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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.
[*]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!
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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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9 Three concurrent chords
v_Enhance   4
N an hour ago by cosmicgenius
Three distinct circles $\Omega_1$, $\Omega_2$, $\Omega_3$ cut three common chords concurrent at $X$. Consider two distinct circles $\Gamma_1$, $\Gamma_2$ which are internally tangent to all $\Omega_i$. Determine, with proof, which of the following two statements is true.

(1) $X$ is the insimilicenter of $\Gamma_1$ and $\Gamma_2$
(2) $X$ is the exsimilicenter of $\Gamma_1$ and $\Gamma_2$.
4 replies
1 viewing
v_Enhance
Yesterday at 8:45 PM
cosmicgenius
an hour ago
J
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Integral with dt
RenheMiResembleRice   2
N an hour ago by RenheMiResembleRice
Source: Yanxue Lu
Solve the attached:
2 replies
RenheMiResembleRice
5 hours ago
RenheMiResembleRice
an hour ago
J
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Show these 2 circles are tangent to each other.
MTA_2024   1
N an hour ago by MTA_2024
A, B, C, and O are four points in the plane such that
\(\angle ABC > 90^\circ\)
and
\( OA = OB = OC \).

Let \( D \) be a point on \( (AB) \), and let \( (d) \) be a line passing through \( D \) such that
\( (AC) \perp (DC) \)
and
\( (d) \perp (AO) \).

The line \( (d) \) intersects \( (AC) \) at \( E \) and the circumcircle of triangle \( ABC \) at \( F \) (\( F \neq A \)).

Show that the circumcircles of triangles \( BEF \) and \( CFD \) are tangent at \( F \).
1 reply
MTA_2024
Yesterday at 1:12 PM
MTA_2024
an hour ago
J
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Inequality with real numbers
JK1603JK   0
an hour ago
Source: unknown
Let a,b,c are real numbers. Prove that (a^3+b^3+c^3+3abc)^4+(a+b+c)^3(a+b-c)^3(-a+b+c)^3(a-b+c)^3>=0
0 replies
+1 w
JK1603JK
an hour ago
0 replies
J
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Find min
hunghd8   7
N 2 hours ago by hunghd8
Let $a,b,c$ be nonnegative real numbers such that $ a+b+c\geq 2+abc $. Find min
$$P=a^2+b^2+c^2.$$
7 replies
hunghd8
Yesterday at 12:10 PM
hunghd8
2 hours ago
J
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inequality marathon
EthanWYX2009   190
N 2 hours ago by EthanWYX2009
There is an inequality marathon now, but the problem is too hard for me to solve, let's start a new one here, please post problems that is not too difficult.
------
P1.
Find the maximum value of ${M}$, such that for $\forall a,b,c\in\mathbb R_+,$
$$a^3+b^3+c^3-3abc\geqslant M(a^2b+b^2c+c^2a-3abc).$$
190 replies
EthanWYX2009
May 21, 2023
EthanWYX2009
2 hours ago
J
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Find interger root
Zuyong   1
N 2 hours ago by Zuyong
Source: ?
Find $(k,m)\in \mathbb{Z}$ satisfying $$9 k^4 + 30 k^3 + 44 k^2 m + 105 k^2 + 20 k m - 120 k + 36 m^2 + 80 m - 240=0$$
1 reply
Zuyong
Oct 24, 2024
Zuyong
2 hours ago
J
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hard..........
Noname23   0
3 hours ago
problem
0 replies
Noname23
3 hours ago
0 replies
J
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Geometry solutions needed of pathfinder senior
SHIVAM_OP-IMO2025   1
N 3 hours ago by S.Ragnork1729
Someone plzz share pathfinder senior by vikas tiwari solutions..
1 reply
SHIVAM_OP-IMO2025
3 hours ago
S.Ragnork1729
3 hours ago
J
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funny title placeholder
pikapika007   46
N 3 hours ago by aliz
Source: USAJMO 2025/6
Let $S$ be a set of integers with the following properties:
[list]
[*] $\{ 1, 2, \dots, 2025 \} \subseteq S$.
[*] If $a, b \in S$ and $\gcd(a, b) = 1$, then $ab \in S$.
[*] If for some $s \in S$, $s + 1$ is composite, then all positive divisors of $s + 1$ are in $S$.
[/list]
Prove that $S$ contains all positive integers.
46 replies
1 viewing
pikapika007
Yesterday at 12:10 PM
aliz
3 hours ago
J
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new playlist in Olympiad Geometry Channel
Plane_geometry_youtuber   3
N 3 hours ago by SHIVAM_OP-IMO2025
Hi,

I create a new playlist called "Problems from Audience". I will put my solution of the problems from audience into this playlist. Welcome to send me your problems and doubts.

https://www.youtube.com/@OlympiadGeometry-2024

my email: planery.geometry@gmail.com
3 replies
Plane_geometry_youtuber
Jan 28, 2025
SHIVAM_OP-IMO2025
3 hours ago
J
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Scary Binomial Coefficient Sum
EpicBird08   31
N 3 hours ago by john0512
Source: USAMO 2025/5
Determine, with proof, all positive integers $k$ such that $$\frac{1}{n+1} \sum_{i=0}^n \binom{n}{i}^k$$is an integer for every positive integer $n.$
31 replies
EpicBird08
Yesterday at 11:59 AM
john0512
3 hours ago
J
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Mathroots
Ruegerbyrd   0
4 hours ago
Has anyone gotten acceptances from MIT's Mathroots yet? Did they ever say they wouldn't send letters to anyone unless accepted?
0 replies
Ruegerbyrd
4 hours ago
0 replies
J
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[TEST RELEASED] Mock Geometry Test for College Competitions
Bluesoul   16
N 4 hours ago by lord_of_the_rook
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
16 replies
Bluesoul
Feb 24, 2025
lord_of_the_rook
4 hours ago
J
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J
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MOHS for Day 1
MajesticCheese   37
N Today at 12:11 AM by vincentwant
What is your opinion for MOHS for day 1?

JMO 1:
JMO 2/AMO 1:
JMO 3:
AMO 2:
AMO 3:
37 replies
MajesticCheese
Thursday at 3:15 PM
vincentwant
Today at 12:11 AM
J
MOHS for Day 1
G H J
Reveal topic tags
L
G H BBookmark kLocked kLocked NReply
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MajesticCheese
16 posts
MajesticCheese
#1 h  Thursday at 3:15 PM
Y by
What is your opinion for MOHS for day 1?

JMO 1:
JMO 2/AMO 1:
JMO 3:
AMO 2:
AMO 3:
Z K Y
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pianoboy
320 posts
pianoboy
#2 h  Thursday at 3:20 PM
Y by
I think AMO 1 was much harder than expected
Z K Y
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pianoboy
320 posts
pianoboy
#3 h  Thursday at 3:21 PM
Y by
amo 1 i think is either 20 or 25.
Z K Y
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bjump
986 posts
bjump
#4 h  Thursday at 3:21 PM
Y by
jmo 10 5 ?
Z K Y
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MajesticCheese
16 posts
MajesticCheese
#5 h  Thursday at 3:42 PM
Y by
pianoboy wrote:
amo 1 i think is either 20 or 25.

Was it that difficult? So is this year day 1 harder than last years?
Z K Y
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Mathandski
720 posts
Mathandski
#6 h  Thursday at 3:45 PM • 2 Y
Y by OronSH, Mr.Sharkman
Subjective Rating for AMO (MOHs)
This post has been edited 1 time. Last edited by Mathandski, Thursday at 3:51 PM
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Speedysolver1
80 posts
Speedysolver1
#7 h  Thursday at 3:53 PM
Y by
see site support
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BS2012
932 posts
BS2012
#8 h  Thursday at 3:59 PM
Y by
Jmo 5 5 >10
Z K Y
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deduck
169 posts
deduck
#9 h  Thursday at 4:01 PM
Y by
my opinion:
amo1 = 5 mohs (number theory)
comment: standard

amo2 = 20 mohs (algebra)
comment: getting the first half of the proof is easy but then you have to realize that u actually have to use information from the failing case which i missed cause i rushed and was being dumb

amo3 = 25 mohs (geometry)
once u understand it and build the construction u win, but it's easy to get convinced that bob can win

Note: i didnt take the olympiad so this is my opinion as observing it
This post has been edited 2 times. Last edited by deduck, Thursday at 4:26 PM
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jellybeanzzz
476 posts
jellybeanzzz
#10 h  Thursday at 4:17 PM
Y by
A1: 5
A2: 25
A3: 20
Z K Y
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vincentwant
1260 posts
vincentwant
#11 h  Thursday at 4:38 PM
Y by
J1 5
J2 10
J3 25
Z K Y
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wuwang2002
1191 posts
wuwang2002
#12 h  Thursday at 9:32 PM
Y by
J1 15 J2 15 J3 15
i got swept what
Z K Y
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KevinChen_Yay
203 posts
KevinChen_Yay
#13 h  Thursday at 9:38 PM
Y by
JMO 10 5 20
Z K Y
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HamstPan38825
8857 posts
HamstPan38825
#14 h  Thursday at 10:49 PM • 1 Y
Y by GrantStar
More of my meta-discourse on the problems than a true difficulty rating, but take it with a grain of salt nonetheless.

A1

A2

A3
This post has been edited 1 time. Last edited by HamstPan38825, Thursday at 10:49 PM
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ethan2011
225 posts
ethan2011
#15 h  Yesterday at 1:42 AM
Y by
KevinChen_Yay wrote:
JMO 10 5 20

jmo p3 maybe 25 ngl
why does no one say mohs of like 6, 21, 18, or any non multiple of 5 :skull:
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vincentwant
1260 posts
vincentwant
#16 h  Yesterday at 1:46 AM
Y by
because mohs is in increments of 5 thioonk
also what are opinions on j3 mohs
This post has been edited 1 time. Last edited by vincentwant, Yesterday at 2:21 AM
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KevinChen_Yay
203 posts
KevinChen_Yay
#17 h  Yesterday at 2:26 AM
Y by
ethan2011 wrote:
jmo p3 maybe 25 ngl
vincentwant wrote:
mohs is in increments of 5 thioonk
also what are opinions on j3 mohs

idrk the sol so its hard to say, should be 20-30 mohs tho
Z K Y
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vincentwant
1260 posts
vincentwant
#18 h  Yesterday at 12:30 PM
Y by
J4 10
J5 5
J6 20
Z K Y
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KevinChen_Yay
203 posts
KevinChen_Yay
#19 h  Yesterday at 12:34 PM
Y by
5 5 20 trust
Z K Y
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bjump
986 posts
bjump
#20 h  Yesterday at 1:00 PM
Y by
jmo day 2

10 5 10-20

me when j4 took me 3.5 hours j2 took 15 minutes j3 took 10 minutes
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BS2012
932 posts
BS2012
#21 h  Yesterday at 1:06 PM
Y by
jmo d2
0 10 15
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arfekete
246 posts
arfekete
#22 h  Yesterday at 1:18 PM
Y by
AMO d1:
5, 25, 30

AMO d2:
5, 15, ???(Probably 45+ based on what I've heard)
This post has been edited 1 time. Last edited by arfekete, Yesterday at 1:21 PM
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vincentwant
1260 posts
vincentwant
#23 h  Yesterday at 1:20 PM
Y by
J6 is not 5 mohs buh theres weird edge cases no matter how you approach it
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EpicBird08
1740 posts
EpicBird08
#24 h  Yesterday at 2:08 PM
Y by
AMO d1:
10, 30, 30
AMO d2:
5, 20, 45+?
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BS2012
932 posts
BS2012
#25 h  Yesterday at 4:51 PM
Y by
vincentwant wrote:
J6 is not 5 mohs buh theres weird edge cases no matter how you approach it

real
fermat primes ruined my d2 sweep
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Mathandski
720 posts
Mathandski
#26 h  Yesterday at 5:06 PM • 1 Y
Y by ihatemath123
Mathandski wrote:
Subjective Rating for AMO (MOHs)

Continued

Subjective Rating for AMO D2 (MOHs)
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ihatemath123
3439 posts
ihatemath123
#27 h  Yesterday at 5:30 PM
Y by
AMO 10/30/35 0/15/40
JMO day 1 is like 15/10/15 but dont quote me on that
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GrantStar
815 posts
GrantStar
#28 h  Yesterday at 5:30 PM
Y by
AMO: 5 30 25 10 15 40
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awesomeguy856
7263 posts
awesomeguy856
#29 h  Yesterday at 5:33 PM
Y by
AMO: 10/30/20 10/30/45
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jasperE3
11102 posts
jasperE3
#30 h  Yesterday at 5:38 PM • 1 Y
Y by megarnie
no functional equationnnnnnnn
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xTimmyG
248 posts
xTimmyG
#31 h  Yesterday at 10:52 PM
Y by
jmo:
day1: 10/0/20,
day2: 0/0/15

edit: actually nvm j2 should be 5 mohs
This post has been edited 2 times. Last edited by xTimmyG, Yesterday at 10:54 PM
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S.Das93
706 posts
S.Das93
#32 h  Yesterday at 10:57 PM
Y by
why i even study fe for oly when there was no fe anywhere
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plang2008
325 posts
plang2008
#33 h  Yesterday at 11:16 PM
Y by
usamo 10/30/anti/0/25/40
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scannose
982 posts
scannose
#34 h  Yesterday at 11:19 PM
Y by
plang2008 wrote:
usamo 10/30/anti/0/25/40
so am i the only person who spent longer on u4 than on u1
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eg4334
614 posts
eg4334
#35 h  Yesterday at 11:21 PM
Y by
jmo 15/10/20 5/0/15

@2below im biased on my j1 rating
This post has been edited 1 time. Last edited by eg4334, Yesterday at 11:38 PM
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jellybeanzzz
476 posts
jellybeanzzz
#36 h  Yesterday at 11:27 PM
Y by
amo 5/25/20/0/15/40
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BS2012
932 posts
BS2012
#37 h  Yesterday at 11:37 PM
Y by
eg4334 wrote:
jmo 15/10/20 5/0/15

no way j1=j6
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vincentwant
1260 posts
vincentwant
#39 h  Today at 12:11 AM
Y by
5/10/25 5/5/20

Problem 1, on bijective functions

Problem 2, on digits greater than d

Problem 3, on domino-tileable grids

Problem 4, on inequality choose 2

Problem 5, on orthocenter geo

Problem 6, on positive integers in S

(copied from blog)
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