work if we have the same parity of rows/columns. Then, odd/even squares so x2. Looking at odd/even only tiles, of which we choose 2 hence 4 choose 2 squares. Hence
2*2*4*(4 choose 2)=96

[sturdy viper]

https://artofproblemsolving.com/community/c5h3446808_aime_qual_10b

[vague temple]

Knights and queens

Actually if I am not mistake, knights is like
2*4*6*4 = 192

[ornate coyote]

i dont think you should take making aime too seriously if you are hovering around the cutoff

you shouhld just focus on improving your own skills

[sturdy viper]

Idgaf about aime

I mean doing well

I jsut wanna qual

And i have lots of time to improve anyway

Its j ust cause i woke up early so i did badly

[ornate coyote]

yes but getting past a cutoff that doesnt really matter isnt something to stress about

you cant really do anything to make the situation better

just focus on improving yourself

not comparing yourself to others

[marble grove]

@swift imp @radiant jasper @ornate coyote thx for the tips

bro math comp is easy

as long as you are smart and not like a neighborhood kid its easy to make comps

like just study around 3 hours a day for around 2 years

easiest 150 of your life

bro who put that

im not joking bruh

alr south

think about it

how many topics does a normal ap calc bc class cover?

around 10 or so?

you already have basics in algebra, geo, and number theory

if you take 1 hour a day with each

you can basically cover everything

[radiant jasper]

What tips did i give you??

[marble grove]

with time to spare for practice

[ornate blade]

You're proving yourself that it's hard

[radiant jasper]

I dont remember lol

[marble grove]

uhm practice tests or sum

[marble grove]

bro

[radiant jasper]

U got 150?

[marble grove]

3 hours is nothing

no

[radiant jasper]

I’d say it’s practically impossible to get a 150 no matter how hard you practice

[ornate blade]

Exactly

And the average student is trying to get along with regular maths

[marble grove]

my friend did question 21 or sum from lat year in like 1 minute

and he studys only like 1 hour a week

[ornate blade]

Let alone have that much energy to spare for contest maths

[marble grove]

bro im not gonna lie

[ornate blade]

There is a really wide ability range for maths yes

[marble grove]

if you know how to do contest math

actual math tests r gonna be easy

plus

people actually studying for 150 probably dont struggle in their math class

ok gn gang

ill gangalank you later

[radiant jasper]

Yeah it depends on what it is

I solved many aime questions under 2 minutes

[ornate coyote]

No matter what there is always a 95 percent chance you will silly a problem or lose on time

Perfect scores are nearly impossiblr on difficult amcs

This and last year were exceptions

[pallid dragon]

i don't think there's a clever trick

c)
the difference from 1 2 3... is 11 19 10 5 14 11 8 10 13 9 6 7 2 6 9 1 18 7 6 9

sort it 1 2 5 6 6 6 7 7 8 9 9 9 10 10 11 11 13 14 18 19

we can save 20 operations by targeting 2 3 4

the smallest diff is 1 again but now it saves 18 operations to increase the target by 1

then the smallest diff is 3, and it saves 3×16 operations

etc.

it looks clever once i wrote it lol

oh i misunderstood the problem

i thought an operation adds 1 stone, it adds a whole bunch

pretty neat actually

[echo hare]

nah, study for 8 hours a day. dont sleep. you gotta put the hours in.

[jade widget]

[hazy island]

Wdym by targeting 2 3 4

?

[hazy island]

Yeah looks like a good method

[shadow spruce]

Anyone knows Mathematics SFTP server?

[ornate blade]

what's SFTP?

[ornate coyote]

If you dont study

8 hours a day the grjnch will eat you

[gleaming warren]

what are theorems, lemmas, etc needed for imo geom

geom is annoying

[vague temple]

Ok so first thing is to convert the problem into a well-known and solved one of minimizing the MAD in a uniform distribution. So compute a new adjusted array A[i] = H[i] - (i - 1) (subtract 0-index). Now we end up with a new array A, for a it would be [2, 3, 4].

Our goal is to minimize the MAD between A and a target uniform distribution U of all values u, and this is done in the unconstrained case by setting u to the median of A. However, we have the additional constraint H[1] >= 1 meaning A[1] = H[1] - 0 >= 1.

But this implies that we cannot blindly pick the median in A to serve as the baseline but rather we require that u >= 1 as well. Hence, u must be chosen to be as either the median or if this median is nonpositive, then u must be as close as possible to the median, hence 1.

Example solution for (a):
H = [2,4,6]
A = [2,3,4] (already sorted)
u = 3
U = [3,3,3]
T = [3,4,5]
Calculating the MAD between the target distribution T and the original distribution H (equivalently, between A and U), we get |2-3|+|3-3|+|4-3| = 2.

(b):

A = [1, 1, 1, -2, -3, 0, -5, -4, -3, -6, 1, 0]
Sort A: [-6, -5, -4, -3, -3, -2, 0, 0, 1, 1, 1, 1]
In this case, we see the median of -1 is < 1, hence doesn’t work. We choose:
u = 1

Using Python brute force search, the answers are found as:
(a) 2
(b) 31
(c) 67
Hopefully this should match the manual way.

[distant pendant]

Anyone else doing BMO1 tomorrow?

What theorems should I know for it?

[hollow loom]

this is a quantative aptitude question please help me with the solution and explain

[vague temple]

500

Distance is constant

Use d = vt

The numbers are somewhat unrealistic, I don't think anyone walks that slow compared to an escalator

[vague temple]

Let
d be length of escalator (distance travelled, constant)
p be speed of person
e be speed of escalator
t be time to cover escalator in normal circumstances (walking and escalator)
We have the equations
Normal:
d = (p+e)t
Also, he walks 50 steps in normal circumstances.
pt = 50
Failure walk for 10s, then remaining is with escalator:
d = 10p + (t+9-10)(p+e) = 10p - (p+e) + t(p+e) = 9p - e + d
Hence
9p - e = 0 so e = 9p (unrealistic part but OK)
Thus, substitute back in:
d = (p+e)t = (p+9p)t = 10pt = 10(50) = 500 steps

[hollow loom]

Thank you sir

brother i had doubt in question number 6 is that question correct or not i am not aware but our sir told that option (a) is the correct answer

[radiant jasper]

,rccw

[safe nacelle]

he is right
the correct answer of question 6 is a

[vague temple]

If you look at the graph on Desmos, you will see it works for a <= -d

[fallen magnet]

wait can u do it in school?

idk since it's like 3.5hrs

[vague temple]

Guys is it possible to do this without PIE, like recursion or something

Six people of different heights are getting in line to buy donuts. Compute the number of ways they can arrange themselves in line such that no three consecutive people are in increasing order of height, from front to back. (2015 ARML I10)

[latent bough]

i noticed that the only way to have no people increasing is obviously decreasing order, so
6 5 4 3 2 1
and swapping any two consecutive creates a single pair with increasing order
6 5 4 3 1 2
while swapping two that are one apart creates an set of three, so cant do that
6 5 4 3 2 1 -> 4 5 6 3 2 1
and swapping one of the back ones for any one that is two or more apart creates two pairs
1 5 4 3 2 6
6 5 4 3 2 1 -> 3 5 4 6 2 1
6 5 4 3 2 1 -> 6 2 4 3 5 1
so maybe you can do something with these operations?

[ornate coyote]

hello doers of math

[latent bough]

actually yk what nvm i think itd be infeasiable

hello

math does me

[vague temple]

I think that misses cases

You'd need even more casework

[latent bough]

yeah

thats why i said it was infeasible completely

i think recursion then

[vague temple]

I'm not even sure recursion works

I think the case n=6 adds complexity

Because you can have 2 consecutive triplets that are increasing

Or it could work but very complicated

How do I avoid getting beaten by combinatorics

It keeps happening, especially in competitions

[swift imp]

To skip it

🤓

Idk how to get at comb too

Twin

[tame burrow]

Finger count: works every time, just gotta have patience. Trust. 👍

[shadow spruce]

Find some books

[shadow spruce]

It's like a google drive, or some cloud drive that hosts all the pdf files in one place

[inner wolf]

What's this channel for?

[latent bough]

competition math

like amc

[ornate coyote]

math is impossible

unless

[inner wolf]

Idk what that is

[latent bough]

American Math Competition

[ornate coyote]

[jade widget]

[hazy island]

Thanks man, great explanation, couldn't have found a better one on the internet(if i used a web browser or stuff)

[distant pendant]

I can

[hollow loom]

Can you give me solution

[hollow loom]

If you do trial and error method with options both option (a) and option (C) are getting same graph

[high goblet]

gl!

[high goblet]

yh i mean most ppl do it in school

[safe nacelle]

Are you there?

[mild epoch]

Anybody help?

[fiery fog]

Pls follow my account.
I'm a new content creator, I really need your support.
Thank you.
https://www.instagram.com/sallys.universe?igsh=bXp2ZXhqOHR0cGV1&utm_source=qr

[hollow loom]

Hi I am here now

[safe nacelle]

Do you use Desmos

[crystal bison]

I didn't find the answer in the option..... because I got -4038090 as answer.

Can anyone help

[vague temple]

Double-check your number of terms

(4019-3)/4 + 1 = 1005 terms

-1005*4022/2

[distant pendant]

Thx

[sleek ivy]

brotha do you not do anything other than math all day

[hollow loom]

What's that

[fallen magnet]

online graphing calculator

[radiant jasper]

Who uses aops here?

[shadow spruce]

Matematicas puras

[plain jacinth]

The answer is -(2010)(2011)/2

[safe nacelle]

hey please dm me when you are free
then I will tell you clearly

[crystal bison]

How?

[soft vigil]

note that n^2-(n+1)^2=-n-(n+1)

[plain jacinth]

1^2-2^2+3^2-4^2…2009^2-2010^2
(1-2)(1+2)+(3-4)(3+4)…(2009-2010)(2009+2010)=-

-1-2-3-4…-2009-2010=-2010(2011)/2

Lmk if you need a better explanation

[crystal bison]

I can't understand that,how 3rd line came from the 2nd line?

[vague temple]

1-2 = -1, 2-3 = -1, … so on. So we have a factor of -1 we can pull out. The remaining terms is just (1+2)+(3+4)+…

[vague temple]

In 2020 AMC 10A Problems/Problem 25, how did this person determine that the condition 2(a+b+c)>=21 has optimal probability by re-rolling 2 dice?
Jason rolls three fair standard six-sided dice. Then he looks at the rolls and chooses a subset of the dice (possibly empty, possibly all three dice) to reroll. After rerolling, he wins if and only if the sum of the numbers face up on the three dice is exactly 7. Jason always plays to optimize his chances of winning. What is the probability that he chooses to reroll exactly two of the dice?

https://youtu.be/B8pt8jF04ZM

[plain jacinth]

(1-2)(1+2)+(3-4)(3+4)…(2009-2010)(2009+2010)->
(-1)(1+2)+(-1)(3+4)…(-1)(2009+2010)->
1-2-3-4…-2009-2010->
-2010(2011)/2

does that makes sense?

[crystal bison]

Ya... thanks

[past sable]

hello everyone i am class 9th student in india i had recently give an olympiad and was not able to find the answer to the question please help me
Q if 3a=4b=4c and a+b+c=24sqr(29) then the value of sqrt(a^2+b^2+c^2)
a)3sqrt(29) b)81 c)87 d) 2sqrt(29)

[ivory ember]

Hint: Let $3a=4b=4c=k$ and solve for $a,b,c$ in terms of $k$

[gilded halo]

Civil Service Pigeon

[past sable]

i did do it like that but i couldnt get anywherre

[ivory ember]

!show

[scarlet root]

Show your work, and if possible, explain where you are stuck.

[ivory ember]

you should do this from the start of asking a question btw

so what did you get so far

[past sable]

a;b;c =4/3:1:1

let a=4k/3,b=k & c=k where k is proptional constant

4k/3+k+k=24sqrt(29)

10k/3+24sqrt(29)

10k=72sqrt(29)

k=72sqrt(29)/10

[ivory ember]

wait a fucking minute

,w 3a=4b=4c, a+b+c=24 sqrt 29

[gilded halo]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[ivory ember]

,w sqrt(a^2+b^2+c^2), a = 48/5 sqrt 29, b = 36/5 sqrt 29, c = 36/5 sqrt 29

[gilded halo]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[ivory ember]

the question legit doesn't have a correct answer

[past sable]

oh

damn

bruh

i thought this shit was going to

[ivory ember]

yeah the 4, 3, 3 was screaming wtf to me

because 4^2 + 3^2 + 3^2 isn't a perfect square

[past sable]

yeah

tysm

[ivory ember]

[vernal axle]

P(a+P(a)) is divisible by P(a) for all a>=1. So, you can take n=a+P(a) which is infinite when a=1,2,....

[glad zinc]

Got cooked in bmo1 😔

I average 35-45 on past papers but I genuinely did so bad in this one

It’s so joever

[deft wraith]

no (public) discussion yet unfortunately

[latent bough]

💀

[glad zinc]

Do you see me mentioning any of the questions?

[deft wraith]

i don't think you're allowed to say like how you found it either

[glad zinc]

no comment

[radiant jasper]

that falls under embargo

[ornate coyote]

math

math

math

where should i go for math questions arounud the late aime level to early usajmo

besides aime and usajmo

[glad zinc]

?

[tame burrow]

ARML

[reef condor]

Hmmt pumac

Pumac is a good source ngl

Especially division b is a great source for that difficulty

Also all the problems are unoriginal which is good because that’s like aime

[ivory ember]

(pumac does have some errors floating around tho)

[radiant jasper]

what you said is part of what is forbidden by the embargo

[reef condor]

Also ngl late aime is harder than early usajmo

Like p13-15 >> usajmo p1,4

[ornate coyote]

i suck at writing proofs so i still think early usajmo is harder than most of the aime

[tame burrow]

I'm so proud of myself

I guessed an AIME problem right

[ornate coyote]

statistically you should get a perfect score if you guess on every problem

[radiant jasper]

what are you saying

[ornate coyote]

gamble

[radiant jasper]

"should"

pumac is dog contest

[jade widget]

[misty belfry]

Yo anybody online?

I quizletted my way through university lol

https://tenor.com/view/tryan-trying-blocks-block-head-tryan-blocks-gif-13157134546106029566

[swift imp]

Yuh

Hi

[jade widget]

Hi

[swift imp]

Hi nerd

[misty belfry]

That was quick ._.

this is from my notes, but I had trouble making it readable from the camera, so i typed it down on symbolab so you can get a quick observation

personally i had trouble on the equal part, so can somebody help me?

[jade widget]

!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.

[jade widget]

I guess

[ornate blade]

is the c a typo, btw?

[misty belfry]

no

x^c

[swift imp]

What competition is this from

[misty belfry]

Penn State University

A great college.

Chapter XIV in my textbook

your techincally paying to sit in a chair with a desk and be bored for many hours

[jade widget]

no clue

[jade widget]

Wait, what is the question

[ornate blade]

wait what's the question then

are you solving for c then

cause this is not true in general

[misty belfry]

im solving for x ._.

what could make this true

[ornate blade]

ohhhhh

,w d/dx (sqrt(x) + pi^(-3/2))/(x^c + 2n) = 3n + 2 sqrt(x) sqrt(pi^(-4))

[gilded halo]

Results provided by WolframAlpha

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

Requested by sooouth.

[misty belfry]

ok thanks 🙂

[ornate blade]

I think you're trolling us

[misty belfry]

https://tenor.com/view/old-man-gif-13213101487078607344

wait a minute.

how?

I typed it into symbolab so it would be readable so instead i wouldent have to picture it directly on my textbook

[ornate blade]

it's just impossible to do algebraically

unless you have a solution that states otherwise

[misty belfry]

i know.

I struggled with this one

[ornate blade]

I'd say not to waste your time on this question

[misty belfry]

im just trying to make my professor proud

[ornate blade]

it doesn't even look like a contest maths problem

[ornate blade]

there is zero reason why you need to do that

if you really want to get into research and work with your supervisor very closely

then once you have a PhD you and your prof can seriously talk

and who knows maybe collaborate on something

[misty belfry]

yeah your right.

thanks for the answer though.

[ornate blade]

like you go into higher education for your own learning and benefit

if you get a bad grade the only person who could be disappointed is yourself

or your family if they are that involved in your life

[ornate blade]

npnp then

[jade widget]

[ornate coyote]

10 second aime problem

number 10 kinda wild

[jade widget]

I don’t understand

[shadow spruce]

I don’t understand

[ornate coyote]

play geometry dash to learn geometry

[radiant jasper]

can someone tell me what the question is even talking about im so confused with what it's stating T.T

[ornate blade]

do you understand the examples?

{1, 2, 3, 6, 9} and {5}?

[radiant jasper]

no

it says alternatively add and subtract

so shouldn't it be 9 + 6 -3 ...?

[ornate blade]

I think the question assumes you subtract first, yeah

[radiant jasper]

ah

[radiant jasper]

wait I'm so confused with how to approach to the question

if n is 7 what would the set even look like?

[ornate blade]

it could be {1, 2}

it could be {2, 4, 5}

it could be {1, 3, 6, 7}

basically the highest number must be 7 or fewer

and you can only choose numbers from 1, 2, 3, 4, 5, 6, 7

[radiant jasper]

oh

where did you get that information from?

like how did u find that out

[ornate blade]

it says in the question

n = 7 so you choose from 1, 2, 3, 4, 5, 6, 7

the important part is

each of its non-empty subsets

[radiant jasper]

which part?

[radiant jasper]

oh

i learned math in korean so im unfamiliar with english terms 😦

[radiant jasper]

do you understand the solution?

[ornate blade]

yeah, basically it's the same idea as the solution on the AoPS page

[radiant jasper]

how is the total sum 12 when n is 3...?

[ornate blade]

https://artofproblemsolving.com/wiki/index.php/1983_AIME_Problems/Problem_13

[radiant jasper]

oh it's problem 13

damn no wonder it was so confusing

[ornate blade]

if you choose a subset $S \in {1, 2, 3}$, say $S = {1, 2}$

take $S \cup {3}$, so ${1, 2, 3}$

when you add the alternating sums together, you get $(2 - 1) + (3 - 2 + 1) = 3$

[ornate blade]

I feel AIME was easier back then

anyways that's not relevant

[radiant jasper]

oh

[gilded halo]

southlander!

[ornate blade]

basically because you have added on a positive term, 3, to the start of the alternating sum

the signs shift one place

so instead of 2 you get -2
instead of -1 you get +1

convince yourself this will be true for any list

[radiant jasper]

i get it now

[ornate blade]

this is the key idea

[radiant jasper]

are set questions commonly found in amc 12 nowadays?

[ornate blade]

also like to justify it, either your set contains 7, or it doesn't contain 7

[radiant jasper]

i feel like im week with set and combination questions

[radiant jasper]

right

[ornate blade]

so the number of sets in the original problem would be (number of subsets of {1, 2, 3, 4, 5, 6}) * 2
= 2^6 * 2 = 2^7

[radiant jasper]

oh

ohhhhhhhhhhhh

[ornate blade]

but then there are 2^7 sets
we want pairs of sets, so divide 2^7 by 2 to get 2^6

like each set A will have a counterpart A'

that's why it's 64 * 7

[radiant jasper]

ah

[ornate blade]

7 being the sum of each pair

[radiant jasper]

makes so much sense now

i was so confused with what the question was even talking about 😦

[ornate blade]

yeah it must be hard when English is not your first language, right

[radiant jasper]

are set questions important in amc 12?

[ornate blade]

I don't see them a lot in the AMCs

[radiant jasper]

i didn't see many in amc 10 but next year im taking 12 so

[ornate blade]

these sorts of counting problems seem more like AIME or higher

[radiant jasper]

oh

[ornate blade]

possible but I think other types are more common

like some kind of geometry

probability

[radiant jasper]

yeah

im confident with geometry

[ornate coyote]

Sometimes there are set problems

[ornate blade]

or like yeah something algebraic is very possible for AMC12

[radiant jasper]

really?

[ornate coyote]

I think so

But very little

[radiant jasper]

but there are like one or two questions right

[radiant jasper]

ah

ok shouldn't stress too much about it for now

[ornate blade]

yeah like try to qualify at least

easier said than done haha, I feel every year the problems get harder and harder for the same level

competitive maths didn't attract so many students 10 years ago

really it's to do with US uni admissions (and possibly other countries) being more and more selective each year I bet

[ornate coyote]

Im getting like 12 or even 13 on 2010 aime practice

But like 8

In recent years

[ornate blade]

yeah Evan Chen said something like this in his blog

[ornate coyote]

But like 10 years ago a lot of the late problems were surprisingly easy

[ornate blade]

yeah and this problem was from 1983

[ornate coyote]

Like one you just calculate a bunch of quadratic formula stuff i think 2011 aime ii problem 15

[ornate blade]

I suspect more and more people are going to move away from competitive maths

if it's just not worth the effort to get recognised

people have other interests

[ornate blade]

that's basically what happened to me

[radiant jasper]

so many chinese students cheat on their exam

no offense to them or anything

[ornate blade]

I switched from my maths degree to sociology and boy, are first-year humanities such a breeze

[radiant jasper]

but someone i know got 138 on amc by cheating

[ornate coyote]

I know someone who got 90 on 10a but 150 on 10b

[ornate blade]

can't say anything for later years but yeah it just feels easier to try when there's not so much pressure on your shoulders

[ornate blade]

oh yeah it is a big problem

don't forget India also

[radiant jasper]

they cheat as well?

from what i heard private chinese organization give the test papers to their students before the test day

[ornate blade]

China seems to be the most blatant though

[ornate coyote]

Leaks are mostly on chinese socialmedia

So yea

[radiant jasper]

that's crazzy

why does mma operate their system like this

[ornate blade]

they definitely cheat but it seems they don't for international competitions

mainly like the civil service exams for India

[radiant jasper]

oh those stuff

[ornate coyote]

More motivation to study harder ig

[radiant jasper]

yessir

[ornate blade]

yes to some extent

but there's always a breaking point

it's like Hooke's law where you can only stretch a rubber band so much before it snaps

[ornate coyote]

With cheaters the bar is raised but i think if you study really hard you can still make jmo

Its not like they are cheating on the jmo so like after you hit that bar of qualifying then the cheaters dont really matter that much

[radiant jasper]

do you think competitive math is all about studying?

because i think until aime it is, but after that, i think you need to have like inborn mathematical brain

@ornate blade how do you find the question directly from aops website?

do you use the image search function? or

[high goblet]

ok now that i've done drunk BMO1

i think i agree, this year's BMO1 was quite a lot harder than previous years

granted i was completely wasted by the time i got to Q4 and then didn't do any of Q4 or Q5 or Q6

(i read the question but like none of it was processing in my brain :(

but yeah Q1 i thought was significantly harder than the previous few years

i think we were expecting it to be an absolute piece of cake, but it stumped some of us for a bit longer than it should've

Q2 i thought was fine

Q3 i solved quite quickly, but i know some of my friends actually found it surprisingly hard

and then i didn't do Q4+ but i know my friends thought Q5 was quite hard asw

and Q6 was really hard

well ok i say i was too drunk to do any more maths problems but like my more sober friends were stuck on Q6 for quite a while until someone very drunk solves it perfectly 💀

when i have time today, i'll try to solve Q4 and Q5

except i'm currently hungover and i've still got tons of work to do

[ornate blade]

Searched the problem text up

[round jackal]

i have a random question could you fit infinite bricks into a 1 by 1 foot box if they got smaller infinitely or is there a limit

[deft wraith]

yeah i think p1 and p3 should be swapped

[ornate blade]

absolutely! something like this is very possible

the infinite sum $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots = 1$

[gilded halo]

southlander!

[ornate blade]

the picture I sent also suggests $\frac{3}{4} + \frac{3}{16} + \frac{3}{64} + \cdots = 1$ as well

[gilded halo]

southlander!

[glad zinc]

I'll share my experiences with it, Q2 was definitely the easiest problem, think it shouldve gone 2,3,1,4,5,6. Got pretty much full answers for 1,2. I had like a billion other things in my mind so i just tried some stuff out for 3, got real close then said fuck this. Tried some random bs for 4,5,6 then just called it a day. Ended up only submitting 1 and 2, it is what it is.

Im really disappointed but life moves on

Im considering doing paid entry for BMO2 and actually studying, I started off pretty well with BMO1 prep but other priorities pushed it to the side

[glad zinc]

What about if each brick had to be smaller then the prior, you have 3 equally sized bricks every time you decrease the size

[latent bough]

wait is there an actual circle given?

oh nvm actually

[high goblet]

ok i've done q5 now, i thought q5 was kinda easy/standard but i've also done a lot of olympiads and i am no longer drunk

drunk me could not do q5 lol

[ornate blade]

England has about the world's worst drinking culture istg

aside from I guess eastern Europe

[high goblet]

ahaha lol

[ornate blade]

Brits drunk on holiday

is enough of a horror story

sorry my mind just jumped to that

[high goblet]

lol no that's fair

[high goblet]

ok done 4 asw

[ornate blade]

wild guess but for question 1 are only n = 3, 4, 6, 12 possible

[high goblet]

nah

[ornate blade]

ah fuck

[high goblet]

actually it's kinda funny

we got trolled a little by the 12

[ornate blade]

3 and all the evens

[high goblet]

the 12 literally has 0 impact on the problem

[ornate blade]

I have the video solution

[high goblet]

yep

[ornate blade]

how would you prove it?

[high goblet]

show it's not possible for n=odd, n>3

[ornate blade]

like the UKMT video solution just used p, pq, q

[high goblet]

then do a construction for n=even

[ornate blade]

oh like a contradiction I see

[high goblet]

you can read my really really shitty write-up that i wrote yesterday lol

[ornate blade]

the video solutions don't tell you how to write it up formally

[high goblet]

like just to clarify, this is an atrociously shitty write up

we were doing it for fun & were drinking so the write ups were never gonna be any good

[ornate blade]

BMO style is not like AIME at all

interesitng

[high goblet]

i am expecting BMO2 grade boundaries to be lower than normal, but you can still pay to do bmo2

ngl i really regret not paying to do bmo2 when i was in y10

[ornate blade]

okay I've decided to think about q3 a bit

[high goblet]

i was quite close to qualifying in y10, and i think if i paid to do it in y10, i would've revised a lot more and would've been a lot better when i did it in y11

[ornate blade]

I've figured out that if the current number is n = k^2 where k is any integer

the player could just choose a = b = k so that |a - b| = 0

so they will have won the game

[high goblet]

has to be different numbers

[ornate blade]

oh shit

knew it

I think working backwards might help still

so if n = 1 that player loses

so if n = 2 that player wins

[high goblet]

spoilers for Q3: ||i think drunk me took a little too long to realise it went R J R J R J R J lol||

[ornate blade]

and for n = p^2 where p is prime the next number has to be p^2 - 1 cause of what you said

oh wait

wow I just clicked the image

[ornate blade]

ah cause this must be even if p is an odd prime

so like (p + 1) - (p - 1) = 2 idk

yeah I think I'm overthinking it

just considering what happens when n = 2, then n = 3 and so on

suffices

[high goblet]

tbh when i did it yesterday

i worked all the way up until 20

you start to see a pattern with how to deal with odd/even cases

&then that solves the problem

[high goblet]

i mean a hint for the problem would be that in general, factorising numbers is a hard problem

[ornate blade]

ahhhhhhhhh

yeah I was like how the fuck

[high goblet]

(they gave u 10^6)

[ornate blade]

I feel these are just dirty tricks

[high goblet]

so it'll be something clever, that you can do no matter what number it is

[ornate blade]

I'm still unconvinced

like on how for any even number, you are guaranteed to lose no matter what

I understand that for an odd number you can subtract 1 to get an even number, which is supposed to be a losing position

for n = 8 for example, can't you do a = 4 and b = 2
so you'd go down to n = 2

oh but then the second player would go to n = 1 and then the first player would be out of moves

ahhhhh so the first player chooses to go down from n = 8 to n = 7 to avoid this

[high goblet]

yep

[ornate blade]

instead of n = 6 to n = 1

[ornate blade]

shouldn't that case be different then

as in if Rhian goes down from n = 6 to n = 1

Jack must be out of moves

ah I see so Rhian wins either way

so Rhian goes down from n = 6 to n = 4 to n = 2 on his turn

ah by making a table I see it

if you put R on the left column and J on the right column

both ways 1 ends up in the right column

so R wins either way if he goes first

so basically this relies on a parity argument of some kind

[ornate blade]

okay it makes a lot of sense

it just seems too simple to be true

like it doesn't make sense how the backward argument, considering how n reduces to n - 1 which we already have figured out

works at first sight