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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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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
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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
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Discuss the Stanford Math Tournament Here
Aaronjudgeisgoat   204
N 41 minutes ago by Agrivulture
I believe discussion is allowed after yesterday at midnight, correct?
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag

Answers for the Algebra Subject Test
Estimated Algebra Cutoffs
Answers for the Geometry Subject Test
Estimated Geo Cutoffs
Answers for the Discrete Subject Test
Estimated Cutoffs for Discrete
Answers for the Team Round
Guts Answers
204 replies
Aaronjudgeisgoat
Yesterday at 1:44 PM
Agrivulture
41 minutes ago
J
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Weird Inequality Problem
Omerking   1
N an hour ago by Nuran2010
Following inequality is given:
$$3\geq ab+bc+ca\geq \dfrac{1}{3}$$Find the range of values that can be taken by :
$1)a+b+c$
$2)abc$

Where $a,b,c$ are positive reals.
1 reply
Omerking
2 hours ago
Nuran2010
an hour ago
J
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Weakly-periodic functions compared with lines
Miquel-point   2
N an hour ago by dgrozev
Source: KoMaL A. 895
Let's call a function $f:\mathbb R\to\mathbb R$ weakly periodic if it is continuous and $f(x+1)=f(f(x))+1$ for all $x\in\mathbb R$.
a) Does there exist a weakly periodic function such that $f(x)>x$ for all $x\in\mathbb R$?
b) Does there exist a weakly periodic function such that $f(x)<x$ for all $x\in\mathbb R$?

Proposed by: András Imolay, Budapest
2 replies
Miquel-point
Jan 13, 2025
dgrozev
an hour ago
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Beatty sequences of continued fractions
Miquel-point   1
N 2 hours ago by starchan
Source: KoMaL A. 903
Let the irrational number
\[\alpha =1-\cfrac{1}{2a_1-\cfrac{1}{2a_2-\cfrac{1}{2a_3-\cdots}}}\]where coefficients $a_1, a_2, \ldots$ are positive integers, infinitely many of which are greater than $1$. Prove that for every positive integer $N$ at least half of the numbers $\lfloor \alpha\rfloor, \lfloor 2\alpha\rfloor, \ldots, \lfloor N\alpha\rfloor$ are even.

Proposed by Géza Kós, Budapest
1 reply
Miquel-point
Yesterday at 5:41 PM
starchan
2 hours ago
J
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Easy Inceter related geometry
Pluto1708   10
N 2 hours ago by ihategeo_1969
Source: STEMS 2021/CAT B/P3
Let $ABC$ be a triangle with $I$ as incenter.The incircle touches $BC$ at $D$.Let $D'$ be the antipode of $D$ on the incircle.Make a tangent at $D'$ to incircle.Let it meet $(ABC)$ at $X,Y$ respectively.Let the other tangent from $X$ meet the other tangent from $Y$ at $Z$.Prove that $(ZBD)$ meets $IB$ at the midpoint of $IB$
10 replies
Pluto1708
Jan 24, 2021
ihategeo_1969
2 hours ago
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Functional Equation:
Omerking   3
N 2 hours ago by Nuran2010
Find all functions $f:\mathbb {R}\rightarrow \mathbb {R}$ such that:
$$f(x^2f(x)+f(y))=(f(x))^3+y$$
3 replies
Omerking
Apr 9, 2025
Nuran2010
2 hours ago
J
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Interesting inequalities
sqing   0
2 hours ago
Source: Own
Let $ a,b $ be reals such that $ a^2+ab+b^2 =1$ . Prove that
$$ \frac{8}{ 5 }> \frac{1}{ a^2+1 }+ \frac{1}{ b^2+1 } \geq 1$$$$ \frac{9}{ 5 }\geq\frac{1}{ a^4+1 }+ \frac{1}{ b^4+1 } \geq 1$$$$ \frac{27}{ 14 }\geq \frac{1}{ a^6+1 }+ \frac{1}{ b^6+1 } \geq 1$$Let $ a,b $ be reals such that $ a^2+ab+b^2 =3$ . Prove that
$$ \frac{13}{ 10 }> \frac{1}{ a^2+1 }+ \frac{1}{ b^2+1 } \geq \frac{1}{ 2 }$$$$ \frac{6}{ 5 }>\frac{1}{ a^4+1 }+ \frac{1}{ b^4+1 } \geq \frac{1}{ 5 }$$$$ \frac{1}{ a^6+1 }+ \frac{1}{ b^6+1 } \geq \frac{1}{ 14 }$$
0 replies
1 viewing
sqing
2 hours ago
0 replies
J
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Yet another inequality
giangtruong13   2
N 2 hours ago by lbh_qys
Source: From my friend
Let $a,b,c$ be real positive number satisfy that: $a+b+c=3$. Find the max: $$\sum_{cyc} \frac{a^3}{a^2+bc}$$
2 replies
giangtruong13
3 hours ago
lbh_qys
2 hours ago
J
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R+ Functional Equation
Mathdreams   10
N 2 hours ago by TestX01
Source: Nepal TST 2025, Problem 3
Find all functions $f : \mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that \[f(f(x)) + xf(xy) = x + f(y)\]for all positive real numbers $x$ and $y$.

(Andrew Brahms, USA)
10 replies
Mathdreams
Apr 11, 2025
TestX01
2 hours ago
J
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hard problem
Cobedangiu   18
N 3 hours ago by giangtruong13
problem
18 replies
Cobedangiu
Mar 27, 2025
giangtruong13
3 hours ago
J
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Not so common problem
m4thbl3nd3r   1
N 3 hours ago by lbh_qys
With each $x\ne -2,-3$, define $f_1(x)=-\frac{3x+7}{x+2},f_2(x)=f_1(f_1(x))=-\frac{3f_1(x)+7}{f_1(x)+2},f_3(x)=f_1(f_2(x))=-\frac{3f_2(x)+7}{f_2(x)+2},\dots$ Find all integers $x$ such that $f_{269}(x)$ is an integer.
1 reply
m4thbl3nd3r
4 hours ago
lbh_qys
3 hours ago
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Is my approach right?
cowcheese   1
N 4 hours ago by YauYauFilter
Source: AMC12B 2019 p11
How many unordered pairs of edges of a given cube determine a plane?

a. 12. b. 28 c. 36 d. 42. e. 66

I ended up with the right answer. However, no solutions resembled the way I did it, which is why I'm skeptical. After a few failed attempts with other ways of solving (didn't get an answer in the answer options), I decided to use complementary counting, and counted invalid pairs (pairs that don't satisfy the condition given by the problem). To do that I drew out the cube and found for each side, there are 4 sides that will make an invalid pair with it. Because there are 12 sides to a cube, I did 12*4. But, each distinct pair in that 12*4 is counted twice. So, dividing 12*4 by 2 will give 24 invalid pairs. Now, for total pairs, it is 12 choose 2, which is 66. 66-24 = 42. Hence, the answer is 42.

So, is there anything wrong with the way I did it? Is there a specific reason this wasn't a posted solution?

Thanks!
1 reply
cowcheese
Yesterday at 9:33 PM
YauYauFilter
4 hours ago
J
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9 Which math contest is your favorite?
mdk2013   80
N 4 hours ago by fidgetboss_4000
links for details on each comp

i think thats all the major ones, comment if you have any more that i forgot to include

upvote if you're like me and you think MATHCOUNTS is obv better!

EDIT: i forgot ARML and JBMO, comment if you like those
80 replies
mdk2013
Mar 30, 2025
fidgetboss_4000
4 hours ago
J
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2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   47
N Today at 3:05 AM by Lightybird
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary

Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


47 replies
audio-on
Jan 26, 2025
Lightybird
Today at 3:05 AM
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Why did my account set back to bronze?
Wisteriaaa   2
N Mar 29, 2025 by ethan2011
Hey, guys! I passed bronze division in Feb 2024 and silver in Jan 2025, but then I found I only could enter bronze division in Feb. What's going wrong with my account? :wacko:
2 replies
Wisteriaaa
Mar 29, 2025
ethan2011
Mar 29, 2025
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Why did my account set back to bronze?
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Reveal topic tags
Usaco
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Wisteriaaa
1 post
Wisteriaaa
#1 h  Mar 29, 2025, 3:02 AM
Y by
Hey, guys! I passed bronze division in Feb 2024 and silver in Jan 2025, but then I found I only could enter bronze division in Feb. What's going wrong with my account? :wacko:
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exp-ipi-1
1073 posts
exp-ipi-1
#2 h  Mar 29, 2025, 3:08 AM
Y by
perhaps you might be cooked
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ethan2011
272 posts
ethan2011
#3 h  Mar 29, 2025, 3:10 AM
Y by
Wisteriaaa wrote:
Hey, guys! I passed bronze division in Feb 2024 and silver in Jan 2025, but then I found I only could enter bronze division in Feb. What's going wrong with my account? :wacko:

Maybe you should send an email to them?
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