competition-math

[snow elm]

Ok

[ornate blade]

like you can consider their projections onto face GFEH

[snow elm]

Okay

The question is how we find the intercepted volume using similarities

[ornate blade]

that's the easy part tbh

[snow elm]

Okay

How

[ornate blade]

you have the volume above the plane z = 1.5 and the volume below the plane z = 1.5

[snow elm]

Don’t use graphs stuffs

[ornate blade]

then just use similarity on ABCDG and EFGHP

[ornate blade]

bruh

I'm not graphing in 3D

[snow elm]

I don’t know those 3d graphics lol

[ornate blade]

it's sufficient to graph in 2D by symmetry

[snow elm]

Where is z

Okay

I see what u mean

Those 2 small pyramid is similar to the whole pyramid?

[ornate blade]

yes

because the shape is a square in the middle of the cube

[snow elm]

The ratio is just 1:2?

Cuz 1.5:3=1:2?

[ornate blade]

well that's the length ratio not the volume ratio

[snow elm]

The volume ratio is 1:8

R?

[ornate blade]

great and (1:4)^3 = 1:64 is the volume ratio for the other one

[snow elm]

72+36-9/2-9/8=102.375?

And that is the final answer?

[ornate blade]

,calc (1/3 * 6 * 6 * 3) * 1/4 + (1/3 * 6 * 6 * 6) * 1/64

[gilded halo]

Result:

10.125

[ornate blade]

well

[snow elm]

Should be *1/8 right?

[ornate blade]

wait no, the square base isn't 1.5 by 1.5 right, let me think

hold on

the problem is where PE cuts GD

[snow elm]

The base is a rectangle?

[ornate blade]

so for AG, FP and PH, GC, yeah I set up the equations wrong

should be y = x and y = 3 - x/2, so that implies y (the height) is 2

[ornate blade]

yeah seems like it

yeah and then for PE, GC it would be:

P = (0, 0, 3), E = (6, -6, 0), G = (0, 0, 0), D = (6, -6, 6)

[snow elm]

I am cooked with 3d

[ornate blade]

,w (6t, -6t, 3 - 6t/2) = (6k, -6k, 6k)

ah wait let me fix

[gilded halo]

Results provided by WolframAlpha

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

Requested by sooouth.

[ornate blade]

yeah so the height is again 2

[ornate blade]

I made a silly error: okay it was a square base, but the height is 2 instead

[snow elm]

So the upper one is 1

[ornate blade]

so yeah the volume ratios are (1/3)^3 and (2/6)^3 respectively

[snow elm]

And the lower one is 2?

Okay

Let me redo it

[snow elm]

I got 104

[ornate blade]

,calc (1/3 * 6 * 6 * 3) * 1/27 + (1/3 * 6 * 6 * 6) * 1/27

[gilded halo]

Result:

4

[snow elm]

Oh btw how u get 2 using y=-1/2x+3?

[ornate blade]

y = -1/2 x + 3 and y = x

like consider P = (0, 3), H = (6, 0), G = (0, 0) and C = (6, 6)

then PH and GC, their intersection

[snow elm]

And then?

[snow elm]

Find the distance?

[snow elm]

Oh wait I got it

Because they are similar

So 3:6=1:2

[snow elm]

Tysm

https://tenor.com/view/baffling-gif-24471655

[scenic sun]

I have a solution I think that works, hopefully. Solution: || Consider the cross section of the wanted 3D region that has its corners of the four other corners (the ones of the 3D region other than P and G). Notice that this cross section has to be a square and that we can cut the 3D region into two square based pyramids that are glued together by the same square base with side length of a. The bottom pyramid is similar to pyramid ABCDG and the top pyramid is similar to pyramid EFGHP clearly. Also notice that the sum of the heights of the two pyramids is PG, so the volume becomes (1/3) * a^2 * 3 since PG is clearly 3, hence the volume is a^2. Now consider plane ABGF to be in the x-y plane where F is the origin, G = (6,0), A=(0,6) and B=(6,6). Notice that equation AG is 6-x and equation FP is (1/2)x, so their intersection is at coordinate (4,2). The distance from this intersection to FG is 2, so therefore the height of the bottom pyramid is 2. Then use similar triangles to see that 2/a = 6/6 = 1 by considering the cross section of the 3D region that is parallel to side ADEF that makes a triangle in the bottom pyramid that is similar to BCG. Therefor a=2 and thus the wanted volume of the 3d region is 4 ||. Hope this helps

Nice problem!

[ashen jacinth]

Yo if i am travelling to point A to point B on the same quadrant but must touch the x axis, how come the problem can be simplified wiht a reflection of point B over the x axis

i can see it intuitively with the drawing and lines but im wondering what the rigorous arugment is

[pallid tundra]

triangle inequality

the distance from A to the point you touch on the x axis equals the distance from the reflection of A to that same point

from there argue that the shortest path from A to B has the same length as the shortest path from reflected A to B (which is just a straight line, must be shortest by triangle inequality)

[vapid crescent]

hi

[ancient yoke]

Do you think they're worth the price, and if I'm not taking a course would you recommend getting one of the books, are they more about text or interesting problems?

[covert narwhal]

If you’re going from point A to point B, and you must touch the x-axis along the way, then you’re essentially looking for a path that starts at A, touches the x-axis somewhere, and ends at B. You can just reflect point B over the x-axis to get point B’

[hushed charm]

If everything is +, I know that the total is 1012 * 2025. Besides that, I know that when a number n is negative and we make it positive, it adds 2n and when n is positive and we make it negative, it removes 2n from the total sum, but I don't know how to proceed

[soft vigil]

the thing covers all evens from -1012*2025 up to 1012*2025

[hushed charm]

Oh, and 1012 * 2025 mod 2024 = 1012 right, so the remainders for 1 <= i <= 2024 are 1010, 1008, 1006, ..., 2, 0, 2022, 2020..., 1012 right

So the answer is 1012

cool

[burnt moon]

8 is 2/3

[pallid tundra]

!noans

[scarlet root]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[pallid tundra]

7,8 are not contest level problems, wrong channel

12 also debatably not contest level either

[urban mountain]

https://youtube.com/shorts/gol1bh8wlS0?si=Z6jcRfmwUp6b39hE

[ashen spoke]

@left axle Can I guide you kindly in solving the problems?

[honest rover]

I can get b/w 160-180 marks in JEE Advanced is it enough?

[granite portal]

Yall r really advanced..

[left axle]

Oh tysm but I figured it out

[hushed charm]

AFGE = GEBH = EDHC = 1cm^2

How do I prove that GJI's height = GIB's height

The solution for the problem says so, but it doesn't give any explanation

If you want to see the problem, here you go

[eternal ether]

is time a constraint while solving this problem?

[hushed charm]

Yes

[eternal ether]

how much time is available?

[hushed charm]

2h and 30min for 5 questions, so 30 minutes for this one

[hushed charm]

not too much at all actually

lol

[eternal ether]

i have one very dumb approach, set B as origin and use coordinate geometry

[hushed charm]

This olympiad targets students that probably aren't familiarized with this one

[eternal ether]

oh, then it will be quite difficult

[hushed charm]

Not at all, I have already solved knowing that the heights are equal if you want to see

I just don't understand why the heights are equal

[eternal ether]

sorry man, i'll try but it may take me days, so don't expect a response now

[snow elm]

Help

[eternal ether]

can you tell me corresponding to which side the height you're talking about?

[hushed charm]

GIJ height's corresponding to GJ and GIB height's corresponding to GB

[pallid tundra]

take a general 3x3 magic square, what do you notice about all the sums going through the middle square?

[snow elm]

They are all the same

[severe dove]

Interesting Question: Connecting Laws of Logarithms to an application in magic square. Do you realize that you will use all the rows (Row 1, 2, 3); all the columns (Column 1, 2, 3); the two diagonals (Left Diagonal and Right Diagonal) to determine <i>x, y, z</i> in terms of <i>a, b, c</i>
Here is the detailed solution: Number (3.) on
https://examssuccess.appspot.com/MATHEMATICS/ExponentsLogarithms.html#one-twenty

[snow elm]

I see im just getting tired of writing those equations in terms of other equations

Thank you mathematics guy

[severe dove]

When you have multiple equations, and you need to use more than one equation, then I guess you have to do it.

[snow elm]

I see

[severe dove]

You are welcome. Let me know if you have any question based on the solution.

[snow elm]

Do u have the full process for solving this question?

Wait nvm I saw it on the website

[severe dove]

Yes Sir...I think I explained my work clearly. Let me know otherwise.

[snow elm]

Why we pick row 1 and row2 , column 1 right diagonal, left diagonal and column 3…….

[severe dove]

We need to use all the rows, all the columns, and the two diagonals because we have to equate rows to columns, columns to rows, rows to diagonals, etc. (based on the definition of a magic square that the sum of each row, each column, and each diagonal is the same). We are given these variables: $x, y, z, a, b, c, p, q, r$ but we only need $x, y, z, a, b, c$. We do not need $p, q, r$ So, how can we isolate p, q, r in our work?

[gilded halo]

The Mathematics Guy

[snow elm]

Okay thx

[hushed charm]

Guys, has anyone read Evan Chen's OTIS-Excerpts? Did you like it?

[pallid tundra]

why don’t you read it yourself and form your own opinion

[frank valve]

An enemy submarine determined to sink your ship is sitting, torpedoes armed, exactly halfway between you and your home port. The submarine submerges to some fixed depth, and your ship now has no further information about its position. The enemy sub has to be directly underneath your ship to sink it — but the sub can track your moves with precision and respond efficiently. If your ship is fast enough, though, you will be able to set a wide course around the sub and reach port safely.

How much faster than the sub does your ship have to be to guarantee you can avoid the sub and get home?

[digital hedge]

The Mushroom Kingdom is a kingdom in the shape of a equilateral triangle with sidelength $2024$ units. The large triangle is divided into $2024^2$ unit triangles where each unit triangle is a city. One day, Bowser attacked the Mushroom Kingdom. He sends an army of Koopas to colonize $4048$ cities in Mushroom Kingdom. It is known that for every four cities that form an equilateral triangle with side lengths 2 units, if three cities in the triangle have been colonized, then the fourth city will also be colonized. This continues until Bowser can no longer colonize cities in the Mushroom Kingdom. Can Bowser choose $4048$ cities that will be colonized first, so that he can successfully colonize the entire Mushroom kingdom?

[gilded halo]

1Bazan

[snow elm]

Wth

[digital hedge]

Example : https://drive.google.com/file/d/1whgHyVyXII09kK0XgK8JI7DqV0HpG3Pf/view?usp=drivesdk

[near hill]

There's a starting configuration with 3·2024-3 cities that works, butt 4048 appears to be a tall order.

[untold thunder]

Let $x,y,z$ with $x^3+5y^3=25y^3$. Prove that $x=y=z=0$. Can anyone give me a really light hint?

[gilded halo]

ProjectTime

[misty torrent]

have you thought about divibility by 5 yet?

[untold thunder]

🙏

Oh my fricking goodness

So ingrossed in mod I forgot about that

thank you

oh my

[misty torrent]

this proof method is called ||infinite descent, and was used by fermat in proving Fermat's little theorem when n=4||

[untold thunder]

Then it's just the infinite

desnetn

This bad boy was the final problem in a section about mods

oh my

[rain ore]

I think aops v1 and v2 covers it deep down if you really throughly solve the problems

[chrome parrot]

Is there a prime Kaprekar number? Not Kaprekar constant, I mean number like 1, 9, 45, 55, 99... Is there a prime one?

[barren sparrow]

Can someone tell me if the method i used to find f(x) is correct or not

[cobalt iris]

hi

peles help me

I have a problem. I'm trying to solve time flexibility with math. We have a vision of a series of numbers that are repeating or a series of decimal numbers that are not divisible by anything at all.

p= 2X *9m =- 11

11 -= 0m + mp2 - 29 = 2.7580088765936458

OM = 0 -9 *1.2 + 0.4

mp = 8 + 7 * 78 - 3

and

x =?

m == X-2 * 82 ms

[pallid tundra]

AoPS 1 and 2 are horribly insufficient on their own

the contest scene was way less competitive 30 years ago when those were written

lots of content holes, problems aren’t hard enough, etc

think of it more as a survey of the most common contest techniques than actual intensive training on any of them

[scenic sun]

Yes, there exists at least one prime Kaprekar number. An example is the 764th Kaprekar number which is 1111111111111111111 (has 19 1’s in its decimal representation), and is apparently the smallest Kaprekar prime. Proof is that 1111111111111111111^2 = 1234567901234567900987654320987654321 and 123456790123456790 + 0987654320987654321 = 1111111111111111111. The first number in the sum has 18 digits and the second number in the sum has 19 digits. This is using the definition of a Kaprekar number that if you have a number of n digits which we call k, and when you square k and add the right n digits to the left n or n-1 digits it equals to k, then it’s a Kaprekar number

[crisp forum]

I mean for AMC level they are solid as those have not changed much. i always thought aops 1 covered AMC 8-10 and aops 2 AMC 12 to early aime.

As far as resources though titu from awesome math is always cranking out new books that are solid in particular topics

[pulsar hare]

Did you guys do the gauss math contest

[ornate blade]

CEMC time

[snow elm]

Is the answer 16?

[ivory ember]

No

https://www.programiz.com/online-compiler/4wQbQrPmfTa0m

[vague temple]

Break down by casework

||Notice that the number of tiles forces you to have 2 vertical 2x1 white blocks, after pairing each white tile with a black tile vertically. The remaining tiles must fit a checkerboard pattern. Depending on the position of these vertical white tiles, you can have 1, 2 or 3 checkerboards. Each checkerboard can have a vertical reflection. There are (13 choose 2) = 78 arrangements up to vertical reflection of checkerboards.
Cases:
1 checkerboard: 1 x w…w, 2 x ww…, giving 3 cases
2 checkerboards: 2 x 10 x w…w… + 10 x …ww… giving 2x10+10=30 cases
3 checkerboards: remaining 78-33=45 cases
Total: 3x2^1+30x2^2+45x2^3=486||

[edgy fog]

Yeah I have....I think they are good..should do!

[snow elm]

Why 13 choose 2?

[tribal fog]

hi, I just finished taking ap precalc and found it pretty easy with a grade of 99%, but competition math like AMC freaks me out and seems so different. how can i practice for competition math?

[pallid tundra]

1. AP is a complete joke difficulty wise im not surprised in the slightest that that’s not sufficient preparation for contests
2. AoPS has a wealth of resources for learning contest math including lots and lots of past contest problems from around the world

[lime zinc]

Why not opt b ( helpp !!)

[pallid tundra]

need to correct for overcounting

for example what if in the initial 8 I pick red ball 1 and red ball 2 from box 1, then I pick red ball 3 in the final 2

or what if I instead pick red ball 2 and red ball 3 first, then red ball 1

[pallid tundra]

@tribal fog most notably they have every past AMC contest there is on their website, super useful when you want to practice under test conditions

[tribal fog]

Ok, thank you

[pallid tundra]

np

[barren sparrow]

ull have to make cases

like C1) you pick 4 balls from one box and 2 balls from the other boxes

and C2) in 2 boxes u pick 3 balls and 2 balls from other 2 boxes

another hint ||while picking 3 balls u can just pick any 3 at random and subtract 1 case for when u pick only 3 red balls||

[scenic sun]

13 choose 2 is because there are 13 vertical 2 by 1 blocks in total. Like the other person said, since there are 11 black tiles used this forces 11 of the vertical blocks to contain a black square (each column must have either one black square (and thus also one white square) or no black squares (which is the same as having two white squares)). Therefore the remaining 13-11 = 2 vertical blocks are fully white. The number of ways of of picking 2 distinct vertical blocks out of the entire 13 vertical blocks is 13 choose 2.

[lime zinc]

is there like any other way ? rather than calculating all the cases?

[lime zinc]

for this too , is making cases the only option?

[dense beacon]

someone help please

i could do the (a) part, but i have no idea how do i even start (b) part

i think a combination of recursion and induction might help, but i'm unable to convert this into something meaningful

[near hill]

If the tallest student arrives first and takes his place, and then the next tallest, and so forth, then:
a) the badness is only ever increasing.
b) the badness after a student arrives depends only of what the badness was before and where in the line-so-far the arriving student ends up standing. It doesn't depend on any other knowledge of the line-so-far.
This should at least enable an O(nk) dynamic-programming algorithm for g_k(n), and possibly also a closed form if you write down the recurrence without any distracting details about lines and heights.

[barren sparrow]

not that i can think of

and i think there should be only 2 cases

so its really not that bad

[lime zinc]

okayyy, thankyouu

[barren sparrow]

also note when you are picking from boxes like in this case pick from one box only once or else ull have some cases of double counting

[dense beacon]

I can’t use programming algorithms, this is from an undergrad subjective math exam

[near hill]

My hope would then be that writing down the recursion explicitly (which I haven't bothered to myself) might inspire a closed-form formula.

[dense beacon]

yeahhhh I tried that

I tried defining a recursive function for n and n-1 orderings

if f(k,n) counts all orderings with badness <=k and f(k-1,n) counts all orderings with badness <=k-1

then their difference should give me g(k,n)

but how do I calculate f(k,n) 😭

[near hill]

I would go for a formula for g(k,n) directly.
Something like g(k,n) = (sum for k<j<n-1 of g(j,n-1)) + (sum for 0<j<=k of g(k,n-1))

where the second term immediately simplifies to k·g(k,n-1).

[dense beacon]

that sounds just as hard—

[near hill]

If nothing else, it would make it possible to compute values up to n=5 or so by hand, and look for patterns.

[ancient gust]

heyy guys wanna try out this problem, its a toughie @everyone

[vernal axle]

represent it as cot(a+kb)-cot(a+(k-1)b), then telescoping summation

[near hill]

Clever.

[barren sparrow]

This is the third time I am seeing it on this server🐿️

[snow elm]

Got it thx

[severe dove]

This is the detailed solution:
Number (7.) on https://examssuccess.appspot.com/MATHEMATICS/Trigonometry.html
Please let me know if you have any question on the solution/explanations.

[autumn niche]

Where u get the questions at ?

[swift imp]

Mods

[near hill]

Wow, that is a very long explanation that almost hides the forest among trees. It would be shorter and clearer just to say something like:

Note that in general, as long as we don't run into division by zero,
$$ \frac{1}{\sin(\alpha)\sin(\beta)} = \frac{1}{\sin(\beta-\alpha)}(\cot(\alpha) - \cot(\beta)) $$
(Namely expand $\cot$ to $\cos/\sin$, put on a common denominator, while separately using the angle-difference formula on $\sin(\beta-\alpha)$.)

In this particular series, $\beta-\alpha$ is just the constant $\pi/6$, and the $\beta$ becomes the $\alpha$ of the next term, so the this rewriting makes the series into
$$ \frac{1}{\sin(\pi/6)} \sum_{k=1}^{13} \cot\left(\frac\pi4 + \frac{(k-1)\pi}6\right) - \cot\left(\frac\pi 4+\frac{k\pi}{6}\right) $$
which telescopes.

[gilded halo]

Troposphere

[azure bloom]

Is anyone else doing ACSL?

[fading bluff]

(π/4 +kπ/6)=t

[fading bluff]

for simplicity

then multiply divide by sinπ/6

write that as sin(t+π/6-t)

sin[t-(t-π/6)]

then use sin(A-B)=sinAcosB-cosAsinB

[lapis crest]

1/24 right

This was on the Cambrdge maths offer holder chat

[raw tree]

mathematical olympiads

[raw tree]

yes

[shell pivot]

i wanna form a study plan for a math competition

basic low-level math competition, nothing crazy

how do i make one?

should i show an example question?

[raw tree]

What competition

[pallid tundra]

this almost sounds gpt’d 😭

[near hill]

Only almost. GPT would blather on about what it's doing in long tedious complete sentences. This one is just formula upon formula with only short headlinese hints about how they relate to each other. Looks human to me ...

[pallid tundra]

reminds me of all those enshittified “homework help” sites shortly before GPT slop took over them

[severe dove]

Did you "really" look at my solution? Wow...

[pallid tundra]

consider improving your prose to not be so full of fluff

[severe dove]

Someone was even complaining of my "long" explanations without considering others who may review the same solution.

Look at my explanations. Then look at your explanations. Compare the two and show them to anyone. Then, ask the person which one is "more clearly" explained.

You did not even appreciate the fact that I verified the solution with a calculator.

[pallid tundra]

ok what does calculator verification have to do with anything

[severe dove]

If you have questions on my solution, ask. Otherwise your criticisms does not help.

[pallid tundra]

if you’re obfuscating the key ideas of the solution behind unmotivated formula spam then that’s not an effectively communicated solution

[severe dove]

Verifying your solutions with TI-Calculator is important...if you are allowed to use a calculator. No one told you that?

[pallid tundra]

it’s entirely unnecessary fluff if your procedure is correct

you shouldn’t need that

[severe dove]

I have noted your name. I shall not attempt any question you post anywhere in any chat.

[pallid tundra]

ok and

cry about it

there is no need to LIST EVERY SINGLE TRIG FORMULA UNDER THE SUN just to preface the solution of one problem

[severe dove]

I shall not argue with you regarding verification with a calculator. It's common sense that if you are allowed a calculator, then you should verify your work with the calculator functions.

Tell me one formula I listed that is unnecessary...just one

Look at that solution and just screenshot one formula I used that is unnecessary...tell me just one.

[pallid tundra]

oh whoops didn’t realize all the actual solutions were buried under that mountain of text

suggestion; add an option to hide/show the formula list

[severe dove]

Also, there is no need to type in uppercase letters. I am asking you for one "unnecessary" formula that I used...list only one

[pallid tundra]

ok my bad I didn’t realize that formula list wasn’t part of any one solution

but still if you’re able to id suggest adding a hide/show option for them

[severe dove]

And for the other person that criticized my explanations, we do not need to argue. Show my work and your work (the one you typed) to any person: student, teacher, etc. Then ask them to tell you whicb one gave clear explanations. Show both works to "diverse" student and teacher population (those with varying degrees of mathematical abilities).

[severe dove]

You write a formula before you use it. You do not list all the formulas that you will use before you begin to solve. As you solve each step, you write the formula needed, then you use it.

Did you notice the dotted lines I used to separate sections of my work?

I do Mathematics for fun and to help people. However, when anyone does not provide constructive criticism, I will just avoid anything that person posts.

[pallid tundra]

you just sound butthurt that people aren’t blindly praising your solutions

[severe dove]

Constructive criticism is welcome. But destructive criticism is not welcome.

[pallid tundra]

that doesn’t mean you can just outright ignore it lmfao

and now having read the solution I do have some technical issues with it:

[severe dove]

You said there is no need to list every trig formula. But any formula I listed is necessary for "all" categories of learners. I do not write solutions for only the mathematically fast learners. I write solutions in a way that anyone who reads it understand what I did.

[pallid tundra]

the “assumed numerator” steps seem rather unmotivated

what is the goal there

[severe dove]

Assumed numerator implies that it is not the numerator in the "original" question. I have to do some modifications to get the telescoping series. Hence, I used the word, "assumed" because some people might be confused if I used only "numerator"

[pallid tundra]

what are you assuming? why are you assuming it?

until I read troposphere’s paraphrased solution it wasn’t clear that you were trying to get sin(pi/6) in the denominator and something that can telescope in the numerator

[severe dove]

I am assuming it because I cannot solve the expression in the original form. I have to do some modifications.

I cannot just write sin(pi/6) without explaining how I got it

[pallid tundra]

then explain that more clearly

[severe dove]

I write solutions so that "anyone" who reads it will understand. Did you really look at my "entire" solution? I showed "all" work

[pallid tundra]

you showed it all but didn’t explain it clearly

[severe dove]

If you look at all the questions I have solved in this chat (and other chats), I show "all" work. I do it to accommodate everyone...no matter your level of mathematical ability

[pallid tundra]

you can list all the arithmetic steps you want but if you don’t explain what you’re doing with each one people still risk getting lost

[severe dove]

Please screenshow what I did not explain clearly. I am a lifelong learner. I want to improve based on your comments.

Screenshot and paste what I did not explain well.

[pallid tundra]

“seeing the product of sines in the denominator, we think to apply product-to-sum in order to express the summand in a form that telescopes…”

more clearly emphasize here that the overarching goal is to make the series telescope

the whole “numerator/denominator” steps are also not explained well

[severe dove]

My dear, did you miss this?

[severe dove]

May you please let me know what is not explained well?

[pallid tundra]

you just throw a wall of equations at the reader without enough explanation

sure you say you want the sum to telescope, but how will you achieve that?

[severe dove]

May I ask you: did you understand what I did? Please be honest.

[pallid tundra]

with some effort

[severe dove]

It's a "yes" or "no" answer. Please tell me.

[pallid tundra]

yes

[severe dove]

Okay. I am waiting for anyone who did not understand it.

[pallid tundra]

I just think it is very poorly presented

[severe dove]

I wrote that anyone who did not understand it should let me know.

[pallid tundra]

the technical details are fine but could be communicated/organized better

[severe dove]

May you write your work in that regard on how it should be presented?

[pallid tundra]

sure

[sage geyser]

^ I prefer the style of invoking formulae/theorems when required

[pallid tundra]

all the actual problems are just buried under the formula list

from a UX perspective that’s not ideal

[sage geyser]

I’m not sure what it looks like on laptop but yeah it’s kinda unreadable on mobile imo

[severe dove]

If anyone has any question about my work, please let me know. Do not mind @pallid tundra because he/she stated already that he/she understood it.

[severe dove]

Mathematics work involving latex is best read on a computer, not on a phone.

[sage geyser]

Agreed

But that doesn’t mean it should be unreadable on a phone either

[severe dove]

It is not unreadable on the phone. The screensize of the phone matters because some work is lengthy on a single line

Some formulas are lengthy on a single line.

Can you read my work on a computer and let me know if it makes sense or not?

[sage geyser]

Some things like ‘pneumonics to remember the quadrants’ are redundant

Regardless of how you read it

An answer should explain the process, a different type of resource is needed to actually learn the content

[severe dove]

You mean this pneumonic? What is wrong with it?

[severe dove]

Poeple have different mathematical abilities regardless of the resource they used to learn the content. Do you agree?

[sage geyser]

It takes up space and is unnecessary

Which means it takes longer to get to the answer

So it’s difficult to keep the flow of logic in the mind

That’s why it’s nicer to invoke theorems on the step you need them

(Or trig values or quadrants in this case)

[severe dove]

If I understand you clearly, you are saying I should not write the pneumonic. Is that correct?

[sage geyser]

Yes

[severe dove]

But did you understand my solution to the question posted by @near hill ?

Did you understand the explanations?

[sage geyser]

You are missing the point

The explanation can be perfect but it doesn’t help if there’s a wall of redundant text before it

And I haven’t read the explanation because it’s so much effort filtering what is and isn’t helpful

I got to that table and quadrant part and gave up

[severe dove]

Did you see that link: Numbers 1 - 20?

If you click on that link, it takes you directly to the questions and the solutions.

Here you go: https://examssuccess.appspot.com/MATHEMATICS/Trigonometry.html#one-twenty

[sage geyser]

Ah I didn’t, that’s probably a phone thing. Can you not make the link go directly to there?

That helps a bit but I still would give the same advice

[severe dove]

Yes Sir, I just posted the direct link to the question.

May I explain the reasons for having that pneumonic?

As I write each step of a solution, say I need to use 3rd Quadrant Identity

One of my readers may ask: what is 3rd Quadrant Identity?

That reader may not have heard of that term before reviewing my solution.

Hence, that reader needs to see it there on the page to help him/her understand. Do you understand what I mean?

I give you another example.

For all problems I do on Circle Theorems, I give a reason for each step.

[sage geyser]

I’d say that the way you memorise values is up to you

Why would you force the reader to understand your memorisation of angles

[severe dove]

If my reason is not found on that page, it may confuse some students. Do you not think so?

[sage geyser]

Why not just focus on the result and not how you memorise it

Oh another point is just vary the text size and colour

It’s makes it way easier to read the solution

[severe dove]

My dear, I am trying to help people. I am not forcing anyone to memorize angles.

[sage geyser]

You’re forcing them to understand the way you were taught

I don’t use pneumonics for example

So that’s just a pain for me

[severe dove]

Have you ever used pneumonics for anything?

[sage geyser]

Yes. I wouldn’t expect an answer sheet to list it

[barren sparrow]

guys when they say limit exists we shud check if RHL=LHL=f(a) right?

[sage geyser]

If you can’t remember something that’s a different problem

[sage geyser]

If it’s defined both sides then generally it’s better to

[severe dove]

Yes, Left Hand Limit should be equal to the Right Hand Limit

[barren sparrow]

so what do they mean by LHL exists or RHl exists

[sage geyser]

I should really reply: yes, and I know other people use other ones

Because that’s the problem

[barren sparrow]

like this question

[sage geyser]

It converges <==> it exists kinda

[pallid tundra]

“left hand limit” is the limit as x increases towards that value

[sage geyser]

(Well is a limit to infinity ‘existent’ actually idk)

[pallid tundra]

you’re “approaching from the left”

[barren sparrow]

what do u mean converges

[sage geyser]

Oh boy

[pallid tundra]

similarly “right hand limit” is the limit as x decreases towards it

[barren sparrow]

i understand that

[sage geyser]

Probably don’t worry about it 🤣

[pallid tundra]

uh don’t worry about that terminology for now lmao

yea

[sage geyser]

Simply, converges means it gets as close as possible to a value

[barren sparrow]

fair

[sage geyser]

But if you think about 1/x near 0, it gets faster and faster and doesn’t reach anything

[pallid tundra]

biggest advice is to state upfront what you’re hoping to prove

[barren sparrow]

so basically what i have to check if lhl and rhl are finte or not?

[pallid tundra]

something like “we claim that $\frac{1}{\sin\alpha\sin\beta}=\frac{\cot\alpha-\cot\beta}{\sin(\beta-\alpha)}$” and then follow it with a proof of the identity

[gilded halo]

elrichardo1337

[sage geyser]

Thank you, much better way of speaking my thoughts

The justification should come after the statement

Or alongside

[pallid tundra]

here you’re supposed to recognize it as the common trig limit $\lim_{x\to 0}\frac{\sin x}{x}=1$

[gilded halo]

elrichardo1337

[pallid tundra]

or wait

things are a bit trickier here bc of the sign issues

but try to express it in terms of that known limit

[barren sparrow]

so basically what i got is lhl=+inf and rhl=0

but i dont know which option is correct

[pallid tundra]

by doing this the reader now knows why you’re going through the computations you do

https://artofproblemsolving.com/blog/articles/how-to-write-a-solution?srsltid=AfmBOoo3ryMN7RqHTzyIGQWmSKYC-tB34nu1VX7oa3jTkBOMCNQJbrUA

[unborn finch]

thanks i guess

[atomic mica]

What is actually competition-math is? why does it really unique

[pallid tundra]

math for competitions

what does it sound like

[ornate blade]

The depth of problem solving goes significantly beyond the school curriculum

You may also encounter topics that you haven't seen before

[atomic mica]

so is it just more Into problem solving

or just speed

or both?

[ornate blade]

Speed isn't that important especially at higher levels

[pallid tundra]

low level contests are more speed based (read: computation focused)

while technically they’re all non calculus they nonetheless involve some highly nontrivial stuff

most of which is excluded from standard k-12 curricula

[unborn finch]

what competitions are happening for 8th graders

[atomic mica]

ohh i see okee thanks

[pallid tundra]

in the US the two big middle school contests are MATHCOUNTS and AMC 8

check also for other regional and/or online contests

well maybe they used to be big

[polar patio]

erm its like geometry stuff and algebra stuff

[pallid tundra]

MATHCOUNTS lost like 75-80% of their participants after 2020 and never recovered

and number theory, and combo

[polar patio]

essentially the four olympiad topics but uhh one could say dumbed-down or say lower in difficulty at least i think so

[radiant jasper]

Evaluate this limit without using l'hôpital rule

[ornate blade]

wrong channel

[radiant jasper]

It's a challenge , i don't need help

[ornate blade]

I know, but you should still post in #precalculus and not this channel

also tell people it's a challenge

otherwise you're leading people to waste their effort

if they already know how

they said they didn't need help....

[sullen blaze]

is it 0?

[radiant jasper]

No

[radiant jasper]

This is not a precalculus limits is really hard

[radiant jasper]

And why doing olympiad at the first place it just a waste of time

[sleek ivy]

?

tf

[pallid tundra]

limits at the “AP calculus” level are completely trivial bruh 😭

[pallid tundra]

ok and

[barren sparrow]

the audacity u had to tell this in maths discord sevrer in the competetion channel is crazy

[radiant jasper]

And ? That your problem bro

[barren sparrow]

nah just a compiment i cud never

[radiant jasper]

I'm just sending it for anyone interested

[near hill]

I think it could easily become your problem if you insist on hanging around in a topic channel just to tell people that the topic of the channel is a waste of time ...

[radiant jasper]

It not like the previous post interested me but i kept quiet but when i shared a fun limit i get hate for no reason

[radiant jasper]

I don't want to debate for now

[radiant jasper]

There might be someone interested in solving this limit i'm not sending it for anyone specific idk why i get all this negative response for nothing

[near hill]

You're getting negative responses because you're posting a problem that doesn't look like a competition problem in the competition-math channel.

[radiant jasper]

Well try to solve it first , were you able ?

[near hill]

Whether or not I can solve it doesn't have any bearing on whether it looks like a competition problem or not.

[radiant jasper]

What a competition problem for you a sommation then doing a little telescoping action ?

[barren sparrow]

omg guys chill

now this has become an arguing channel😂

lets stick to maths

[radiant jasper]

You can literally give him any sort of sommation and he will count it as an olympiad , and don't let me talk about pigma this will break his mind

[acoustic nova]

??

[radiant jasper]

HOW MANY HOURS YALL PRACTICE PER DAY

[swift imp]

40

[radiant jasper]

🫑

[ornate blade]

LING LING 40 HRS

@radiant jasper

[pallid tundra]

ew

l*ng l*ng

[vernal axle]

substitute x=t^6 and do it the usual way. Factor out 1-t and then cancel it. You get -1/12.

[radiant jasper]

Yep you're right

[digital hedge]

For any non-negative reals a≥b≥c≥d satisfying ab+bc+cd+da=4, is it always true that a+b+c+d≥4?

[vernal axle]

Let x=a+c and y=b+d. Then xy=4, so x+y≥2√(xy)=4

[radiant jasper]

Suuure papi 40 hours a day

Super realistic

[lament stream]

1+1=2

[storm mortar]

damn such a clean observation

[pure mauve]

impeccably outstanding

[snow elm]

Am I doing it correctly?

[near hill]

(This is really not a computation you need to render with TeX to make it readable, I think.)

[unborn sun]

$$\ p^2 + q^2 = r^2$$
$$\ a^2 = 2 * p^2$$
$$\ b^2 = 2 * q^2$$
$$\ c^2 = 2 * r ^ 2$$
$$\ a^2 + b ^ 2 = 2 * ( p^2 + q ^2 ) = 2 * r^2 = c^2$$

[gilded halo]

Angular | Ionic Dev

[pallid tundra]

||the triangle with side lengths a, b, c is similar to the central triangle (all lengths scaled up by sqrt2), done||

[dusty fable]

does anyone wanna try some of my homemade questions

[harsh apex]

what site is this

[hexed oak]

hm

[storm mortar]

Havent figured out yet

posted in every online math websites like aops

[hexed oak]

oare you fine with spoilers?

[storm mortar]

nobody gave a correct solution yet

[storm mortar]

sure

Invented this problem 5 days ago

Am craving for a solution

[hexed oak]

ok

so my first though is to try and check when two eggs are indistinguishable

[storm mortar]

thats when we drop two eggs of consecutive hardness from the same floor

[hexed oak]

so, let us say after a throw from height a-1, the possible set of weights is [b,...,c]

then before it, the possible set of weights before is [ab,....,ac]

with n = 1, any m is enough

[storm mortar]

and n = 2 m>= 3

[hexed oak]

what strat?

is it for m = 3

[storm mortar]

we drop the each two eggs from floor 1 and 2

The one that breaks is 1 and the one that does not is 2

[hexed oak]

then dont we have m = 2?

also floor (2/(2+1)) = 0

[storm mortar]

oh yea right

[hexed oak]

actually m = 1 suffices

n = 1, m = 0
n = 2, m = 1

[storm mortar]

but above that i cant make it work

whatever you are cooking please tell it next day

im feeling very sleeply

also consider posting your solution in https://artofproblemsolving.com/community/u1185903h3579317p34960010

[hexed oak]

n = 3,2,1

2 is useless
2 -> 3,1 2,0 1,0
1 -> 3,1 2,1 1,0

drop something from 1, if it breaks then its 0
if it doesnt break, it is currently 1, we have one more one, and we have a number we are trying to find out
we cant drop the number we are interested in from floor 1, otherwise we lose information
hence drop another egg from floor 2, if it doesnt break, it was 3, we started with a 2, and ther last egg is 1, if it breaks, then we either dropped a 1, or we dropped a 2, and so the possible outputs are (1,0,2) (1,0,3) (1,0,1), now we cant figure out what state the last egg is in, so it is impossible

this qn is impossible

[hexed oak]

i dont use aops much

[storm mortar]

oh ok

[hexed oak]

also, i am embarrased to say, but idk latex

[storm mortar]

neither do i i just use chatgpt

[hexed oak]

oh

[storm mortar]

but if it is impossible to find the correct order there must be a proof

[hexed oak]

i gave proof

for n = 3

for n > 3, n = 3 is a subproblem that must be solved

so it is impossible

[storm mortar]

we could carry on induction

[storm mortar]

oh ok

its kind of sad man to see my problem having this easy sol

anyway thanks

[hexed oak]

trust me, its worse when your prob has no sol

i once made a random prime number prob

[storm mortar]

gtg bye

[hexed oak]

bye

[storm mortar]

wait tell me the problem

[hexed oak]

i forgot

but i asked a sir

oh yeh i remember

show, or prove false, there are infinitely many primes numbers which are a distance of 1 from the product of the first n primes for some n

[unborn finch]

guys what r some global competitions

like for all the countries

[pallid tundra]

watch your spelling

there are probably a good deal of online competitions out there

the most highly respected international competition for high schoolers is IMO

[radiant jasper]

imo imo imo imo

[quaint oyster]

what other competitions are well known among the universities?

[ornate blade]

unis don't care about contests in general

[quaint oyster]

hmm

[ornate blade]

except as extracurriculars for the purposes of admission, but I mean that's not a requirement at all, nor do most successful mathematicians need contest maths

[quaint oyster]

yeah, its for admission purpose

[ornate blade]

but I mean the specific contest doesn't matter

if you can't get into IMO, at least try to qualify for a regional olympiad, then a national olympiad or continental olympiad

then if you do well

being on your country's training team is already a big accomplishment

[iron drift]

How do i actually practice the problems

I feel demotivated everytime i fail

And dont want to sit and do it when i fail

[storm mortar]

its okay

normally i take a break when i fail to solve a problem

but i atleast make sure i gave it my best try and also that i understood its solution

[iron drift]

oh

I dont, maybe thats the problem

[storm mortar]

hehe

its okay bro

only 500 students get bronze or better in imo

[iron drift]

But i still dont understand how people come up with elegant solution

[storm mortar]

its just they spend too much time with the problem

[iron drift]

i go up halfway then my brain halts

[storm mortar]

haha

same

[iron drift]

Well i cant even solve pre regional level problems

[storm mortar]

unless its a easy problem i dont even know how to approach it

[storm mortar]

same

[iron drift]

Same

[storm mortar]

lol

[iron drift]

XD

so which country you from

I am from India

[storm mortar]

me too

[iron drift]

I am preparing for IOQM

oh lol

[storm mortar]

haha lol

[iron drift]

Which class are you studying in

[storm mortar]

i gave ioqm last year

[storm mortar]

9th

[iron drift]

Same

[iron drift]

Oo im in 10th

[storm mortar]

so did you qual?

[iron drift]

nope, i only got 12

[storm mortar]

oh its ok

[iron drift]

did u qual?

[storm mortar]

since we both started early maybe we can atleast attend imotc before college

[iron drift]

Hopefully

[storm mortar]

yes barely i got 33 cutoff 32

[iron drift]

oo nice

[storm mortar]

thanks

[iron drift]

Well I started my prep this summer

I am very clueless

[storm mortar]

and its not like all mathematicians are inmo awardees

[storm mortar]

same lol

[iron drift]

But you got 33

So you are atleast way better than me, I need tips XD

[storm mortar]

For example this how tf am I gonna aproach

[storm mortar]

yea sure first of all do you have a excursion in mathematics?

[iron drift]

I have all the books

Burton, Excursion, Hall and knight, Pre college, Mcgraw hills IIT, u say it

[storm mortar]

hall and knight isnt of much use

[iron drift]

oh ok

So Excursion

?

[storm mortar]

yes

very good

[iron drift]

Algebra?

[storm mortar]

tho a bit overkill for ioqm

[iron drift]

Is it beginner friendly though

[storm mortar]

no

[iron drift]

.

[storm mortar]

so do you take coaching anywhere?

[iron drift]

nope

[storm mortar]

cuz it rlly helps

where u from?

[iron drift]

hmmmmm, alr

[iron drift]

Assam

[storm mortar]

oh

u can see khan academy

[iron drift]

Hmm

[storm mortar]

vendantu olympiad school

[iron drift]

Alr

[iron drift]

Alr

[storm mortar]

im not telling you to enroll there

[iron drift]

the YT channel?

[storm mortar]

just watch their youtube vids

[storm mortar]

yes

[iron drift]

like Those random IOQM videos that pop up

[storm mortar]

they explain so easily

[iron drift]

oh ok

[iron drift]

They come in my short feed

Currently im doing PnC, any good book for that

[storm mortar]

and for beyond ioqm i suggest egmo and otis excerpts by evan chen

[iron drift]

I have EGMO

but it bashed me

before i could Bash it

[storm mortar]

yea i saw a aops user say once "only bash if you are prepared to be bashed"

oh and art of problem solving is also a very good website

[iron drift]

I did the "100" Geometry Problem section

out of the total 100 i could only solve 10

😭

[storm mortar]

its completly normal

[next cosmos]

do you guys actually buy the books or use a pdf or something??

[iron drift]

Pdf, and xerox

[storm mortar]

who buys books?

[next cosmos]

ok thanks

[iron drift]

Well i have a copy of excursion

my dad used it

[storm mortar]

damn

also see problem primer

[iron drift]

I have that one

[storm mortar]

written by the same authors of excursion

an exploration of Olympiad combinatorics

[iron drift]

Yeah 2012 and 2013(first few problems) were bearable

[iron drift]

is that one by rushil mathur?

[storm mortar]

yes

gold medalist

very good book

[iron drift]

oo

[storm mortar]

but only for inmo or higher

[iron drift]

oh

so did u go till INMO

[storm mortar]

yes

[iron drift]

oh, how are the problems

[storm mortar]

completly "hagh diya"

[storm mortar]

what do you expect?

i only solved Q1 correctly

[iron drift]

So, uh When did u start

[storm mortar]

7th grade

[iron drift]

6th grade

omg

I didnt even know what JEE was until 8th 💀

[storm mortar]

hey i want to cheer you up so see isi ugb 2025

[iron drift]

hmm, ok

[storm mortar]

I bet you can solve 2 questions

maybe even 3

[iron drift]

ye, maybe..

[storm mortar]

and the rest three are calculus

[iron drift]

eyy the binomial coefficient ones can be solved by me

[storm mortar]

see i told ya

and isi is the second best math institute in india

[iron drift]

is the 7th one just cosine rule or smth

wait nvm

[storm mortar]

its the third one actually

[iron drift]

problem 3 is binomial right?

[storm mortar]

7th is a one liner. You use the property that the orthic triangle of a triangle has its incenter O

[iron drift]

oh wait nvm i was seeing UGA 🤣

[storm mortar]

oh haha

[iron drift]

Although u sound very familiar

I also have another friend who started in 6th

[storm mortar]

who?

i may know him

[hollow raven]

If I was planning to score high (at least 65/80) on the COMC (Canadian Open Math Competition) and the next stage of the competition (CMO, Canadian Math Olympiad), what types of resources would be appropriate from now until the COMC on October 30 this year (currently in Grade 10 so I might have to wait until COMC 2026 instead of 2025 to have more time to improve)? I’m currently working through AoPS v1 and v2 but not sure what other resources to use. Also tried Alcumus in the past but didn’t really jive with it. Ty in advance!

[snow elm]

CMO? Impossible

Focus on score in the top 25% of Euclid or COMC first

For resources u can use like the Element by Euclid

Very helpful

If there are many geometric questions in the context

[hollow raven]

Element? Sorry not very familiar with other works in general

[snow elm]

The author is Euclid

Just search The Element by Euclid

Very useful

[hollow raven]

Would qualification for the CMO be out of the question? I see that it's unrealistic to aim to suddenly improve to become high-ranking in the CMO, but at the very least qualifying for CMO I think is possible.

[snow elm]

Maybe idk

[hollow raven]

Alright well after I finish the aops books ill check out your suggestion. Ty for your help!

[snow elm]

Np

Oh yeah how was the v1 and v2 book in aops

Is it useful ?

[hollow raven]

well I had recently started the v1 so I can't say too much

[snow elm]

Oh

[hollow raven]

but so far im learning new things so i would say look at the table of contents and see if anything is of interest

[snow elm]

Good

In recent years those contests are just like stupid and boring for me, cuz so many people cheated

My friend brought the contest online and he just needs to memorize those answers and steps

He got in lol

[agile ocean]

can any1 help me prep of ioqm and rmo?

[twilit hazel]

yes maybe i can

[hushed charm]

I am not sure about that, math changed a little bit, just a little bit from more than 2000 years ago to now

Mainly olympiad math

[pallid tundra]

sure elements is a foundational text for the field of Euclidean geometry but it’s absolutely not well suited for a modern audience

unironically recommending it to learn geometry is a terrible idea

there are plenty of modern treatments that present the material in a more accessible format; once your basics are solid I’d recommend Evan Chen’s EGMO

[high goblet]

AHAHAHA there's no way someone actually recommended Elements by Euclid unironically for maths competitions in the 21st century

[high goblet]

honestly grind through as many past papers as possible

[ornate blade]

Hi!

[high goblet]

there's not really some magic bullet you can use to like instantly get better, the way all the olympiad top scorers get good is just by doing an insane amount of past papers

[sleek ivy]

Just a 2000 year old text

[high goblet]

AOPS has a very large collection of past papers for various olympiads and competitions, which can be helpful if you've done all the past papers for the competition ur grinding for

as for books, lemme quickly check what level COMC is like quickly

right i'd say probably with a maths competition like that, you don't really need to focus on books & learning theory, it's probably better just to do problems

for olympiads evan chen's OTIS excerpts and EGMO are really useful

[high goblet]

hi!

[hollow raven]

Alright, tysm for the advice!

[high goblet]

also btw check out MODS, it's here

MODS is more suited for competition maths, so ur overall gonna get better advice lol

[snow elm]

Have u read the book? lol I find it rlly helpful for me

Morden maths competition ( not maths Olympiad ) are not rigorous. Do u know why Chinese can get that much gold medals? Because they have a rigorous proof for everything. Teacher even use those books in class

[high goblet]

...

they are not studying from elements by euclid

also you seem to...not understand what rigorous means if u think what the ancient greeks did was somehow more rigorous than what we teach nowadays

[high goblet]

china can get that many gold medals because they care about olympiads in general and have a large population, nothing to do with how rigorous they teach X vs how they teach X in other countries

i'd say it's the fact that they do more problem solving that makes them better at maths

[high goblet]

also elrichardo already explained why recommending elements is a bad idea

[snow elm]

Do u think practice more problems will help u get in to Olympiad maths? Lmao

It’s a stage for geniuses not for hard working Dube

[snow elm]

Only a large population? What about India ? They are smarter than other people cuz they have a rigorous maths background and education system better than other countries

[lean yarrow]

Elements by Euclid is genuinely wild

[snow elm]

That is just my own opinion cuz I found it helpful. I used some theorems in COMC.

[lean yarrow]

recommending it for competitive math is so what

[snow elm]

What?

Just my own PoV

It’s not suitable for everyone lol

[lean yarrow]

it's not particularly suited for modern math olympiads

[snow elm]

Are u in IMO or something

[lean yarrow]

sure, it's a very formal and down to the nitty gritty stuff, but not suited for actual problems

[lean yarrow]

Not in it but I've solved my share of problems. Got into it too late

[snow elm]

Oh

Well good advice might be just give up lol

Focus on calculus

[lean yarrow]

but yeah like in practice you don't need such detailed and elementary math

[snow elm]

You can’t beat those Chinese anyway

[lean yarrow]

I mean, competitive math isn't just about winning competitions. It's about doing math because it's fun :p

[snow elm]

Imagine your opponent is Gauss

[lean yarrow]

although calc is also cool

[snow elm]

Fun?

Only fun for geniuses

Stressful for normal people

[lean yarrow]

I mean, firstly, I wouldn't say it's a divide between "geniuses" and "normal people". Anyone can get into it, and it's suited for all levels. And yeah, it's fun and rewarding

[snow elm]

It’s so easy to score a 100%on those contests except Olympiad

Those contests are literally selling online

[lean yarrow]

I don't see how that's related but ok

[snow elm]

Not anyone

Only someone

[lean yarrow]

yeah, anyone

with some amount of preparation anyone can solve idk a modular arithmetic problem

and then try out a diophantine

and then maybe move on to something involving cyclotomic

and so on

it's a progression, you don't have to start by solving IMO P6s

[high goblet]

almost made the team for my country

but i have friends that made IMO

and i don't think they'd recommend reading elements for that either lol

[high goblet]

that's the wrong attitude to have

sure it can look like the top imoers are just geniuses but like you don't see the amount of effort and problems they practise

[lean yarrow]

mhm

[sleek ivy]

they also have a large population tf

[snow elm]

?

We all know they have a large population but did they do rlly well in IMO? Compared to China

[ornate blade]

well the top students are too busy trying to crack JEE

in China, if you do well in the IMO, you can get guaranteed admission to a top college

to my knowledge that doesn't really happen in India

IIT Kanpur and a few other places

[sleek ivy]

plus its a cultural thing in china

[ornate blade]

well by now it's also a cultural thing in India

[sleek ivy]

they put a lot of pressure on kids to excel in everything which isnt really healthy at all

[ornate blade]

but yes it's normal for primary school kids to go to maths olympiad training in China

STEM is seen as prestigious and yeah

[snow elm]

Yep so China is better is not only about their culture

[ornate blade]

of course there are a million countries with intense study culture

not all of them care about IMO

[snow elm]

Also their education

[snow elm]

Yeah

Maybe idk

[lean yarrow]

I wouldn't say China's education itself is really excellent, or at least it isn't usually regarded as such. It's more the use and abuse of excessive studying and pressure on children

[sleek ivy]

well not really

there aint even a million countries

[snow elm]

Education for maths

[ornate blade]

it's hyperbole

[ornate blade]

it's just as braindead as Indian education, trust me

search up 'gaofen dineng'

high test scores, low ability at life

[snow elm]

Yeah but that is what u need for top uni

lol

[sleek ivy]

not really

in us or uk they dont rlly gaf about olympiads that much

[ornate blade]

all Western countries in general

[snow elm]

MIT does

Harvard

[ornate blade]

they don't

[snow elm]

Rlly?

[sleek ivy]

the only one who does rlly

[ornate blade]

yeah

[sleek ivy]

nope

mit does

[lean yarrow]

they do care, but in a different way. Not as in a requirement, but more as a fun activity

[snow elm]

Seriously?

[sleek ivy]

most other ivies dont

[ornate blade]

I mean out of all of those MIT does see the most value in IMO

but that's a vanishingly small number of people anyways

[snow elm]

Yeah

[sleek ivy]

like yes it looks good but it wont make or break your app probably

[ornate blade]

it's not like they can survive based on IMO participants alone

[sleek ivy]

a good essay and a passion project are prolly better

[snow elm]

Cure cancer 🤓🤓🤓🤓

[ornate blade]

there's a million other things that you could do that would be just as worthwhile to unis

[lean yarrow]

ye

[ornate blade]

and no it's not just research and comps

[lean yarrow]

the main thing ig would be showing dedication

[snow elm]

Plus daddy donate a building

[ornate blade]

blog.evanchen.cc/2024/04/05/grief/#fnrefresearch

more people should go read this

[snow elm]

School too easy and jump to maths Olympiad directly? lol😭

[sleek ivy]

honestly inflation for getting into unis has gotten crazy

[ornate blade]

but yes it's talking about the inflation in unis

[lean yarrow]

all inflation has gotten crazy :p

[snow elm]

The question in IMO in the future will be prove Rieman’s hypothesis

[lean yarrow]

doubt

[dapper magnet]

arent u that mf i argued with before, that the chinese are somehow better at math than the others

[lean yarrow]

that's like saying FLT would be in IMO, just not sensible

[snow elm]

Bruh what ?

Do I know u ?

[lean yarrow]

they did comment about China being very good at IMO in this convo but dunno

[snow elm]

What did they say

[snow elm]

Chill don’t swear

[dapper magnet]

found it

[snow elm]

I forgot

[ornate blade]

China is by no means unique

[snow elm]

Let me check

[lean yarrow]

In a way, they are, just not in a good way

[snow elm]

Is it too hard for you guys to admit that China has better education in maths than other countries?

[lean yarrow]

at least in this sense

[ornate blade]

I'm literally Chinese what are you talking about

[sleek ivy]

thats crazy ahaaaahaha

[lean yarrow]

it just isn't really that way, nor is it known for that

[snow elm]

They teach u guys calculus in grade 10 right?

[ornate blade]

but yes that work mentality filters down everywhere in society

[dapper magnet]

im literally chinese brah (although only ethnically)

[lean yarrow]

it's known for its oppressive education

[ornate blade]

China isn't in the OECD so you have to trust government statistics

but even if people work the government-stated number, that would still be one of the highest working hours in the world

[snow elm]

Their education is like stressful ig but under that certain conditions gifted people born

[lean yarrow]

I mean it in the specific case of math education, and without offense to anyone

[snow elm]

Oh

[dapper magnet]

i literally told u that

a long time ago

when we argued

[ornate blade]

it also hinders a lot of gifted students

gifted underachievers for example

[lean yarrow]

gifted people aren't born like that, plus gifted people underperform long term. It's not good

[ornate blade]

that person who seems like the class clown could be acting dumb all the time

cause they're afraid of all the extra tuition, pressure, and expectations if they were to be in the gifted class

[snow elm]

Probably change that to “people that can bear pressure “

[dapper magnet]

also can we all stop using the term gifted

i dont actually think they exist

[snow elm]

Ok

[ornate blade]

sigh

[dapper magnet]

its jsut a term made up for parents to feel better about their child

[ornate blade]

they do

[dapper magnet]

ok

[ornate blade]

that's a position borne out of pure ignorance

[dapper magnet]

even if they do

[sleek ivy]

the earth is flat ah

[dapper magnet]

why bother using any term that is comparative

[ornate blade]

giftedness is not just eye-cue

[ornate blade]

it's like why do we bother using the term ADHD

so that kids can receive better learning opportunities and accommodations

[lean yarrow]

sure, that's more like it. But it's in detriment of everyone else

[dapper magnet]

gifted is not a neurodevelopmental disorder ❤️

[snow elm]

Maybe

[ornate blade]

catering for the gifted means we can also cater for people with learning disabilities, neurodivergences, and those who are falling behind

[ornate blade]

it's part of neurodivergence

[lean yarrow]

I'd say some people have ease for some things, and that's what's meant by it. It's just that long term they stop because of less effort and such

[ornate blade]

also there's a lot of gifted people who are also autistic and so on

just cause you have a higher 'natural ability' doesn't mean you'll automatically succed in life

if only it were that easy

[snow elm]

At least they are geniuses in some categories💀

As long as u have achievements, u have to care about your personal life?

[sleek ivy]

uh

yes

you should

[snow elm]

Why?

I mean it didn’t matter thou

As long as u got what u need like achievement

[sleek ivy]

whats the point of those achievements if you arent well rounded and happy

[dapper magnet]

"Giftedness" isn’t a real clinical or diagnostic category — unlike autism or ADHD, which have identifiable genetic markers and diagnostic criteria. Second, Intelligence is influenced more by environment than genetics, especially in childhood. Third, the term "gifted" is often used because people want to believe their child is special or smarter, and sometimes to avoid labeling a child as neurodivergent due to stigma. Finally, the label "gifted" is comparative and subjective, and can be socially isolating or misleading, rather than materially helpful.

[ornate blade]

okay I don't want to argue with you on this, except the fact that just cause a label can be misused, doesn't mean we should get rid of the label altogether

[dapper magnet]

??? We don't use the r-word anymore for a reason yk

[ornate blade]

I never said anything close to the r-word

[dapper magnet]

It's a response to "just cause a label can be misused, doesn't mean we should get rid of the label altogether"

[ornate blade]

well the reason why no one should use the r-word is that people mean something hateful when they use it

[dapper magnet]

So you argue that no one should use the r-word beacuse they have malicious/bad intent, correct? If so, consider the fact that saying someone is "gifted" is just a euphemistic way of saying "smarter than everyone else".

[snow elm]

What r word

[ornate blade]

that's not what gifted means

[dapper magnet]

And if you wanna make a point about how it can be used as a complement

[ornate blade]

let me show you the columbus group definition

[dapper magnet]

huh

[ornate blade]

“Giftedness is asynchronous development in which advanced cognitive abilities and heightened intensity combine to create inner experiences and awareness that are qualitatively different from the norm. This asynchrony increases with higher intellectual capacity. The uniqueness of the gifted renders them particularly vulnerable and requires modifications in parenting, teaching and counseling in order for them to develop optimally.”

[dapper magnet]

Make what you want out of it, I just don't think that the label gifted is necessary and/or important

[ornate blade]

sure

but you shouldn't hate on people who want to use that label

[dapper magnet]

I can and I will, even using your definition, at the end of the day, it still counts as a comparative term

[ornate blade]

I never said giftedness was absolute

or that it was innate

[dapper magnet]

the fact that it is innate or not is also irrelevant

[snow elm]

Can we use the term like prodigy ?

[ornate blade]

eh of course it's a very touchy subject

[dapper magnet]

Eh...

Hm

[ornate blade]

I'd say labelling kids as prodigies is unhelpful

[dapper magnet]

^

I agree

[ornate blade]

cause it implies that they'll be nothing if they don't become brilliant adults

[dapper magnet]

It just alienates them socially, similar to the arguments I made about labels like gifted, etc.

[snow elm]

Rlly?

[ornate blade]

it's so dumb how psychologists and clinicians thought of ADHD and autism as only a kid thing

[ornate blade]

from my experience, yes

[snow elm]

That happened on adults too

[ornate blade]

yes, now adults are getting diagnosed which is great!

[snow elm]

lol

[dapper magnet]

I also think that calling kids prodigy will put immense pressure on them

[ornate blade]

it's also very dehumanising

you're not seeing the actual human or their personality

[snow elm]

Yeah but no choices

[ornate blade]

you're just seeing: oh they're smart! they're not normal!

[ornate blade]

agreed

[snow elm]

Depends on person perhaps

[dapper magnet]

choices of ?

what choice

[snow elm]

Social media’s

For example

[ornate blade]

there's what academics mean when they say 'gifted' (and there's so many different views even in the academic community)

[snow elm]

Says someone is a child prodigy

[ornate blade]

and then there's all the ways the label gets interpreted by society

a huge difference

[snow elm]

Who know how to do calculus at age of 9 (I’m just postulating )

Or smth

Someone may love the label but some might feel pressured

[dapper magnet]

I think if they love the label, they're in for a hard reality check

If they don't, great, that means they have self awareness, which is the first step into recognizing any problem

[snow elm]

Recognising realistic social problems?

[dapper magnet]

Well, thats one of them. 😭

[snow elm]

Mental problems. Self- consciousness problems. The connection between the society and the world problems?

3 major categories of problems

[amber thunder]

Does anyone know some good questions about aithmetic functions (like d(n), sum of divisors, mobius function, dirichlet convolution). IMO/USAMO level

[high goblet]

imo wasn't as big of a thing in india a few years ago cus it wasn't that well-known, but now that it's becoming a bigger thing more ppl r doing it & they're doing quite well now

[wind lance]

can anyone help in preparaion for IOQM

[high goblet]

i mean everyone else has commented that this just isn't true

and also even if we are looking at it statswise that they perform better at IMO than say other countries, if we adjust for population wouldn't that suggest US has a better education than china?

[snow elm]

What

I dont know what u mean

[wind lance]

anyone? pls

[snow elm]

Find a private tutor online

They are professional

[wind lance]

i have a teacher but i wanted someone that can discuss questions and help me out a bit

[snow elm]

Then just post in this channel

[wind lance]

alr ty 😄

[harsh apex]

guys how can i practice comp math there is a site or some thing

[pallid tundra]

aops.com

[untold thunder]

then go to resources and then to alcumus or the community tab

[harsh apex]

ok

someone here doing the putnam problems

[rancid stratus]

someone please break down this question
its for a computing competition that i did in the past but it involves summations

the solutions are uploaded but it looks like a PhD thesis

[green elm]

Sorry its a bit of a strain to read it
Do you mind taking a screenshot from your computer instead? Or even just sending the file if its possible?

[ornate blade]

wrong server

this channel is for maths competitions cause this is the maths server

[fresh zenith]

Hey ,
I got a JEE Advanced Question
Can you solve it

[polar patio]

!da2a

[scarlet root]

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

[fresh zenith]

Let f(x)=∫₀ˣ t³/(t⁴+1) dt and f⁻¹ denote the inverse function of f. Find (f⁻¹)'(π/8).