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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.

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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.
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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
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9 What motivates you
AndrewZhong2012   60
N a few seconds ago by giangtruong13
What got you guys into math? I'm asking because I got ~71 on the AMC 12B and 94.5 on 10A last year. This year, my dad expects me to get a 130 on 12B and 10 on AIME, but I have sort of lost motivation, and I know these goals will be impossible to achieve without said motivation.
60 replies
AndrewZhong2012
Feb 22, 2025
giangtruong13
a few seconds ago
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U.S.J.A.M.O tips from a superstar!
K-Cliquey   28
N a few seconds ago by scannose
Source: smart people
Hi every body. I know it is very stressful because the U.S.J.A.M.O. is soon, I just want to make sure everyone pays attention to their mental health. Every day, remember mental health is more important than U.S.J.A.M.Ο.

And I used to be worse than my friend at U.S.J.A.M.O., but I improve, so here are my tips for making sure mental health on the U.S.J.A.M.O.


1. Drink water. You are not cactus.


2. Don't drink too much water. Or else you will pee.


3. Get protein. I recommend cow meat.


4. (I am serious) Have a girlfriend or a boyfriend. I got rejected 8 times before I met Lennon Court, but he is my best emotional support on the U.S.J.A.M.O. now. It is good emotional support.


5. Sleep early. I know you guys are scared of dreaming about bad U.S.J.A.M.O. grade, but just think about #4 so you can get mental healthy from sleep instead of nightmare.


6. Social to your friends! They are also good mental healthy support.



Now, most importantly, ADD YOUR TIPS TO THIS LIST. PLEASE COMMENT DOWN BELOW YOUR TIPS FOR GOOD MENTAL HEALTH. We are a TEAM to have good MENTAL HEALTH.
28 replies
+2 w
K-Cliquey
Today at 4:56 AM
scannose
a few seconds ago
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BMN is equilateral iff rectangle ABCD is square
parmenides51   4
N an hour ago by Tsikaloudakis
Source: 2004 Romania NMO SL - Shortlist VII-VIII p8 https://artofproblemsolving.com/community/c3950157_
Consider a point $M$ on the diagonal $BD$ of a given rectangle $ABCD$, such that $\angle AMC = \angle CMD$. The point $N$ is the intersection point between $AM$ and the parallel line to $CM$ that contains $B$. Prove that the triangle $BMN$ is equilateral if and only if $ABCD$ is a square.

Valentin Vornicu
4 replies
parmenides51
Sep 16, 2024
Tsikaloudakis
an hour ago
J
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Loop of Logarithms
scls140511   10
N an hour ago by SomeonecoolLovesMaths
Source: 2024 China Round 1 (Gao Lian)
Round 1

1 Real number $m>1$ satisfies $\log_9 \log_8 m =2024$. Find the value of $\log_3 \log_2 m$.
10 replies
scls140511
Sep 8, 2024
SomeonecoolLovesMaths
an hour ago
J
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Proving a kite
Bugi   4
N an hour ago by ali123456
Source: Serbian JBTST 3, Day 2
Let $ ABCD$ be a convex quadrilateral, such that

$ \angle CBD=2\cdot\angle ADB, \angle ABD=2\cdot\angle CDB$ and $ AB=CB$.

Prove that quadrilateral $ ABCD$ is a kite.
4 replies
Bugi
May 31, 2009
ali123456
an hour ago
J
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Inequality
Marinchoo   6
N 2 hours ago by sqing
If $abc=1$ prove that $8(a^3+b^3+c^3) \geq 3(a^2+bc)(b^2+ac)(c^2+ab)$
6 replies
Marinchoo
Apr 28, 2020
sqing
2 hours ago
J
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Interesting inequality
sqing   4
N 2 hours ago by sqing
Source: Own
Let $ a,b,c\geq 2 . $ Prove that
$$(a^2-1)(b-1)(c^2-1) -\frac{9}{4}abc\geq -9$$$$(a^2-1)(b-1)(c^2-1) -\frac{11}{5}abc\geq -\frac{43}{5}$$$$(a^2-1)(b-1)(c^2-1) -2abc\geq -7$$$$(a-1)(b^2-1)(c-1) -\frac{3}{4}abc\geq -3$$$$(a-1)(b^2-1)(c-1) -\frac{3}{5}abc\geq -\frac{9}{5}$$$$(a-1)(b^2-1)(c-1) -\frac{1}{2}abc\geq -1$$
4 replies
sqing
3 hours ago
sqing
2 hours ago
J
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Orthocentre is collinear with two tangent points
vladimir92   42
N 2 hours ago by AshAuktober
Source: Chinese MO 1996
Let $\triangle{ABC}$ be a triangle with orthocentre $H$. The tangent lines from $A$ to the circle with diameter $BC$ touch this circle at $P$ and $Q$. Prove that $H,P$ and $Q$ are collinear.
42 replies
vladimir92
Jul 29, 2010
AshAuktober
2 hours ago
J
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Problem 4
den_thewhitelion   3
N 2 hours ago by DensSv
Source: Second Romanian JBMO TST 2016
We have a 4x4 board.All 1x1 squares are white.A move is changing colours of all squares of a 1x3 rectangle from black to white and from white to black.It is possible to make all the 1x1 squares black after several moves?
3 replies
den_thewhitelion
Jun 15, 2016
DensSv
2 hours ago
J
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Find the period
Anto0110   2
N 2 hours ago by YaoAOPS
Let $a_1, a_2, ..., a_k, ...$ be a sequence that consists of an initial block of $p$ positive distinct integers that then repeat periodically. This means that $\{a_1, a_2, \dots, a_p\}$ are $p$ distinct positive integers and $a_{n+p}=a_n$ for every positive integer $n$. The terms of the sequence are not known and the goal is to find the period $p$. To do this, at each move it possible to reveal the value of a term of the sequence at your choice.
If $p$ is one of the first $k$ prime numbers, find for which values of $k$ there exist a strategy that allows to find $p$ revealing at most $8$ terms of the sequence.
2 replies
Anto0110
Yesterday at 7:37 PM
YaoAOPS
2 hours ago
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Good luck on olympiads tomorrow!
observer04   5
N 2 hours ago by ElectricWolverine
Hello mortals!

For those of you that qualified for the USAMO / USAJMO, I have a message for you! Remember to have fun! And enjoy the experience! Personally, I did not qualify for the USAMO / USAJMO! But I am still eager to try the high quality thought-provoking problems! As I once said... it's not all about the score!

Furthermore, for those like myself who failed along the way, it's A-OK! Don't worry, fellows! Remember to smile and enjoy your lives! There is more than math out there!


Warmest Regards
5 replies
observer04
Today at 1:27 AM
ElectricWolverine
2 hours ago
J
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Very interesting inequality
sqing   0
2 hours ago
Source: Own
Let $ a,b,c\geq 2 . $ Prove that
$$(a-1)(b^2-2)(c^3-3)- \frac{5}{2}abc\geq -10$$$$(a-\frac{3}{2})(b^2-2)(c^3-3)- \frac{5}{2}abc\geq -15$$$$(a-\frac{3}{2})(b^2-\frac{3}{2})(c^3-3)- \frac{25}{8}abc\geq - \frac{155}{8}$$$$(a-\frac{3}{2})(b^2-\frac{3}{2})(c^3-3)- 3abc\geq - \frac{363}{20}$$$$(a-\frac{3}{2})(b^2-\frac{3}{2})(c^3-\frac{5}{2})- \frac{55}{16}abc\geq - \frac{341}{16}$$
0 replies
sqing
2 hours ago
0 replies
J
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inequality
senku23   3
N 2 hours ago by SunnyEvan
Let x,y,z in R+ prove that 8(x^3+y^3+z^3)2≥9(x^2+yz)(y^2+zx)(z^2+xy).
3 replies
senku23
5 hours ago
SunnyEvan
2 hours ago
J
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College Math Competitions
gavinhaominwang   6
N Today at 7:41 AM by xHypotenuse
What are the major competitions that take place at college? For example HMMT.
6 replies
gavinhaominwang
Today at 1:39 AM
xHypotenuse
Today at 7:41 AM
J
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J
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AMC 12 Question
sadas123   12
N Today at 2:50 AM by jb2015007
Hello! I am a 6th grader this year about to become 7th grade next year. I was wondering if I should take the AMC 12 next year because I think I am ready for it, I was thinking to do AMC 10 A and AMC 12 B, do you think it is a good idea? Here are the courses I finished and now I am working on:

Finished:
1. Intro Algebra
2. Intro Number Theory
3. Intro Counting and Probability
4. Volume 1

Working on:
1. Intermdiate Counting and Probability
2. Three Year Mathcounts Marathon

Upcoming:
1. Intro Geomtery (Next Month)
2. Intro to Alg (May)
3. Pre-calc (Summer)
4. Volume 2???

Stats for AMC 12 (Mocked):

1. AMC 12 A 2024: 100.5
2. AMC 12 B 2024: 105
3. AMC 12 A 2023: 96

The reason why I sometimes I get 100+ is because sometimes I know how to do the first step of the problem but the last step I have to kind of infrence but still i know how to do the problem.
12 replies
sadas123
Yesterday at 5:11 PM
jb2015007
Today at 2:50 AM
J
AMC 12 Question
G H J
Reveal topic tags
AMC
AMC 12
AMC 10
AMC 10 A
AMC 12 B
number theory
probability
L
G H BBookmark kLocked kLocked NReply
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sadas123
1057 posts
sadas123
#1 h  Yesterday at 5:11 PM
Y by
Hello! I am a 6th grader this year about to become 7th grade next year. I was wondering if I should take the AMC 12 next year because I think I am ready for it, I was thinking to do AMC 10 A and AMC 12 B, do you think it is a good idea? Here are the courses I finished and now I am working on:

Finished:
1. Intro Algebra
2. Intro Number Theory
3. Intro Counting and Probability
4. Volume 1

Working on:
1. Intermdiate Counting and Probability
2. Three Year Mathcounts Marathon

Upcoming:
1. Intro Geomtery (Next Month)
2. Intro to Alg (May)
3. Pre-calc (Summer)
4. Volume 2???

Stats for AMC 12 (Mocked):

1. AMC 12 A 2024: 100.5
2. AMC 12 B 2024: 105
3. AMC 12 A 2023: 96

The reason why I sometimes I get 100+ is because sometimes I know how to do the first step of the problem but the last step I have to kind of infrence but still i know how to do the problem.
This post has been edited 2 times. Last edited by sadas123, Yesterday at 5:15 PM
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Stormbreaker7984
839 posts
Stormbreaker7984
#2 h  Yesterday at 5:49 PM • 1 Y
Y by tofubear
no harm in trying man if you don't qualify you can always try in 8th 9th and on. but those mocks are rlly good u def have a chance of aime qual on both more so 10 than 12
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jb2015007
1703 posts
jb2015007
#3 h  Yesterday at 6:00 PM • 2 Y
Y by tofubear, ibmo0907
take AMC 10 bro AMC 12 only in 11,12 trust
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sadas123
1057 posts
sadas123
#4 h  Yesterday at 6:09 PM
Y by
Ok thanks! I guess I will still decide, because I am taking the pre-calc online course and this is the only online course I will ever take because I am buying the books for everything else.
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PhoenixMathClub
21 posts
PhoenixMathClub
#5 h  Yesterday at 6:34 PM
Y by
I think you should take AMC 12
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wuwang2002
1190 posts
wuwang2002
#6 h  Yesterday at 6:53 PM
Y by
typically up until 8th grade you want to take amc 10
and you can decide from there
note that it is much easier to qual for jmo than amo (and mop from jmo than mop from amo), and if you make both JMO and AMO you're forced to take AMO
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gavinhaominwang
72 posts
gavinhaominwang
#7 h  Yesterday at 7:04 PM • 1 Y
Y by NaturalSelection
You should only take amc 12 is when you have to or you already make usajmo and have a good chance to make usamo. You haven't "mastered" amc 10, an easier competition, so why should you take a harder one? It makes no sense. Some may say that it is good to get a taste of harder problems. I think that you should be able to solve most of the problems on the amc 10 before moving on.
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sadas123
1057 posts
sadas123
#8 h  Yesterday at 8:03 PM
Y by
gavinhaominwang wrote:
You should only take amc 12 is when you have to or you already make usajmo and have a good chance to make usamo. You haven't "mastered" amc 10, an easier competition, so why should you take a harder one? It makes no sense. Some may say that it is good to get a taste of harder problems. I think that you should be able to solve most of the problems on the amc 10 before moving on.

alright, thanks.
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Aaronjudgeisgoat
824 posts
Aaronjudgeisgoat
#9 h  Yesterday at 8:06 PM
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sadas123 wrote:
Hello! I am a 6th grader this year about to become 7th grade next year. I was wondering if I should take the AMC 12 next year because I think I am ready for it, I was thinking to do AMC 10 A and AMC 12 B, do you think it is a good idea? Here are the courses I finished and now I am working on:

Finished:
1. Intro Algebra
2. Intro Number Theory
3. Intro Counting and Probability
4. Volume 1

Working on:
1. Intermdiate Counting and Probability
2. Three Year Mathcounts Marathon

Upcoming:
1. Intro Geomtery (Next Month)
2. Intro to Alg (May)
3. Pre-calc (Summer)
4. Volume 2???

Stats for AMC 12 (Mocked):

1. AMC 12 A 2024: 100.5
2. AMC 12 B 2024: 105
3. AMC 12 A 2023: 96

The reason why I sometimes I get 100+ is because sometimes I know how to do the first step of the problem but the last step I have to kind of infrence but still i know how to do the problem.

in my opinion, there is genuinely no reason to take amc 12 if you knw you will qualify for aime via the amc 10, unless you are looking to qualify for mop. but can seventh graders even mop qual? or, unless ur sure u will make usamo
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cowstalker
268 posts
cowstalker
#10 h  Today at 1:24 AM
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why in the world are u taking amc12 as a 6th grader if you arent jmo level in the first place. worry about making jmo and then do amc 12 for usamo. you have a good schedule escept it doesnt make snse why ur repeating the same books agian.
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gavinhaominwang
72 posts
gavinhaominwang
#11 h  Today at 1:27 AM
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cowstalker wrote:
why in the world are u taking amc12 as a 6th grader if you arent jmo level in the first place. worry about making jmo and then do amc 12 for usamo. you have a good schedule escept it doesnt make snse why ur repeating the same books agian.

He's a 6th grader. He's asking for help. There's no need to criticize him like that.
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elizhang101412
1184 posts
elizhang101412
#12 h  Today at 2:37 AM
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Why? What's the point?
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jb2015007
1703 posts
jb2015007
#13 h  Today at 2:50 AM
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gavinhaominwang wrote:
cowstalker wrote:
why in the world are u taking amc12 as a 6th grader if you arent jmo level in the first place. worry about making jmo and then do amc 12 for usamo. you have a good schedule escept it doesnt make snse why ur repeating the same books agian.

He's a 6th grader. He's asking for help. There's no need to criticize him like that.

:skull: we arent we just think its absolutely insane to take AMC 12 as a 7th grader only take when u are a jmo qual
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