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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 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
J
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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
J
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hard problem
Noname23   3
N 30 minutes ago by Noname23
problem
3 replies
Noname23
Sunday at 4:57 PM
Noname23
30 minutes ago
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average FE
KevinYang2.71   78
N 35 minutes ago by rhydon516
Source: USAJMO 2024/5
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ that satisfy
\[ f(x^2-y)+2yf(x)=f(f(x))+f(y) \]for all $x,y\in\mathbb{R}$.

Proposed by Carl Schildkraut
78 replies
KevinYang2.71
Mar 21, 2024
rhydon516
35 minutes ago
J
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Roots, bounding and other delusions
anantmudgal09   28
N 37 minutes ago by kes0716
Source: INMO 2021 Problem 6
Let $\mathbb{R}[x]$ be the set of all polynomials with real coefficients. Find all functions $f: \mathbb{R}[x] \rightarrow \mathbb{R}[x]$ satisfying the following conditions:

[list]
[*] $f$ maps the zero polynomial to itself,
[*] for any non-zero polynomial $P \in \mathbb{R}[x]$, $\text{deg} \, f(P) \le 1+ \text{deg} \, P$, and
[*] for any two polynomials $P, Q \in \mathbb{R}[x]$, the polynomials $P-f(Q)$ and $Q-f(P)$ have the same set of real roots.
[/list]

Proposed by Anant Mudgal, Sutanay Bhattacharya, Pulkit Sinha
28 replies
anantmudgal09
Mar 7, 2021
kes0716
37 minutes ago
J
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square geometry bisect $\angle ESB$
GorgonMathDota   11
N 41 minutes ago by miiirz30
Source: BMO SL 2019, G1
Let $ABCD$ be a square of center $O$ and let $M$ be the symmetric of the point $B$ with respect to point $A$. Let $E$ be the intersection of $CM$ and $BD$, and let $S$ be the intersection of $MO$ and $AE$. Show that $SO$ is the angle bisector of $\angle ESB$.
11 replies
GorgonMathDota
Nov 8, 2020
miiirz30
41 minutes ago
J
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Inspired by my own results
sqing   5
N an hour ago by sqing
Source: Own
Let $ a , b $ be reals such that $ a+b+ab=1. $ Show that$$ 1-\frac{1 }{\sqrt2}\le \frac{1}{a^2+1}+\frac{1}{b^2+1}\le 1+\frac{1 }{\sqrt2} $$Let $ a , b\geq 0 $ and $ a+b+ab=1. $ Show that$$ \frac{3}{2}\le \frac{1}{a^2+1}+\frac{1}{b^2+1}\le 1+\frac{1 }{\sqrt2} $$
5 replies
sqing
Yesterday at 8:32 AM
sqing
an hour ago
J
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Interesting inequality
sqing   0
an hour ago
Source: Own
Let $ a,b\geq 2 . $ Prove that
$$ (a^2-1)(b^2-1) (1-ab)+\frac{27}{8}a^2b^2\leq 27$$$$ (a^2-1)(b^2-1)(1-a^2b^2 )+\frac{81}{4}a^2b^2 \leq 189$$$$ (a^2-1)(b^2-1)(1-a^2b^2 )+ 162 ab \leq 513$$$$ (a^2-1)(b^2-1) (1-a^2b^2 )+21 a^2b^2\leq \frac{3219}{16}$$$$ (a^2-1)(b^2-1) (1-ab)+\frac{27}{8}a^2b^2\leq\frac{415+61\sqrt{61}}{18}$$
0 replies
1 viewing
sqing
an hour ago
0 replies
J
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Polygon formed by the edges of an infinite chessboard
AlperenINAN   1
N an hour ago by AlperenINAN
Source: Turkey TST 2025 P5
Let $P$ be a polygon formed by the edges of an infinite chessboard, which does not intersect itself. Let the numbers $a_1,a_2,a_3$ represent the number of unit squares that have exactly $1,2\text{ or } 3$ edges on the boundary of $P$ respectively. Find the largest real number $k$ such that the inequality $a_1+a_2>ka_3$ holds for each polygon constructed with these conditions.
1 reply
AlperenINAN
2 hours ago
AlperenINAN
an hour ago
J
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Interesting inequality
sqing   5
N an hour ago by sqing
Source: Own
Let $ a,b\geq 2 . $ Prove that
$$(a^2-1)(b^2-1) -6ab\geq-15$$$$(a^2-1)(b^2-1) -7ab\geq -\frac{58}{3}$$$$(a^3-1)(b^3-1) -\frac{21}{4}a^2b^2\geq -35$$$$(a^3-1)(b^3-1) -6a^2b^2\geq-\frac{2391}{49}$$
5 replies
sqing
4 hours ago
sqing
an hour ago
J
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Problem 2830
sqing   1
N an hour ago by invisibleman
Source: SXTB (2)2025
Let $ a,b>0 $ and $ \frac{1}{a^2+1}+ \frac{1}{b^2+1}=t $ $(1<t<2). $ Find the value range of $ a+b. $
h
1 reply
sqing
Yesterday at 8:15 AM
invisibleman
an hour ago
J
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Polynomials and powers
rmtf1111   26
N an hour ago by ihategeo_1969
Source: RMM 2018 Day 1 Problem 2
Determine whether there exist non-constant polynomials $P(x)$ and $Q(x)$ with real coefficients satisfying
$$P(x)^{10}+P(x)^9 = Q(x)^{21}+Q(x)^{20}.$$
26 replies
rmtf1111
Feb 24, 2018
ihategeo_1969
an hour ago
J
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A problem
kwin   3
N an hour ago by kwin
Let x, y, z > 0 and sqrt(x) + sqrt(y) + sqrt(z) >= 1. Prove that:
x^2+y^2+z^2 + 7(xy+yz+zx) >= 2.sqrt(2).sqrt((a+b)(b+c)(c+a)
Sorry, This is the first time I post so I don't know how to text as mathtype.
3 replies
kwin
Feb 10, 2025
kwin
an hour ago
J
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Gunn Math Competition
the_math_prodigy   13
N 2 hours ago by the_math_prodigy
Gunn Math Circle is excited to host the fourth annual Gunn Math Competition (GMC)! GMC will take place at Gunn High School in Palo Alto, California on Sunday, March 30th. Gather a team of up to four and compete for over $7,500 in prizes! The contest features three rounds: Individual, Guts, and Team. We welcome participants of all skill levels, with separate Beginner and Advanced divisions for all students.

Registration is free and now open at compete.gunnmathcircle.org. The deadline to sign up is March 27th.

Special Guest Speaker: Po-Shen Loh!!!
We are honored to welcome Po-Shen Loh, a world-renowned mathematician, Carnegie Mellon professor, and former coach of the USA International Math Olympiad team. He will deliver a 30-minute talk to both students and parents, offering deep insights into mathematical thinking and problem-solving in the age of AI!

View competition manual, schedule, prize pool at compete.gunnmathcircle.org . Stay updated by joining our Discord discord.gg/fqcxukv3Dq server. For any questions, reach out at ghsmathcircle@gmail.com or ask in Discord.
13 replies
the_math_prodigy
Mar 8, 2025
the_math_prodigy
2 hours ago
J
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[TEST RELEASED] Mock Geometry Test for College Competitions
Bluesoul   12
N 3 hours ago by Bluesoul
Hi AOPSers,

I have finished writing a mock geometry test for fun and practice for the real college competitions like HMMT/PUMaC/CMIMC... There would be 10 questions and you should finish the test in 60 minutes, the test would be close to the actual test (hopefully). You could sign up under this thread, PM me your answers!. The submission would close on March 31st at 11:59PM PST.

I would create a private discussion forum so everyone could discuss after finishing the test. This is the first mock I've written, please sign up and enjoy geometry!!

~Bluesoul

Leaderboard
12 replies
Bluesoul
Feb 24, 2025
Bluesoul
3 hours ago
J
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[Registration Open] Mustang Math Tournament 2025
MustangMathTournament   31
N 5 hours ago by ethan2011
Mustang Math is excited to announce that registration for our annual tournament, MMT 2025, is open! This year, we are bringing our tournament to 9 in-person locations, as well as online!

Locations include: Colorado, Norcal, Socal, Georgia, Illinois, Massachusetts, New Jersey, Nevada, Washington, and online. For registration and more information, check out https://mustangmath.com/competitions/mmt-2025.

MMT 2025 is a math tournament run by a group of 150+ mathematically experienced high school and college students who are dedicated to providing a high-quality and enjoyable contest for middle school students. Our tournament centers around teamwork and collaboration, incentivizing students to work with their teams not only to navigate the challenging and interesting problems of the tournament but also to develop strategies to master the unique rounds. This includes a logic puzzle round, a strategy-filled hexes round, a race-like gallop round, and our trademark ‘Mystery Mare’ round!

Awards:
[list]
[*] Medals for the top teams
[*] Shirts, pins, stickers and certificates for all participants
[*] Additional awards provided by our wonderful sponsors!
[/list]

We are also holding a free MMT prep seminar from 3/15-3/16 to help students prepare for the upcoming tournament. Join the Google Classroom! https://classroom.google.com/c/NzQ5NDUyNDY2NjM1?cjc=7sogth4
31 replies
MustangMathTournament
Mar 8, 2025
ethan2011
5 hours ago
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AMC 10.........
BAM10   8
N Today at 2:19 AM by ChickensEatGrass
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
8 replies
BAM10
Mar 2, 2025
ChickensEatGrass
Today at 2:19 AM
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AMC 10.........
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Reveal topic tags
AMC 10
AMC 8
MATHCOUNTS
AIME
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BAM10
67 posts
BAM10
#1 h  Mar 2, 2025, 8:02 PM
Y by
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
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orangebear
610 posts
orangebear
#2 h  Mar 2, 2025, 8:04 PM
Y by
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.
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CYW
326 posts
CYW
#3 h  Mar 2, 2025, 9:06 PM
Y by
Dunno, opposite way for me. I got 80-something on AMC 10 (cutoff mid 90's) and got 37 on MATHCOUNTS chapter
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Airbus320-214
77 posts
Airbus320-214
#4 h  Mar 3, 2025, 3:07 AM
Y by
Practice past problems of amc 10/12
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nxchman
21 posts
nxchman
#5 h  Mar 3, 2025, 9:09 PM
Y by
BAM10 wrote:
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?

Im in the same boat lol. Im in 8th grade and I never took amc 10, but this year I got 22 on amc 8.
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iwillregretthisnamelater
1 post
iwillregretthisnamelater
#6 h  Today at 1:59 AM
Y by
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard
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sadas123
1034 posts
sadas123
#7 h  Today at 2:04 AM
Y by
iwillregretthisnamelater wrote:
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard

Same except I am a 6th grader that got 24 on AMC 8 and a 37 on mathcounts chapter :(
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jb2015007
1698 posts
jb2015007
#8 h  Today at 2:09 AM
Y by
orangebear wrote:
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.

bruh i got a 51 on AMC 10 and got a 35 on mc chapter
(im better now relax im mocking 90+)
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ChickensEatGrass
26 posts
ChickensEatGrass
#9 h  Today at 2:19 AM
Y by
I'm an 8th grader and I got 25 on amc8 but only 40 on chapter, I made aime barely this year but I got like problem 4 wrong on 10a :wallbash_red:
so yes with your stats you have a decent chance, just study more and do past mocks, you can find them here on aops.
try to aim for at least 100. This year's cutoff for 10a was really low (94.5) but most years it's higher.
because you are in alg2, I'd recommend doing some geometry because there are several of those problems. maybe also start trig because they can provide faster solutions to them. but alg2 is a good start.
And make sure to not make sillies!!!!!!!!!! but I cant rlly say anything about that because i myself make 100000000 sillies every day :whistling:
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