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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
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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[$10K+ IN PRIZES] Poolesville Math Tournament (PVMT) 2025
qwerty123456asdfgzxcvb   2
N 21 minutes ago by jkim0656
Hi everyone!

After the resounding success of the first three years of PVMT, the Poolesville High School Math Team is excited to announce the fourth annual Poolesville High School Math Tournament (PVMT)! The PVMT team includes a MOPper and multiple USA(J)MO and AIME qualifiers!

PVMT is open to all 6th-9th graders in the country (including rising 10th graders). Students will compete in teams of up to 4 people, and each participant will take three subject tests as well as the team round. The contest is completely free, and will be held virtually on June 7, 2025, from 10:00 AM to 4:00 PM (EST).

Additionally, thanks to our sponsors, we will be awarding approximately $10K+ worth of prizes (including gift cards, Citadel merch, AoPS coupons, Wolfram licenses) to top teams and individuals. More details regarding the actual prizes will be released as we get closer to the competition date.

Further, newly for this year we might run some interesting mini-events, which we will announce closer to the competition date, such as potentially a puzzle hunt and integration bee!

If you would like to register for the competition, the registration form can be found at https://pvmt.org/register.html.

Additionally, more information about PVMT can be found at https://pvmt.org

If you have any questions not answered in the below FAQ, feel free to ask in this thread or email us at falconsdomath@gmail.com!

We look forward to your participation!

FAQ
2 replies
qwerty123456asdfgzxcvb
4 hours ago
jkim0656
21 minutes ago
J
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AMC 10/AIME Study Forum
PatTheKing806   117
N 36 minutes ago by PatTheKing806
[center]

Me (PatTheKing806) and EaZ_Shadow have created a AMC 10/AIME Study Forum! Hopefully, this forum wont die quickly. To signup, do /join or \join.

Click here to join! (or do some pushups) :P

People should join this forum if they are wanting to do well on the AMC 10 next year, trying get into AIME, or loves math!
117 replies
PatTheKing806
Mar 27, 2025
PatTheKing806
36 minutes ago
J
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IMO ShortList 1998, algebra problem 1
orl   37
N an hour ago by Marcus_Zhang
Source: IMO ShortList 1998, algebra problem 1
Let $a_{1},a_{2},\ldots ,a_{n}$ be positive real numbers such that $a_{1}+a_{2}+\cdots +a_{n}<1$. Prove that

\[ \frac{a_{1} a_{2} \cdots a_{n} \left[ 1 - (a_{1} + a_{2} + \cdots + a_{n}) \right] }{(a_{1} + a_{2} + \cdots + a_{n})( 1 - a_{1})(1 - a_{2}) \cdots (1 - a_{n})} \leq \frac{1}{ n^{n+1}}. \]
37 replies
orl
Oct 22, 2004
Marcus_Zhang
an hour ago
J
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Integer Coefficient Polynomial with order
MNJ2357   9
N an hour ago by v_Enhance
Source: 2019 Korea Winter Program Practice Test 1 Problem 3
Find all polynomials $P(x)$ with integer coefficients such that for all positive number $n$ and prime $p$ satisfying $p\nmid nP(n)$, we have $ord_p(n)\ge ord_p(P(n))$.
9 replies
MNJ2357
Jan 12, 2019
v_Enhance
an hour ago
J
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Regarding Maaths olympiad prepration
omega2007   2
N an hour ago by omega2007
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compiled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your perspective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
2 replies
omega2007
Yesterday at 3:13 PM
omega2007
an hour ago
J
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Inspired by bamboozled
sqing   0
an hour ago
Source: Own
Let $ a,b,c $ be reals such that $(a^2+1)(b^2+1)(c^2+1) = 27. $Prove that $$1-3\sqrt 3\leq ab + bc + ca\leq 6$$
0 replies
sqing
an hour ago
0 replies
J
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Range of ab + bc + ca
bamboozled   1
N 2 hours ago by sqing
Let $(a^2+1)(b^2+1)(c^2+1) = 9$, where $a, b, c \in R$, then the number of integers in the range of $ab + bc + ca$ is __
1 reply
bamboozled
2 hours ago
sqing
2 hours ago
J
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Functional Equation
AnhQuang_67   4
N 2 hours ago by AnhQuang_67
Find all functions $f: \mathbb{R} \to \mathbb{R}$ satisfying $$2\cdot f\Big(\dfrac{-xy}{2}+f(x+y)\Big)=xf(y)+yf(x), \forall x, y \in \mathbb{R} $$
4 replies
AnhQuang_67
Yesterday at 4:50 PM
AnhQuang_67
2 hours ago
J
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Inradius and ex-radii
bamboozled   0
2 hours ago
Let $ABC$ be a triangle and $r, r_1, r_2, r_3$ denote its inradius and ex-radii opposite to the vertices $A, B, C$ respectively. If $a> r_1, b > r_2$ and $c > r_3$, then which of the following is/are true?
(A) $\angle{B}$ is obtuse
(B) $\angle{A}$ is acute
(C) $3r > s$, where $s$ is semi perimeter
(D) $3r < s$, where $s$ is semi perimeter
0 replies
bamboozled
2 hours ago
0 replies
J
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Inspired by giangtruong13
sqing   1
N 2 hours ago by sqing
Source: Own
Let $ a,b\in[\frac{1}{2},1] $. Prove that$$ 64\leq (a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})\leq\frac{6889}{16} $$Let $ a,b\in[\frac{1}{2},2] $. Prove that$$ 8(3+2\sqrt 2)\leq (a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})\leq\frac{6889}{16} $$
1 reply
sqing
2 hours ago
sqing
2 hours ago
J
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Conditional maximum
giangtruong13   2
N 2 hours ago by sqing
Source: Specialized Math
Let $a,b$ satisfy that: $1 \leq a \leq2$ and $1 \leq b \leq 2$. Find the maximum: $$A=(a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})$$
2 replies
giangtruong13
Mar 22, 2025
sqing
2 hours ago
J
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9 Which math contest is your favorite?
mdk2013   62
N 2 hours ago by abbominable_sn0wman
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
62 replies
mdk2013
Mar 30, 2025
abbominable_sn0wman
2 hours ago
J
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USA(J)MO qualification
mathkidAP   13
N 2 hours ago by PatTheKing806
Hello. I am an 8th grade student who wants to make jmo or usamo. How much practice do i need for this? i have a 63 on amc 10b and i mock roughly 90-100s on most amc 10s.
13 replies
mathkidAP
Yesterday at 2:03 AM
PatTheKing806
2 hours ago
J
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Inspired by JK1603JK
sqing   16
N 2 hours ago by sqing
Source: Own
Let $ a,b,c\geq 0 $ and $ab+bc+ca=1.$ Prove that$$\frac{abc-2}{abc-1}\ge \frac{4(a^2b+b^2c+c^2a)}{a^3b+b^3c+c^3a+1} $$
16 replies
sqing
Yesterday at 3:31 AM
sqing
2 hours ago
J
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J
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Colored Pencils for Math Competitions
Owinner   17
N Apr 1, 2025 by lord_of_the_rook
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.
17 replies
Owinner
Mar 29, 2025
lord_of_the_rook
Apr 1, 2025
J
Colored Pencils for Math Competitions
G H J
Reveal topic tags
geometry
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Owinner
53 posts
Owinner
#1 h  Mar 29, 2025, 5:56 PM
Y by
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.
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mathprodigy2011
260 posts
mathprodigy2011
#2 h  Mar 29, 2025, 6:49 PM
Y by
Owinner wrote:
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.

i think colored pencils are more useful for really complicated and involved geometry problems. So I would think they are useful for AMC 10 but mathcounts and amc8 usually have geometry problems with simple-ish solutions
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LearnMath_105
139 posts
LearnMath_105
#3 h  Mar 29, 2025, 7:19 PM
Y by
I would say that they are most helpful for marking concyclic/colinear/concurrent objects so later aime - olyis where its most commonly used
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Andyluo
903 posts
Andyluo
#4 h  Mar 29, 2025, 7:43 PM
Y by
they're useless for the competitions listed, it's way too fast-paced to spend time and color a diagram, maybe on olympiads but you're losing precious time if you do it on those. Maybe the AIME would utilize this? But I highly doubt that it would give any benefits

@below coloring lines is basically the same thing c'mon
This post has been edited 1 time. Last edited by Andyluo, Mar 29, 2025, 7:49 PM
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cheltstudent
550 posts
cheltstudent
#5 h  Mar 29, 2025, 7:48 PM
Y by
Bruh, andyluo, literally not colouring just marking different lines they talked about this in my AMC 10 seminar

@above nah like drawing lines with a colour pencil bro
This post has been edited 1 time. Last edited by cheltstudent, Mar 29, 2025, 7:51 PM
Reason: gg
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ChaitraliKA
1003 posts
ChaitraliKA
#6 h  Mar 29, 2025, 7:57 PM
Y by
It can be useful, but I feel like in the actual competition you would end up not using it because you would be too invested in thinking about how to solve the problem instead of "oh, I should mark this with a different color", and would just end up drawing over your diagram with your regular pencil again. Drawing a specific part of your diagram with harder pressure compared to other areas of your diagram can also help you too, especially if it's just mathcounts or AMC 8.
I brought a ruler, a pen, and a compass to Aime, but didn't use any of those materials. Didn't touch them at all. No time to think ¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯
The only time I've ever used different colors is when I draw my diagrams on my chromebook canvas, and I'm lazy to get paper and pencil.
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mathprodigy2011
260 posts
mathprodigy2011
#7 h  Mar 29, 2025, 10:45 PM
Y by
Andyluo wrote:
they're useless for the competitions listed, it's way too fast-paced to spend time and color a diagram, maybe on olympiads but you're losing precious time if you do it on those. Maybe the AIME would utilize this? But I highly doubt that it would give any benefits

@below coloring lines is basically the same thing c'mon

i mean i used different colors to get aime p14 correct so they are useful just not for faster paced competitions. It really depends on how you think.
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mdk2013
568 posts
mdk2013
#8 h  Mar 29, 2025, 11:38 PM • 1 Y
Y by Exponent11
colored pencils way better for olympiads so you can show your steps, for example, there were a few problems on the BAMO and SDMO that i took that i could have used colored pencils to more accurately show my proofs. however
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Jack_w
108 posts
Jack_w
#9 h  Mar 30, 2025, 5:52 PM
Y by
it’s not very helpful
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resources
748 posts
resources
#10 h  Mar 30, 2025, 5:56 PM
Y by
they can be extremely helpful if used correctly.
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vincentwant
1283 posts
vincentwant
#11 h  Mar 30, 2025, 6:31 PM
Y by
I used colored pencils on jmo p3
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EaZ_Shadow
1166 posts
EaZ_Shadow
#12 h  Mar 30, 2025, 6:37 PM
Y by
Owinner wrote:
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.

Ofc u can use it for those comp if u want
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ChaitraliKA
1003 posts
ChaitraliKA
#13 h  Mar 30, 2025, 7:13 PM
Y by
@op, you're getting a bunch of different responses, but in the end, it's your decision obv, whether you wanna use it or not
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Andyluo
903 posts
Andyluo
#14 h  Mar 30, 2025, 7:23 PM
Y by
the general consensus is using colored pencils is a waste of time unless you're doing AIME/Olympiads, at that point, you choose if you should or should not.
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BS2012
970 posts
BS2012
#15 h  Mar 30, 2025, 7:28 PM
Y by
for contests AIME difficulty or easier the geo diagrams are usually simple enough that using colored pencils would be useless, for oly could be useful though
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Mr.Sharkman
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Mr.Sharkman
#16 h  Mar 31, 2025, 8:16 PM
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vincentwant wrote:
I used colored pencils on jmo p3

Lol same; it kinda helped solve it
I also did on #2 of last year but still got it wrong anyway
This post has been edited 1 time. Last edited by Mr.Sharkman, Mar 31, 2025, 8:17 PM
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deduck
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deduck
#17 h  Mar 31, 2025, 9:48 PM • 1 Y
Y by fake123
colored pencils make me confused but i think on olympiads it's personal preference

i think on mathcounts/amc8/10/12 and other fast paced comeptition it's not worth it. if u cant solve the problem in pencil black/white it probably wont get solved just bc u colored it xd because usually the solutions arent that invovled about concyclic/collinear/etc

just my opinion xd
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lord_of_the_rook
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lord_of_the_rook
#18 h  Apr 1, 2025, 1:33 AM
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@op I feel like you should try them out at home, and see if you find them useful.
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