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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jun 2, 2025
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
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[*]AMC 10 Problem Series[/list]
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0 replies
jlacosta
Jun 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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Interesting inequality of sequence
GeorgeRP   3
N an hour ago by dgrozev
Source: Bulgaria IMO TST 2025 P2
Let $d\geq 2$ be an integer and $a_0,a_1,\ldots$ is a sequence of real numbers for which $a_0=a_1=\cdots=a_d=1$ and:
$$a_{k+1}\geq a_k-\frac{a_{k-d}}{4d}, \forall_{k\geq d}$$Prove that all elements of the sequence are positive.
3 replies
GeorgeRP
May 14, 2025
dgrozev
an hour ago
J
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D1042 : A strange inequality
Dattier   1
N an hour ago by Dattier
Source: les dattes à Dattier
Let $a,b>0$.

$$\dfrac 1{12 a^2b^2} \geq \dfrac1{b-a}\ln\left(\dfrac{b(1+a)}{a(1+b)}\right)-\ln\left(\dfrac{1+a}a\right)\ln\left(\dfrac{1+b}b\right)\geq \dfrac 1 {12(a+1)^2(b+1)^2}$$
1 reply
Dattier
Jun 3, 2025
Dattier
an hour ago
J
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Easy Geometry
pokmui9909   7
N an hour ago by RANDOM__USER
Source: FKMO 2025 P4
Triangle $ABC$ satisfies $\overline{CA} > \overline{AB}$. Let the incenter of triangle $ABC$ be $\omega$, which touches $BC, CA, AB$ at $D, E, F$, respectively. Let $M$ be the midpoint of $BC$. Let the circle centered at $M$ passing through $D$ intersect $DE, DF$ at $P(\neq D), Q(\neq D)$, respecively. Let line $AP$ meet $BC$ at $N$, line $BP$ meet $CA$ at $L$. Prove that the three lines $EQ, FP, NL$ are concurrent.
7 replies
pokmui9909
Mar 30, 2025
RANDOM__USER
an hour ago
J
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MOP Emails Out! (2025)
Mathandski   122
N an hour ago by ohiorizzler1434
What an emotional roller coaster the past 34 days have been.

Congrats to all that qualified!
122 replies
Mathandski
Apr 22, 2025
ohiorizzler1434
an hour ago
J
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polonomials
Ducksohappi   4
N an hour ago by ohiorizzler1434
Let $P(x)$ be the real polonomial such that all roots are real and distinct. Prove that there is a rational number $r\ne 0 $ that all roots of $Q(x)=$ $P(x+r)-P(x)$ are real numbers
4 replies
Ducksohappi
Apr 10, 2025
ohiorizzler1434
an hour ago
J
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Cute geometry
Rijul saini   6
N an hour ago by mathscrazy
Source: India IMOTC Practice Test 1 Problem 3
Let scalene $\triangle ABC$ have altitudes $BE, CF,$ circumcenter $O$ and orthocenter $H$. Let $R$ be a point on line $AO$. The points $P,Q$ are on lines $AB,AC$ respectively such that $RE \perp EP$ and $RF \perp FQ$. Prove that $PQ$ is perpendicular to $RH$.

Proposed by Rijul Saini
6 replies
Rijul saini
Yesterday at 6:51 PM
mathscrazy
an hour ago
J
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Cycle in a graph with a minimal number of chords
GeorgeRP   6
N 2 hours ago by dgrozev
Source: Bulgaria IMO TST 2025 P3
In King Arthur's court every knight is friends with at least $d>2$ other knights where friendship is mutual. Prove that King Arthur can place some of his knights around a round table in such a way that every knight is friends with the $2$ people adjacent to him and between them there are at least $\frac{d^2}{10}$ friendships of knights that are not adjacent to each other.
6 replies
GeorgeRP
May 14, 2025
dgrozev
2 hours ago
J
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2019 IGO Advanced P1
Dadgarnia   12
N 2 hours ago by fe.
Source: 6th Iranian Geometry Olympiad (Advanced) P1
Circles $\omega_1$ and $\omega_2$ intersect each other at points $A$ and $B$. Point $C$ lies on the tangent line from $A$ to $\omega_1$ such that
$\angle ABC = 90^\circ$. Arbitrary line $\ell$ passes through $C$ and cuts $\omega_2$ at points $P$ and $Q$. Lines $AP$ and $AQ$ cut $\omega_1$ for the second time at points $X$ and $Z$ respectively. Let $Y$ be the foot of altitude from $A$ to $\ell$. Prove that points $X, Y$ and $Z$ are collinear.

Proposed by Iman Maghsoudi
12 replies
Dadgarnia
Sep 20, 2019
fe.
2 hours ago
J
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Beware the degeneracies!
Rijul saini   5
N 2 hours ago by atdaotlohbh
Source: India IMOTC 2025 Day 1 Problem 1
Let $a,b,c$ be real numbers satisfying $$\max \{a(b^2+c^2),b(c^2+a^2),c(a^2+b^2) \} \leqslant 2abc+1$$Prove that $$a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) \leqslant 6abc+2$$and determine all cases of equality.

Proposed by Shantanu Nene
5 replies
Rijul saini
Yesterday at 6:30 PM
atdaotlohbh
2 hours ago
J
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How many approaches you got? (A lot)
IAmTheHazard   87
N 2 hours ago by MuradSafarli
Source: USAMO 2023/2
Let $\mathbb{R}^+$ be the set of positive real numbers. Find all functions $f \colon \mathbb{R}^+ \to \mathbb{R}^+$ such that, for all $x,y \in \mathbb{R}^+$,
$$f(xy+f(x))=xf(y)+2.$$
87 replies
IAmTheHazard
Mar 23, 2023
MuradSafarli
2 hours ago
J
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Easy Diff NT
xToiletG   0
3 hours ago
Prove that for every $n \geq 2$ there exists positive integers $x, y, z$ such that
$$\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$$
0 replies
xToiletG
3 hours ago
0 replies
J
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Might be slightly generalizable
Rijul saini   5
N 3 hours ago by guptaamitu1
Source: India IMOTC Day 3 Problem 1
Let $ABC$ be an acute angled triangle with orthocenter $H$ and $AB<AC$. Let $T(\ne B,C, H)$ be any other point on the arc $\stackrel{\LARGE\frown}{BHC}$ of the circumcircle of $BHC$ and let line $BT$ intersect line $AC$ at $E(\ne A)$ and let line $CT$ intersect line $AB$ at $F(\ne A)$. Let the circumcircles of $AEF$ and $ABC$ intersect again at $X$ ($\ne A$). Let the lines $XE,XF,XT$ intersect the circumcircle of $(ABC)$ again at $P,Q,R$ ($\ne X$). Prove that the lines $AR,BC,PQ$ concur.
5 replies
Rijul saini
Yesterday at 6:39 PM
guptaamitu1
3 hours ago
J
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star on a quilt
derekwang2048   22
N Today at 4:11 AM by RedFireTruck
Source: 2025 AMC 8 #1
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire $4$-by-$4$ grid is covered by the star?

$\textbf{(A)}\ 40\qquad \textbf{(B)}\ 50\qquad \textbf{(C)}\ 60\qquad \textbf{(D)}\ 75\qquad \textbf{(E)}\ 80$
IMAGE

Thank you @zhenghua for the diagram!
22 replies
derekwang2048
Jan 30, 2025
RedFireTruck
Today at 4:11 AM
J
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Frustration with Olympiad Geo
gulab_jamun   18
N Today at 4:07 AM by cooljoseph
Ok, so right now, I am doing the EGMO book by Evan Chen, but when it comes to problems, there are some that just genuinely frustrate me and I don't know how to deal with them. For example, I've spent 1.5 hrs on the second to last question in chapter 2, and used all the hints, and I still am stuck. It just frustrates me incredibly. Any tips on managing this? (or.... am I js crashing out too much?)
18 replies
gulab_jamun
May 29, 2025
cooljoseph
Today at 4:07 AM
J
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J
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Question
HopefullyMcNats2025   19
N Apr 29, 2025 by MC_ADe
Is it more difficult to make MOP or make usajmo, usapho, and usabo
19 replies
HopefullyMcNats2025
Apr 7, 2025
MC_ADe
Apr 29, 2025
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Question
G H J
Reveal topic tags
USA(J)MO
USAPhO
usabo
AMC
USAJMO
MOP
L
G H BBookmark kLocked kLocked NReply
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#1 h  Apr 7, 2025, 2:00 AM
Y by
Is it more difficult to make MOP or make usajmo, usapho, and usabo
Z K Y
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#2 h  Apr 7, 2025, 2:02 AM
Y by
Btw Usabo and usapho no one cares, I mean usapho and usabo camps
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ConfidentKoala4
612 posts
ConfidentKoala4
#3 h  Apr 7, 2025, 2:07 AM
Y by
all hard, usabo prolly easiest
mop prolly hardest
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#4 h  Apr 7, 2025, 2:12 AM
Y by
Thanks man
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xHypotenuse
789 posts
xHypotenuse
#5 h  Apr 7, 2025, 4:44 PM • 3 Y
Y by happyhippos, aidan0626, Elephant200
No one cares about USABO/USAPhO is wild
This post has been edited 1 time. Last edited by xHypotenuse, Apr 7, 2025, 7:41 PM
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Ruegerbyrd
1108 posts
Ruegerbyrd
#6 h  Apr 7, 2025, 9:09 PM
Y by
MOP, USA(J)MO, usapho, usabo
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MC_ADe
182 posts
MC_ADe
#7 h  Apr 7, 2025, 9:16 PM
Y by
u should talk about camping in these respective things instead cuz MOP is literally camping so u need to like say phys camp or bio camp not jst usapho or usabo
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TetraFish
1089 posts
TetraFish
#8 h  Apr 8, 2025, 12:47 AM
Y by
I think he means MOP vs making that stage in all 3 of them combined.
Z K Y
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LockingIN2026
5 posts
LockingIN2026
#9 h  Apr 8, 2025, 1:13 AM
Y by
TetraFish wrote:
I think he means MOP vs making that stage in all 3 of them combined.

prob the latter
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elasticwealth
342 posts
elasticwealth
#10 h  Apr 8, 2025, 1:17 PM • 1 Y
Y by Sunhaops
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME
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NoSignOfTheta
1752 posts
NoSignOfTheta
#11 h  Apr 8, 2025, 1:25 PM
Y by
MC_ADe wrote:
u should talk about camping in these respective things instead cuz MOP is literally camping so u need to like say phys camp or bio camp not jst usapho or usabo
HopefullyMcNats2025 wrote:
Btw Usabo and usapho no one cares, I mean usapho and usabo camps
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sadas123
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sadas123
#13 h  Apr 8, 2025, 8:37 PM
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elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

That is somewhat of the list.
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happyhippos
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happyhippos
#14 h  Apr 8, 2025, 8:59 PM
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HopefullyMcNats2025 wrote:
Btw Usabo and usapho no one cares, I mean usapho and usabo camps

That's an interesting thing to say, considering USAPhO-style physics is much more relevant to actually useful real-life things than USAMO-style math.
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mdk2013
650 posts
mdk2013
#15 h  Apr 8, 2025, 9:08 PM • 1 Y
Y by ChristianYoo
fake123 wrote:
elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

wdym qualifying for AMC 8 is harder

:ewpu: wut
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Jack_w
111 posts
Jack_w
#16 h  Apr 8, 2025, 9:55 PM
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TetraFish wrote:
I think he means MOP vs making that stage in all 3 of them combined.

MOP harder
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nsking_1209
175 posts
nsking_1209
#17 h  Apr 9, 2025, 2:42 AM
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MOP > usabo camp > usapho camp > usaco camp > usajmo
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Sunhaops
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Sunhaops
#18 h  Apr 29, 2025, 6:53 PM
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elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

well said, only before AIME should be >> instead of >
This post has been edited 1 time. Last edited by Sunhaops, Apr 29, 2025, 6:54 PM
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xHypotenuse
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xHypotenuse
#19 h  Apr 29, 2025, 7:37 PM
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Not really, usapho qual isn't severely difficult compared to aime.

Also, I think usapho camp is around equal or harder than usabo camp for sure
This post has been edited 1 time. Last edited by xHypotenuse, Apr 29, 2025, 7:38 PM
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Lijin
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Lijin
#20 h  Apr 29, 2025, 10:19 PM
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I thought you had to make USA(J)MO first to make MOP?
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MC_ADe
182 posts
MC_ADe
#21 h  Apr 29, 2025, 10:29 PM
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by usabo do u mean semifinals, camp or what
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