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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
5 hours ago
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
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have a transformative summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
Our full course list for upcoming classes is below:
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0 replies
jlacosta
5 hours ago
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
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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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Share your favorite problem
the_mathtrovert_next_door   6
N a minute ago by garfield0515
hi, this is my first post, so consider yourselves warned, here's how this thread works: you send your favorite problem, and send the solutions to the previous problem that was sent, here's mine;

Consider a circle that has 2n points on the circumference that are equally spaced. Alice and Bob are playing a game such that Alice will pick a number d such that d is less than or equal to n. Bob wins if he can colour the 2n points with n colours such that the 2 points of the same colour have exactly d-1 points between them. Devise a winning strategy for Alice.
6 replies
+1 w
the_mathtrovert_next_door
5 hours ago
garfield0515
a minute ago
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Goofy Ahh Rickety Roo Ahh Uncle
EugeneDingleBerry   11
N 8 minutes ago by Spacepandamath13
Aight so boom It’s ya boy Eugene Dingleberry, and lemme put y’all on real quick about my rickety roo ahh uncle who's holding me captive, Quandale Dingle III. This man is different. Like actually unhinged. Bro not even human at this point. He be walkin’ around the block in a Snuggie, some busted Yeezys, and them gas station shades like he finna drop the hottest mixtape of 3025. Bro say he invented oxygen and that he “talked to aliens in the Waffle House bathroom” like it's normal. One time he pulled up to church with a pet lizard on his shoulder and said “he finna get baptized too.” The lizard, bro. He don’t got a job but always got $3.47 in his pocket and a bag of old McNuggets “for emergencies.” He be drinking pickle juice like it's Gatorade, and says he can smell WiFi. Bro yelled “I’M HIM” at a vending machine 'cause it didn’t give him his Doritos. Then he drop-kicked it and left with a Capri Sun like nothing happened. Unc always got some wild story like “I fought a raccoon in an Arby’s parking lot and won” and we just be like “on god??” and he be like “ON BABY.” But no cap, Uncle Quandale might be weird, but he the realest. He got that main character energy. He finna pull up to your school assembly wearing crocs and a cape talkin’ bout “knowledge is power” and then moonwalk out. That’s my uncle. That’s Quandale Dingle III. And y’all ain’t ready for him.

But no cap, Uncle Quandale might be weird, but he the realest. He got that main character energy. He finna pull up to your school assembly wearing crocs and a cape talkin’ bout “knowledge is power” and then moonwalk out.

That’s my uncle. That’s Quandale Dingle III. And y’all ain’t ready for him.
11 replies
EugeneDingleBerry
2 hours ago
Spacepandamath13
8 minutes ago
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2500th Post!
PikaPika999   29
N 9 minutes ago by Spacepandamath13
I may be a bit late for this, but this is my 2500th post :)
Also this is going to be my last one until another big milestone bc I don't wanna clog up the MSM forum with my milestones

Also, since my 1000th post math story was locked due to a flamewar, here is my math story with a few updates :)
(This was also scripted so if there are any problems in my story, um... well, it is what it is)

Script starts:


When I had less than 25 posts on AoPS, I saw many people create threads about them getting 1000th posts and their math story. I thought I would never hit 1000 posts, but I did, and that thread got locked...Please


So, lol here we are, writing my math story again :)


Daycare

Preschool

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

In conclusion, AoPS has helped me improve my math. Minor side note, but

Finally, I would like to say thank you to all the new friends I made and all the instructors on AoPS that taught me!

Another minor side note, but

and here are some problems ig :)

Problems

hopefully these problems weren't too easy lol
29 replies
PikaPika999
May 29, 2025
Spacepandamath13
9 minutes ago
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Trouble focusing
GallopingUnicorn45   6
N 16 minutes ago by Spacepandamath13
Hi all,

So I'm currently hard-grinding for AIME in AMC 10 this year (I'm taking both A and B) and I'm having a hard time focusing and my productivity is slipping; I can't finish all of the stuff I plan daily and weekly. Before, during the school year, I was also grinding and listening to K-pop while working, and now I have songs stuck in my head as I work, which also makes me unable to focus.

Any tips on how to concentrate for longer periods of time? Thanks!
6 replies
GallopingUnicorn45
6 hours ago
Spacepandamath13
16 minutes ago
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Channel name changed
Plane_geometry_youtuber   10
N an hour ago by Yiyj
Hi,

Due to the search handle issue in youtube. My channel is renamed to Olympiad Geometry Club. And the new link is as following:

https://www.youtube.com/@OlympiadGeometryClub

Recently I introduced the concept of harmonic bundle. I will move on to the conjugate median soon. In the future, I will discuss more than a thousand theorems on plane geometry and hopefully it can help to the students preparing for the Olympiad competition.

Please share this to the people may need it.

Thank you!
10 replies
Plane_geometry_youtuber
Yesterday at 9:31 PM
Yiyj
an hour ago
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Ducks can play games now apparently
MortemEtInteritum   35
N 3 hours ago by pi271828
Source: USA TST(ST) 2020 #1
Let $a$, $b$, $c$ be fixed positive integers. There are $a+b+c$ ducks sitting in a
circle, one behind the other. Each duck picks either rock, paper, or scissors, with $a$ ducks
picking rock, $b$ ducks picking paper, and $c$ ducks picking scissors.
A move consists of an operation of one of the following three forms:

[list]
[*] If a duck picking rock sits behind a duck picking scissors, they switch places.
[*] If a duck picking paper sits behind a duck picking rock, they switch places.
[*] If a duck picking scissors sits behind a duck picking paper, they switch places.
[/list]
Determine, in terms of $a$, $b$, and $c$, the maximum number of moves which could take
place, over all possible initial configurations.
35 replies
MortemEtInteritum
Nov 16, 2020
pi271828
3 hours ago
J
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2017 IGO Advanced P3
bgn   18
N 3 hours ago by Circumcircle
Source: 4th Iranian Geometry Olympiad (Advanced) P3
Let $O$ be the circumcenter of triangle $ABC$. Line $CO$ intersects the altitude from $A$ at point $K$. Let $P,M$ be the midpoints of $AK$, $AC$ respectively. If $PO$ intersects $BC$ at $Y$, and the circumcircle of triangle $BCM$ meets $AB$ at $X$, prove that $BXOY$ is cyclic.

Proposed by Ali Daeinabi - Hamid Pardazi
18 replies
bgn
Sep 15, 2017
Circumcircle
3 hours ago
J
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Own made functional equation
JARP091   1
N 3 hours ago by JARP091
Source: Own (Maybe?)
\[ \text{Find all functions } f : \mathbb{R} \to \mathbb{R} \text{ such that:} \\ f(a^4 + a^2b^2 + b^4) = f\left((a^2 - f(ab) + b^2)(a^2 + f(ab) + b^2)\right) \]
1 reply
JARP091
May 31, 2025
JARP091
3 hours ago
J
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Euler line of incircle touching points /Reposted/
Eagle116   6
N 4 hours ago by pigeon123
Let $ABC$ be a triangle with incentre $I$ and circumcentre $O$. Let $D,E,F$ be the touchpoints of the incircle with $BC$, $CA$, $AB$ respectively. Prove that $OI$ is the Euler line of $\vartriangle DEF$.
6 replies
Eagle116
Apr 19, 2025
pigeon123
4 hours ago
J
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Parallel lines on a rhombus
buratinogigle   1
N 4 hours ago by Giabach298
Source: Own, Entrance Exam for Grade 10 Admission, HSGS 2025
Given the rhombus $ABCD$ with its incircle $\omega$. Let $E$ and $F$ be the points of tangency of $\omega$ with $AB$ and $AC$ respectively. On the edges $CB$ and $CD$, take points $G$ and $H$ such that $GH$ is tangent to $\omega$ at $P$. Suppose $Q$ is the intersection point of the lines $EG$ and $FH$. Prove that two lines $AP$ and $CQ$ are parallel or coincide.
1 reply
buratinogigle
5 hours ago
Giabach298
4 hours ago
J
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Orthocenter lies on circumcircle
whatshisbucket   90
N 4 hours ago by bjump
Source: 2017 ELMO #2
Let $ABC$ be a triangle with orthocenter $H,$ and let $M$ be the midpoint of $\overline{BC}.$ Suppose that $P$ and $Q$ are distinct points on the circle with diameter $\overline{AH},$ different from $A,$ such that $M$ lies on line $PQ.$ Prove that the orthocenter of $\triangle APQ$ lies on the circumcircle of $\triangle ABC.$

Proposed by Michael Ren
90 replies
whatshisbucket
Jun 26, 2017
bjump
4 hours ago
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Polish MO Finals 2014, Problem 4
j___d   3
N 4 hours ago by ariopro1387
Source: Polish MO Finals 2014
Denote the set of positive rational numbers by $\mathbb{Q}_{+}$. Find all functions $f: \mathbb{Q}_{+}\rightarrow \mathbb{Q}_{+}$ that satisfy
$$\underbrace{f(f(f(\dots f(f}_{n}(q))\dots )))=f(nq)$$for all integers $n\ge 1$ and rational numbers $q>0$.
3 replies
j___d
Jul 27, 2016
ariopro1387
4 hours ago
J
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S(an) greater than S(n)
ilovemath0402   1
N 5 hours ago by ilovemath0402
Source: Inspired by an old result
Find all positive integer $n$ such that $S(an)\ge S(n) \quad \forall a \in \mathbb{Z}^{+}$ ($S(n)$ is sum of digit of $n$ in base 10)
P/s: Original problem
1 reply
ilovemath0402
5 hours ago
ilovemath0402
5 hours ago
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Hagge-like circles, Jerabek hyperbola, Lemoine cubic
kosmonauten3114   0
5 hours ago
Source: My own
Let $\triangle{ABC}$ be a scalene oblique triangle with circumcenter $O$ and orthocenter $H$, and $P$ ($\neq \text{X(3), X(4)}$, $\notin \odot(ABC)$) a point in the plane.
Let $\triangle{A_1B_1C_1}$, $\triangle{A_2B_2C_2}$ be the circumcevian triangles of $O$, $P$, respectively.
Let $\triangle{P_AP_BP_C}$ be the pedal triangle of $P$ with respect to $\triangle{ABC}$.
Let $A_1'$ be the reflection in $P_A$ of $A_1$. Define $B_1'$, $C_1'$ cyclically.
Let $A_2'$ be the reflection in $P_A$ of $A_2$. Define $B_2'$, $C_2'$ cyclically.
Let $O_1$, $O_2$ be the circumcenters of $\triangle{A_1'B_1'C_1'}$, $\triangle{A_2'B_2'C_2'}$, respectively.

Prove that:
1) $P$, $O_1$, $O_2$ are collinear if and only if $P$ lies on the Jerabek hyperbola of $\triangle{ABC}$.
2) $H$, $O_1$, $O_2$ are collinear if and only if $P$ lies on the Lemoine cubic (= $\text{K009}$) of $\triangle{ABC}$.
0 replies
kosmonauten3114
5 hours ago
0 replies
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Something Interesting
ilikemath247365   11
N Apr 25, 2025 by ilikemath247365
I just realized: The 2013 National MathCounts Sprint #24 is the EXACT SAME as the 2001 National MathCounts Sprint #28.
11 replies
ilikemath247365
Apr 25, 2025
ilikemath247365
Apr 25, 2025
J
Something Interesting
G H J
Reveal topic tags
MATHCOUNTS
L
G H BBookmark kLocked kLocked NReply
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ilikemath247365
278 posts
ilikemath247365
#1 h  Apr 25, 2025, 5:03 AM
Y by
I just realized: The 2013 National MathCounts Sprint #24 is the EXACT SAME as the 2001 National MathCounts Sprint #28.
Z K Y
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ethan2011
354 posts
ethan2011
#2 h  Apr 25, 2025, 12:05 PM
Y by
Can you share the problem then?
Z K Y
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Charizard_637
125 posts
Charizard_637
#3 h  Apr 25, 2025, 2:44 PM
Y by
OH SHOOT YOU'RE RIGHT I MOCKED 2013 AND KNEW I'VE SEEN SPRINT 28 BEFORE

If $a+b = 1$ and $a^2+b^2 = 2$, what is the value of $a^3+b^3$? Express your answer as a common fraction.
Answer
If you want the solution I can post that too
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K1mchi_
155 posts
K1mchi_
#4 h  Apr 25, 2025, 2:47 PM
Y by
ilikemath247365 wrote:
I just realized: The 2013 National MathCounts Sprint #24 is the EXACT SAME as the 2001 National MathCounts Sprint #28.

what did u expect

u cant have new problems every year or smth
Z K Y
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Charizard_637
125 posts
Charizard_637
#5 h  Apr 25, 2025, 2:52 PM
Y by
you can with that many problem writers for the national competition
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K1mchi_
155 posts
K1mchi_
#6 h  Apr 25, 2025, 2:54 PM
Y by
Charizard_637 wrote:
you can with that many problem writers for the national competition

then with that many writers then they must come up with the same problem at some point

must have been coincidental

or smth


ngl tho this topic is pretty random
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MathPerson12321
3797 posts
MathPerson12321
#7 h  Apr 25, 2025, 2:58 PM
Y by
K1mchi_ wrote:
Charizard_637 wrote:
you can with that many problem writers for the national competition

then with that many writers then they must come up with the same problem at some point

must have been coincidental

or smth


ngl tho this topic is pretty random

The exact same?
The problems being about the same thing is different
This is most definitely intentional
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K1mchi_
155 posts
K1mchi_
#8 h  Apr 25, 2025, 3:33 PM
Y by
MathPerson12321 wrote:
K1mchi_ wrote:
Charizard_637 wrote:
you can with that many problem writers for the national competition

then with that many writers then they must come up with the same problem at some point

must have been coincidental

or smth


ngl tho this topic is pretty random

The exact same?
The problems being about the same thing is different
This is most definitely intentional

intentionally doing the same problem? thats a new low
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MathPerson12321
3797 posts
MathPerson12321
#9 h  Apr 25, 2025, 3:36 PM
Y by
I am sure this is not accidental
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K1mchi_
155 posts
K1mchi_
#10 h  Apr 25, 2025, 3:37 PM
Y by
MathPerson12321 wrote:
I am sure this is not accidental

that makes more sense

idk anyone could be lazy

except me lol
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iwastedmyusername
190 posts
iwastedmyusername
#11 h  Apr 25, 2025, 4:06 PM
Y by
yes mathcounts has a habit of reusing problbems
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ilikemath247365
278 posts
ilikemath247365
#12 h  Apr 25, 2025, 11:56 PM
Y by
Yeah it was something really random, I just happened to mock those two tests and saw the same problems.
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