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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
4 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:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
4 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
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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MIT PRIMES STEP
pingpongmerrily   6
N 23 minutes ago by Multpi12
Anyone else applying? How cooked am I for the placement test... (106.5 AMC 10, 5 AIME, 36/27 States/Nationals)
6 replies
pingpongmerrily
May 30, 2025
Multpi12
23 minutes ago
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Goofy Ahh Rickety Roo Ahh Uncle
EugeneDingleBerry   6
N 24 minutes ago by smbellanki
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.
6 replies
EugeneDingleBerry
an hour ago
smbellanki
24 minutes ago
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2500th Post!
PikaPika999   28
N 31 minutes ago by ZMB038
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
28 replies
PikaPika999
May 29, 2025
ZMB038
31 minutes ago
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1 x 3 pieces in a 3 x 25 board,m max no of pieces placed
parmenides51   1
N an hour ago by TheBaiano
Source: Lusophon 2018 CPLP P6
In a $3 \times 25$ board, $1 \times 3$ pieces are placed (vertically or horizontally) so that they occupy entirely $3$ boxes on the board and do not have a common point.
What is the maximum number of pieces that can be placed, and for that number, how many configurations are there?

original formulation
1 reply
parmenides51
Sep 13, 2018
TheBaiano
an hour ago
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smallest a so that S(n)-S(n+a) = 2018, where S(n)=sum of digits
parmenides51   3
N an hour ago by TheBaiano
Source: Lusophon 2018 CPLP P3
For each positive integer $n$, let $S(n)$ be the sum of the digits of $n$. Determines the smallest positive integer $a$ such that there are infinite positive integers $n$ for which you have $S (n) -S (n + a) = 2018$.
3 replies
parmenides51
Sep 13, 2018
TheBaiano
an hour ago
J
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Ducks can play games now apparently
MortemEtInteritum   35
N 2 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
2 hours ago
J
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Share your favorite problem
the_mathtrovert_next_door   4
N 2 hours ago by CJB19
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.
4 replies
the_mathtrovert_next_door
4 hours ago
CJB19
2 hours ago
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2017 IGO Advanced P3
bgn   18
N 2 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
2 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 3 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
3 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
J
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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 4 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
4 hours ago
J
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J
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Mathpath acceptance rate
fossasor   15
N Apr 22, 2025 by ZMB038
Does someone have an estimate for the acceptance rate for MathPath?
15 replies
fossasor
Dec 21, 2024
ZMB038
Apr 22, 2025
J
Mathpath acceptance rate
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Reveal topic tags
summer program
MathPath
L
G H BBookmark kLocked kLocked NReply
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fossasor
611 posts
fossasor
#1 h  Dec 21, 2024, 10:20 PM
Y by
Does someone have an estimate for the acceptance rate for MathPath?
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oinava
509 posts
oinava
#2 h  Dec 21, 2024, 11:25 PM
Y by
Years ago it was about 15%, but probably much lower now.
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fossasor
611 posts
fossasor
#3 h  Dec 22, 2024, 4:42 AM
Y by
Ugh, that's unfortunate. Is there any suggestion you can make for me to improve my chances of acceptance?
Z K Y
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lily2030
599 posts
lily2030
#4 h  Dec 22, 2024, 6:37 AM
Y by
How hard is mathpath?
What is the level that people are at to get in? (in terms of mathcounts, amc 10, amc 8, etc.)
Z K Y
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oinava
509 posts
oinava
#5 h  Dec 22, 2024, 1:47 PM
Y by
fossasor wrote:
Ugh, that's unfortunate. Is there any suggestion you can make for me to improve my chances of acceptance?

Convince some mathematicians to open more middle school math camps or increase the size of existing ones.

Anything an applicant does to improve their chances makes everyone else's chances lower.
Z K Y
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oinava
509 posts
oinava
#6 h  Dec 22, 2024, 1:59 PM
Y by
lily2030 wrote:
How hard is mathpath?
What is the level that people are at to get in? (in terms of mathcounts, amc 10, amc 8, etc.)

It's a secret. The staff don't want applicants to know.

I gather that the theory is that it's not supposed to matter, because the Qualifying Test is mostly self-selecting as a preview of the MathPath experience. MathCamp is like an all day, all week, all month Qualifying Test.

Only attempt as much of the Qualifying Test as you enjoy. Then if you get in, trust that they know you are ready for camp (which is highly adaptive with dozens of different courses to choose from, and no grades), because there are many more qualified applicants than spots.
And if you don't get in, it's OK because not getting everything you want is just how life is, and no harm done because you enjoyed the time you spent taking the test.

The only big problem with this theory is that the Qualifying Test is a solitary, lonely experience, but camp is very social and interactive.

https://www.mathpath.org/life/faq
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fossasor
611 posts
fossasor
#7 h  Dec 22, 2024, 3:07 PM
Y by
oinava wrote:
fossasor wrote:
Ugh, that's unfortunate. Is there any suggestion you can make for me to improve my chances of acceptance?

Convince some mathematicians to open more middle school math camps or increase the size of existing ones.

Anything an applicant does to improve their chances makes everyone else's chances lower.

... any ACTUAL advice?
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dragonborn56
1536 posts
dragonborn56
#8 h  Dec 22, 2024, 9:26 PM
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I don;t think that there is much that you can do apart from trying your best on the qualifying test and submitting early. Also, if you are rejected, try again next year if you are able. I myself was rejected the first time that I applied, and tried again and was admitted.
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SOAR1231
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SOAR1231
#9 h  Jan 30, 2025, 5:08 PM
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apply earlier
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fossasor
611 posts
fossasor
#10 h  Jan 30, 2025, 11:24 PM
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I have - my application was submitted completely this Sunday, so it's all out of my hands now. Thank you for the advice!
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SOAR1231
28 posts
SOAR1231
#11 h  Jan 31, 2025, 1:46 AM
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oh nice, some decisions already came out
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DreamineYT
299 posts
DreamineYT
#12 h  Jan 31, 2025, 3:21 AM
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lily2030 wrote:
How hard is mathpath?
What is the level that people are at to get in? (in terms of mathcounts, amc 10, amc 8, etc.)

imo i dont think they focus on this very much. I think they focus more on like ur hobbies and stuff because they want u to have a life outside of math

all of the courses have very different difficulties, and the ones that are together(plenaries) can sometimes be challeniging. Also, it's not like AMSP where comp math is the main focus. It's more about research math or theoretical math(topology, for example)
This post has been edited 1 time. Last edited by DreamineYT, Jan 31, 2025, 3:22 AM
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ZMB038
303 posts
ZMB038
#13 h  Apr 10, 2025, 12:18 PM
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This summer will be my first year going, what's math Path like?
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ZMB038
303 posts
ZMB038
#14 h  Apr 14, 2025, 12:28 PM
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DreamineYT wrote:
lily2030 wrote:
How hard is mathpath?
What is the level that people are at to get in? (in terms of mathcounts, amc 10, amc 8, etc.)

imo i dont think they focus on this very much. I think they focus more on like ur hobbies and stuff because they want u to have a life outside of math

all of the courses have very different difficulties, and the ones that are together(plenaries) can sometimes be challeniging. Also, it's not like AMSP where comp math is the main focus. It's more about research math or theoretical math(topology, for example)

It looks really fun, can't wait to go. I like proofs better than comp math anyway.
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RainbowSquirrel53B
595 posts
RainbowSquirrel53B
#15 h  Apr 15, 2025, 10:30 PM
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ZMB038 wrote:
This summer will be my first year going, what's math Path like?

fun :D you meet lots of cool people
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ZMB038
303 posts
ZMB038
#16 h  Apr 22, 2025, 6:15 PM
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RainbowSquirrel53B wrote:
ZMB038 wrote:
This summer will be my first year going, what's math Path like?

fun :D you meet lots of cool people

Cool, are you going this year?
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