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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
Need help with combi problems
JARP091   0
24 minutes ago
I want to create a problem set of some of the hardest combi problems that are yet to appear in any contest. Can anyone help me out? Also can anyone give me some tips to create combi problems.
0 replies
JARP091
24 minutes ago
0 replies
graph thory
o.k.oo   0
an hour ago
There are 10 people at a party. None of the 3 friends of each person are friends with each other. What is the maximum number of friends at this party?
0 replies
o.k.oo
an hour ago
0 replies
IMO Shortlist 2012, Geometry 8
lyukhson   33
N an hour ago by awesomeming327.
Source: IMO Shortlist 2012, Geometry 8
Let $ABC$ be a triangle with circumcircle $\omega$ and $\ell$ a line without common points with $\omega$. Denote by $P$ the foot of the perpendicular from the center of $\omega$ to $\ell$. The side-lines $BC,CA,AB$ intersect $\ell$ at the points $X,Y,Z$ different from $P$. Prove that the circumcircles of the triangles $AXP$, $BYP$ and $CZP$ have a common point different from $P$ or are mutually tangent at $P$.

Proposed by Cosmin Pohoata, Romania
33 replies
lyukhson
Jul 29, 2013
awesomeming327.
an hour ago
Proof Writing Help
gulab_jamun   1
N an hour ago by Gavin_Deng
Ok so like, i'm working on proofs, and im prolly gonna use this page for any questions. My question as of now is what can I cite? Like for example, if for a question I use Evan Chen's fact 5, in my proof do I have to prove fact 5 all over again or can i say "this result follows from Evan Chen's fact 5"?
1 reply
gulab_jamun
3 hours ago
Gavin_Deng
an hour ago
for the contest high achievers, can you share your math path?
HCM2001   30
N an hour ago by mhgelgi
Hi all
Just wondering if any orz or high scorers on contests at young age (which are a lot of u guys lol) can share what your math path has been like?
- school math: you probably finish calculus in 5th grade or something lol then what do you do for the rest of the school? concurrent enrollment? college class? none (focus on math competitions)?
- what grade did you get honor roll or higher on AMC 8, AMC 10, AIME qual, USAJMO qual, etc?
- besides aops do you use another program to study? (like Mr Math, Alphastar, etc)?

You're all great inspirations and i appreciate the answers.. you all give me a lot of motivation for this math journey. Thanks
30 replies
HCM2001
Wednesday at 7:50 PM
mhgelgi
an hour ago
Consecutive squares are floors
ICE_CNME_4   11
N 2 hours ago by ICE_CNME_4

Determine how many positive integers \( n \) have the property that both
\[
\left\lfloor \sqrt{2n - 1} \right\rfloor \quad \text{and} \quad \left\lfloor \sqrt{3n + 2} \right\rfloor
\]are consecutive perfect squares.
11 replies
ICE_CNME_4
Yesterday at 1:50 PM
ICE_CNME_4
2 hours ago
Finding all possible $n$ on a strange division condition!!
MathLuis   10
N 2 hours ago by justaguy_69
Source: Bolivian Cono Sur Pre-TST 2021 P1
Find the sum of all positive integers $n$ such that
$$\frac{n+11}{\sqrt{n-1}}$$is an integer.
10 replies
1 viewing
MathLuis
Nov 12, 2021
justaguy_69
2 hours ago
IMO 2012 P5
mathmdmb   123
N 2 hours ago by SimplisticFormulas
Source: IMO 2012 P5
Let $ABC$ be a triangle with $\angle BCA=90^{\circ}$, and let $D$ be the foot of the altitude from $C$. Let $X$ be a point in the interior of the segment $CD$. Let $K$ be the point on the segment $AX$ such that $BK=BC$. Similarly, let $L$ be the point on the segment $BX$ such that $AL=AC$. Let $M$ be the point of intersection of $AL$ and $BK$.

Show that $MK=ML$.

Proposed by Josef Tkadlec, Czech Republic
123 replies
mathmdmb
Jul 11, 2012
SimplisticFormulas
2 hours ago
Fixed line
TheUltimate123   14
N 2 hours ago by amirhsz
Source: ELMO Shortlist 2023 G4
Let \(D\) be a point on segment \(PQ\). Let \(\omega\) be a fixed circle passing through \(D\), and let \(A\) be a variable point on \(\omega\). Let \(X\) be the intersection of the tangent to the circumcircle of \(\triangle ADP\) at \(P\) and the tangent to the circumcircle of \(\triangle ADQ\) at \(Q\). Show that as \(A\) varies, \(X\) lies on a fixed line.

Proposed by Elliott Liu and Anthony Wang
14 replies
TheUltimate123
Jun 29, 2023
amirhsz
2 hours ago
Convolution of order f(n)
trumpeter   76
N 2 hours ago by ray66
Source: 2019 USAMO Problem 1
Let $\mathbb{N}$ be the set of positive integers. A function $f:\mathbb{N}\to\mathbb{N}$ satisfies the equation \[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]for all positive integers $n$. Given this information, determine all possible values of $f(1000)$.

Proposed by Evan Chen
76 replies
trumpeter
Apr 17, 2019
ray66
2 hours ago
Computing functions
BBNoDollar   7
N 2 hours ago by ICE_CNME_4
Let $f : [0, \infty) \to [0, \infty)$, $f(x) = \dfrac{ax + b}{cx + d}$, with $a, d \in (0, \infty)$, $b, c \in [0, \infty)$. Prove that there exists $n \in \mathbb{N}^*$ such that for every $x \geq 0$
\[
f_n(x) = \frac{x}{1 + nx}, \quad \text{if and only if } f(x) = \frac{x}{1 + x}, \quad \forall x \geq 0.
\](For $n \in \mathbb{N}^*$ and $x \geq 0$, the notation $f_n(x)$ represents $\underbrace{(f \circ f \circ \dots \circ f)}_{n \text{ times}}(x)$. )
7 replies
BBNoDollar
May 18, 2025
ICE_CNME_4
2 hours ago
RMO 2024 Q2
SomeonecoolLovesMaths   14
N 2 hours ago by Adywastaken
Source: RMO 2024 Q2
For a positive integer $n$, let $R(n)$ be the sum of the remainders when $n$ is divided by $1,2, \cdots , n$. For example, $R(4) = 0 + 0 + 1 + 0 = 1,$ $R(7) = 0 + 1 + 1 + 3 + 2 + 1 + 0 = 8$. Find all positive integers such that $R(n) = n-1$.
14 replies
SomeonecoolLovesMaths
Nov 3, 2024
Adywastaken
2 hours ago
Decimal functions in binary
Pranav1056   3
N 3 hours ago by ihategeo_1969
Source: India TST 2023 Day 3 P1
Let $\mathbb{N}$ be the set of all positive integers. Find all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that $f(x) + y$ and $f(y) + x$ have the same number of $1$'s in their binary representations, for any $x,y \in \mathbb{N}$.
3 replies
Pranav1056
Jul 9, 2023
ihategeo_1969
3 hours ago
Beautiful numbers in base b
v_Enhance   21
N 3 hours ago by Martin2001
Source: USEMO 2023, problem 1
A positive integer $n$ is called beautiful if, for every integer $4 \le b \le 10000$, the base-$b$ representation of $n$ contains the consecutive digits $2$, $0$, $2$, $3$ (in this order, from left to right). Determine whether the set of all beautiful integers is finite.

Oleg Kryzhanovsky
21 replies
v_Enhance
Oct 21, 2023
Martin2001
3 hours ago
How is it possible
deduck   4
N Apr 17, 2025 by EaZ_Shadow
I see a lot of people on aops who get "lucky" sometimes and get "unlucky" sometimes, and i think i have had lucky and unlucky times before.

but i want to know what exactly causes you get lucky or unlucky? i heard people saying the more u work the luckier u get. but i bombed amc and aime this year despite working alot (i mean mainly olympiad problems but i did do mocks and computational problems before :|). so why do u just get lucky or unlucky. Is it possible to get lucky if ur under pressure too much, like if u care too much about ur results?

Also, on another topic this year my aime testing room (i took it at my school) was super loud and kids kept walking through and talking. it's like the only free room in the school, the other one smells really bad and has 0 ventilation and gives lung cancer. i get distracted sometimes when people talk so loudly and for some reason maybe pressure i ended up doing alot worse than my usual mocks and missed usamo :/. if i solved 1 more problem wouldve made. sucks cuz i mainly grinded olympiads. so what do u guys think i should do, should i take it at the aops academy near me? or should i just stay at my school?

has this situation happened for anyone else, what did u do about it?
4 replies
deduck
Apr 17, 2025
EaZ_Shadow
Apr 17, 2025
How is it possible
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deduck
237 posts
#1 • 6 Y
Y by PikaPika999, KevinYang2.71, Alex-131, Awesomeness_in_a_bun, megarnie, bjump
I see a lot of people on aops who get "lucky" sometimes and get "unlucky" sometimes, and i think i have had lucky and unlucky times before.

but i want to know what exactly causes you get lucky or unlucky? i heard people saying the more u work the luckier u get. but i bombed amc and aime this year despite working alot (i mean mainly olympiad problems but i did do mocks and computational problems before :|). so why do u just get lucky or unlucky. Is it possible to get lucky if ur under pressure too much, like if u care too much about ur results?

Also, on another topic this year my aime testing room (i took it at my school) was super loud and kids kept walking through and talking. it's like the only free room in the school, the other one smells really bad and has 0 ventilation and gives lung cancer. i get distracted sometimes when people talk so loudly and for some reason maybe pressure i ended up doing alot worse than my usual mocks and missed usamo :/. if i solved 1 more problem wouldve made. sucks cuz i mainly grinded olympiads. so what do u guys think i should do, should i take it at the aops academy near me? or should i just stay at my school?

has this situation happened for anyone else, what did u do about it?
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Alex-131
5392 posts
#2 • 4 Y
Y by PikaPika999, Pengu14, deduck, pineapply
“luck is not something to be found just anywhere. Rather, it is something that descends only upon those standing where it will drop.” (Ego).

Imo, I believe that luck is just luck. Consider this scenario, you're walking on a street and you have to get to a store. You can either go right or left. You randomly pick the right side, and coincidentally, a group of pigeons sht on you. Was it really the pigeons fault? Or rather, was it your mistake to go right?

You might ask, I did not know that there would be pigeons on the right side. But, that does not matter. The analogy is the same if you went right and suddenly encountered a leprechaun, and now you're a millionaire.

Whatever path you choose, you don't know what happens ahead, so just pick one and go. (slightly off-topic, but perhaps relevant).

To answer your question (im even worse at amcs, but still), I don't think that working hard = or even implies success. I had a personal experience in sports where I genuinely worked harder than my teammates or other athletes, went to nationals, and completely bombed. The recipients of luck mostly happen to be those people at the top of their respective fields.

I also found this article slightly interesting: https://jurisarrozy.wordpress.com/2021/11/15/eng-two-types-of-luck-and-their-mechanisms/
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LearnMath_105
154 posts
#3
Y by
just watch blue lock atp, i have a similar situation (not as bad as yours though) so I found a different center even though its way farther away.
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abbominable_sn0wman
62 posts
#4
Y by
there's so much about these contests entirely out of your control. a few personal examples:
mathcounts states 2022:
- bad cough and no water, literally was dying the entire target round
2023 10A:
- had to rush to comp from orthodontist apt.
- mild nose bleed 10 mins in (i forced my math teacher to get me tissues cuz no way was i getting up)
- computers glitched out last 30 mins & no paper test
2024 AIME:
- guy tuning a piano outside during the 2nd hour

oh yeah also im a lefty so essentially every college contest if i dont get a lefty seat im cooked
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EaZ_Shadow
1275 posts
#5
Y by
Alex-131 wrote:
“luck is not something to be found just anywhere. Rather, it is something that descends only upon those standing where it will drop.” (Ego).

Imo, I believe that luck is just luck. Consider this scenario, you're walking on a street and you have to get to a store. You can either go right or left. You randomly pick the right side, and coincidentally, a group of pigeons sht on you. Was it really the pigeons fault? Or rather, was it your mistake to go right?

You might ask, I did not know that there would be pigeons on the right side. But, that does not matter. The analogy is the same if you went right and suddenly encountered a leprechaun, and now you're a millionaire.

Whatever path you choose, you don't know what happens ahead, so just pick one and go. (slightly off-topic, but perhaps relevant).

To answer your question (im even worse at amcs, but still), I don't think that working hard = or even implies success. I had a personal experience in sports where I genuinely worked harder than my teammates or other athletes, went to nationals, and completely bombed. The recipients of luck mostly happen to be those people at the top of their respective fields.

I also found this article slightly interesting: https://jurisarrozy.wordpress.com/2021/11/15/eng-two-types-of-luck-and-their-mechanisms/

Blue lock reference yessir!
Veritasium has a really great video about it. makes a lot of sense
This post has been edited 1 time. Last edited by EaZ_Shadow, Apr 17, 2025, 11:27 PM
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