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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.

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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
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Website to learn math
hawa   70
N 3 minutes ago by valisaxieamc
Hi, I'm kinda curious what website do yall use to learn math, like i dont find any website thats fun to learn math
70 replies
hawa
Apr 9, 2025
valisaxieamc
3 minutes ago
J
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Counting graph theory
MathSaiyan   1
N 29 minutes ago by biomathematics
Source: PErA 2025/6
Let $m$ and $n$ be positive integers. For a connected simple graph $G$ on $n$ vertices and $m$ edges, we consider the number $N(G)$ of orientations of (all of) its edges so that, in the resulting directed graph, every vertex has even outdegree.
Show that $N(G)$ only depends on $m$ and $n$, and determine its value.
1 reply
MathSaiyan
Mar 17, 2025
biomathematics
29 minutes ago
J
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hard problem
Cobedangiu   14
N an hour ago by IceyCold
Let $a,b,c>0$ and $a+b+c=3$. Prove that:
$\dfrac{4}{a+b}+\dfrac{4}{b+c}+\dfrac{4}{c+a} \le \dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+3$
14 replies
Cobedangiu
Apr 21, 2025
IceyCold
an hour ago
J
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Vasc = 1?
Li4   8
N 2 hours ago by IceyCold
Source: 2025 Taiwan TST Round 3 Independent Study 1-N
Find all integer tuples $(a, b, c)$ such that
\[(a^2 + b^2 + c^2)^2 = 3(a^3b + b^3c + c^3a) + 1. \]
Proposed by Li4, Untro368, usjl and YaWNeeT.
8 replies
Li4
Apr 26, 2025
IceyCold
2 hours ago
J
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\sqrt{(1^2+2^2+...+n^2)/n}$ is an integer.
parmenides51   7
N 2 hours ago by lightsynth123
Source: Singapore Open Math Olympiad 2017 2nd Round p3 SMO
Find the smallest positive integer $n$ so that $\sqrt{\frac{1^2+2^2+...+n^2}{n}}$ is an integer.
7 replies
parmenides51
Mar 26, 2020
lightsynth123
2 hours ago
J
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Intersection of circumcircles of MNP and BOC
Djile   39
N 2 hours ago by bjump
Source: Serbian National Olympiad 2013, Problem 3
Let $M$, $N$ and $P$ be midpoints of sides $BC, AC$ and $AB$, respectively, and let $O$ be circumcenter of acute-angled triangle $ABC$. Circumcircles of triangles $BOC$ and $MNP$ intersect at two different points $X$ and $Y$ inside of triangle $ABC$. Prove that \[\angle BAX=\angle CAY.\]
39 replies
Djile
Apr 8, 2013
bjump
2 hours ago
J
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Good divisors and special numbers.
Nuran2010   2
N 2 hours ago by BR1F1SZ
Source: Azerbaijan Al-Khwarizmi IJMO TST 2024
$N$ is a positive integer. Call all positive divisors of $N$ which are different from $1$ and $N$ beautiful divisors.We call $N$ a special number when it has at least $2$ beautiful divisors and difference of any $2$ beautiful divisors divides $N$ as well. Find all special numbers.
2 replies
Nuran2010
Yesterday at 4:52 PM
BR1F1SZ
2 hours ago
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Inspired by old results
sqing   3
N 2 hours ago by Jamalll
Source: Own
Let $ a,b>0 , a^2+b^2+ab+a+b=5 . $ Prove that
$$ \frac{ 1 }{a+b+ab+1}+\frac{6}{a^2+b^2+ab+1}\geq \frac{7}{4}$$$$ \frac{ 1 }{a+b+ab+1}+\frac{1}{a^2+b^2+ab+1}\geq \frac{1}{2}$$$$ \frac{41}{a+b+2}+\frac{ab}{a^3+b^3+2} \geq \frac{21}{2}$$
3 replies
1 viewing
sqing
Yesterday at 12:29 PM
Jamalll
2 hours ago
J
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Question on Balkan SL
Fmimch   0
3 hours ago
Does anyone know where to find the Balkan MO Shortlist 2024? If you have the file, could you send in this thread? Thank you!
0 replies
Fmimch
3 hours ago
0 replies
J
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hard inequalities
pennypc123456789   0
3 hours ago
Given $x,y,z$ be the positive real number. Prove that

$\frac{2xy}{\sqrt{2xy(x^2+y^2)}} + \frac{2yz}{\sqrt{2yz(y^2+z^2)}} + \frac{2xz}{\sqrt{2xz(x^2+z^2)}} \le \frac{2(x^2+y^2+z^2) + xy+yz+xz}{x^2+y^2+z^2}$
0 replies
pennypc123456789
3 hours ago
0 replies
J
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inequality problem
pennypc123456789   2
N 3 hours ago by pennypc123456789
Given $a,b,c$ be positive real numbers . Prove that
$$\frac{ab}{(a+b)^2} +\frac{bc}{(b+c)^2}+\frac{ac}{(a+c)^2} \ge \frac{6abc }{(a+b)(b+c)(a+c)}$$
2 replies
pennypc123456789
Yesterday at 2:42 PM
pennypc123456789
3 hours ago
J
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Can someone explain this one
hawa   10
N Yesterday at 8:23 PM by VivaanKam
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
10 replies
hawa
Yesterday at 1:36 AM
VivaanKam
Yesterday at 8:23 PM
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Alcumus specs
YeohZY   5
N Yesterday at 7:23 PM by PikaPika999
Hi, can I ask about how Alcumus gives you points? (I mean the number on the red/orange/green/blue line on top that gains once you get correct answers. I'll just call it the score). I want to get my score up to 100, but I always can't and get stuck at like 98 or sth. Why is this so, and also how does alcumus make that "score" higher?
5 replies
YeohZY
Apr 27, 2025
PikaPika999
Yesterday at 7:23 PM
J
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Math Problem I cant figure out how to do without bashing
equalsmc2   3
N Yesterday at 3:55 PM by NovaFrost
Hi,
I cant figure out how to do these 2 problems without bashing. Do you guys have any ideas for an elegant solution? Thank you!
Prob 1.
An RSM sports field has a square shape. Poles with letters M, A, T, H are located at the corners of the square (see the diagram). During warm up, a student starts at any pole, runs to another pole along a side of the square or across the field along diagonal MT (only in the direction from M to T), then runs to another pole along a side of the square or along diagonal MT, and so on. The student cannot repeat a run along the same side/diagonal of the square in the same direction. For instance, she cannot run from M to A twice, but she can run from M to A and at some point from A to M. How many different ways are there to complete the warm up that includes all nine possible runs (see the diagram)? One possible way is M-A-T-H-M-H-T-A-M-T (picture attached)

Prob 2.
In the expression 5@5@5@5@5 you replace each of the four @ symbols with either +, or, or x, or . You can insert one or more pairs of parentheses to control the order of operations. Find the second least whole number that CANNOT be the value of the resulting expression. For example, each of the numbers 25=5+5+5+5+5 and 605+(5+5)×5+5 can be the value of the resulting expression.

Prob 3. (This isnt bashing I don't understand how to do it though)
Suppose BC = 3AB in rectangle ABCD. Points E and F are on side BC such that BE = EF = FC. Compute the sum of the degree measures of the four angles EAB, EAF, EAC, EAD.

P.S. These are from an RSM olympiad. The answers are
3 replies
equalsmc2
Apr 6, 2025
NovaFrost
Yesterday at 3:55 PM
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What Are The Chances?
IbrahimNadeem   65
N Apr 27, 2025 by peelybonehead
Hello, I'm curious to have honest advice on how far I can make it (by 11th-12th grade-ish);

If I have:

- Started AMC 8 study in 6th grade
- Started AMC 10 study in 7th grade
- Started practicing harder & went from 60 to around 100 on AMC 10 (on practice tests with official conditions)
- Started AMC 12 study in 8th grade
- Currently (fall of 8th grade) getting ~120 on AMC 10/12 & 7-10 while practicing AIME

At this rate, what are the chances of me making the USA(J)MO, for example, by ~11th grade?

Please be completely honest and don't hold back; This can be useful to see if I have the need to practice harder.
65 replies
IbrahimNadeem
Oct 31, 2021
peelybonehead
Apr 27, 2025
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What Are The Chances?
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Reveal topic tags
improvement
AMC 10
AMC
AIME
USA(J)MO
L
G H BBookmark kLocked kLocked NReply
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sadas123
1247 posts
sadas123
#55 h  Feb 9, 2025, 7:47 PM • 1 Y
Y by PikaPika999
Spacepandamath13 wrote:
He's in 11th right?

I am pretty sure..
Z K Y
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IbrahimNadeem
888 posts
IbrahimNadeem
#56 h  Feb 14, 2025, 7:20 AM • 1 Y
Y by PikaPika999
For math I utterly failed despite
JMO qual last year being free
I qualled for usapho, now it is my only light
but it is no stranger to me

My sights are set on a new horizon
and to conquer, skill is what I must show
not getting distracted by my verizon
my solemn wish is to make IPhO. $\blacksquare$
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Spacepandamath13
379 posts
Spacepandamath13
#57 h  Feb 22, 2025, 8:48 PM
Y by
This is honestly very sad.
Z K Y
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Math-lover1
127 posts
Math-lover1
#58 h  Mar 10, 2025, 2:03 AM
Y by
IbrahimNadeem wrote:
For math I utterly failed despite
JMO qual last year being free
I qualled for usapho, now it is my only light
but it is no stranger to me

My sights are set on a new horizon
and to conquer, skill is what I must show
not getting distracted by my verizon
my solemn wish is to make IPhO. $\blacksquare$

Respect :weightlift:
This post has been edited 1 time. Last edited by Math-lover1, Mar 10, 2025, 2:04 AM
Reason: latex
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hashbrown2009
180 posts
hashbrown2009
#59 h  Mar 10, 2025, 2:18 AM
Y by
IbrahimNadeem wrote:
Hello, I'm curious to have honest advice on how far I can make it (by 11th-12th grade-ish);

If I have:

- Started AMC 8 study in 6th grade
- Started AMC 10 study in 7th grade
- Started practicing harder & went from 60 to around 100 on AMC 10 (on practice tests with official conditions)
- Started AMC 12 study in 8th grade
- Currently (fall of 8th grade) getting ~120 on AMC 10/12 & 7-10 while practicing AIME

At this rate, what are the chances of me making the USA(J)MO, for example, by ~11th grade?

Please be completely honest and don't hold back; This can be useful to see if I have the need to practice harder.

Honestly? 90-97% chance. I'm in 9th grade and last year I made JMO. The year before I had a cutoff around 190. If you work hard enough, you definitely could pull of JMO qualification. Try to aim for DHR on AMC10/12 + 11-13 on AIME
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IbrahimNadeem
888 posts
IbrahimNadeem
#60 h  Apr 8, 2025, 5:51 AM • 1 Y
Y by Aaronjudgeisgoat
The day of fate nears
USAPhO in three days
after failing everything these years
my confidence is like twin rays

diffracting and interfering with eachother
unable to determine a definite fate
and yet, a path will emerge, one worther of shudder
my aura will rise as I succeed on this date

everything, every moment, every vacuum fluctuation within my atoms
all the hope, all the suffering, all the insatiable urge for victory
at last, will be satiated as this victory builds my future's stratums
After all, there is no purity in my story

It is a path paved by excruciating failure,
longing, doom, tears and playing roblox to wash them away
but that horrid path must terminate its tenure
even I cannot imagine losing any more and feeling gray

my days end and simultaneously renew
I might return here for another notice if yet another chapter begins
although for now, my thoughts take me to the moon or even Peru
until next time, my past shall not rinse. $\blacksquare$
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martianrunner
187 posts
martianrunner
#61 h  Apr 8, 2025, 2:22 PM
Y by
you got this!
best of luck
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martianrunner
187 posts
martianrunner
#62 h  Apr 13, 2025, 4:53 PM
Y by
how did it go?
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sadas123
1247 posts
sadas123
#63 h  Apr 13, 2025, 7:05 PM
Y by
Claim: Top Prize USAPhO Winner

Proof: If $(x+y)^2=z$ and x and y are the roots of the equation $x^2-2x+1$ then there is an real value of $z$ that means that they can actually win USAPhO so that is actually correct and we can also use marchov-chains also to prove this with expected value $\blacksquare$
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michaelqiu
36 posts
michaelqiu
#64 h  Apr 13, 2025, 10:10 PM
Y by
Did you make it?
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sadas123
1247 posts
sadas123
#65 h  Apr 13, 2025, 10:23 PM
Y by
michaelqiu wrote:
Did you make it?

Do you think I can get a 35+ on USABO if I start in 6th grade?
This post has been edited 1 time. Last edited by sadas123, Apr 13, 2025, 10:26 PM
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martianrunner
187 posts
martianrunner
#66 h  Apr 13, 2025, 11:00 PM
Y by
i think you could get a good score on the usabo if you start in 10th
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IbrahimNadeem
888 posts
IbrahimNadeem
#67 h  Apr 26, 2025, 10:02 PM
Y by
Dead is luck
voided is my life
animated is my failure but inanimate my emotion
every morning I wake up, it ignites more strife

Paranoia I gain
humanity I lose
for when success is right within reach
I redeem none; failure does my fate choose

I missed the camp cutoff by hardly 5 points
but no hope for what lies
lending me mind to revise matrix adjoints
yet no flame of ambition--it now dies. $\blacksquare$
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Math-lover1
127 posts
Math-lover1
#68 h  Apr 26, 2025, 10:12 PM
Y by
IbrahimNadeem wrote:
Dead is luck
voided is my life
animated is my failure but inanimate my emotion
every morning I wake up, it ignites more strife

Paranoia I gain
humanity I lose
for when success is right within reach
I redeem none; failure does my fate choose

I missed the camp cutoff by hardly 5 points
but no hope for what lies
lending me mind to revise matrix adjoints
yet no flame of ambition--it now dies. $\blacksquare$

Bro has suffered too much :(
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peelybonehead
6290 posts
peelybonehead
#69 h  Apr 27, 2025, 3:33 AM
Y by
IbrahimNadeem wrote:
Dead is luck
voided is my life
animated is my failure but inanimate my emotion
every morning I wake up, it ignites more strife

Paranoia I gain
humanity I lose
for when success is right within reach
I redeem none; failure does my fate choose

I missed the camp cutoff by hardly 5 points
but no hope for what lies
lending me mind to revise matrix adjoints
yet no flame of ambition--it now dies. $\blacksquare$

usapho gold is very impressive
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