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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next 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 an enriching 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][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
k i Suggestion Form
jwelsh   0
May 6, 2021
Hello!

Given the number of suggestions we’ve been receiving, we’re transitioning to a suggestion form. If you have a suggestion for the AoPS website, please submit the Google Form:
Suggestion Form

To keep all new suggestions together, any new suggestion threads posted will be deleted.

Please remember that if you find a bug outside of FTW! (after refreshing to make sure it’s not a glitch), make sure you’re following the How to write a bug report instructions and using the proper format to report the bug.

Please check the FTW! thread for bugs and post any new ones in the For the Win! and Other Games Support Forum.
0 replies
jwelsh
May 6, 2021
0 replies
k i Read me first / How to write a bug report
slester   3
N May 4, 2019 by LauraZed
Greetings, AoPS users!

If you're reading this post, that means you've come across some kind of bug, error, or misbehavior, which nobody likes! To help us developers solve the problem as quickly as possible, we need enough information to understand what happened. Following these guidelines will help us squash those bugs more effectively.

Before submitting a bug report, please confirm the issue exists in other browsers or other computers if you have access to them.

For a list of many common questions and issues, please see our user created FAQ, Community FAQ, or For the Win! FAQ.

What is a bug?
A bug is a misbehavior that is reproducible. If a refresh makes it go away 100% of the time, then it isn't a bug, but rather a glitch. That's when your browser has some strange file cached, or for some reason doesn't render the page like it should. Please don't report glitches, since we generally cannot fix them. A glitch that happens more than a few times, though, could be an intermittent bug.

If something is wrong in the wiki, you can change it! The AoPS Wiki is user-editable, and it may be defaced from time to time. You can revert these changes yourself, but if you notice a particular user defacing the wiki, please let an admin know.

The subject
The subject line should explain as clearly as possible what went wrong.

Bad: Forum doesn't work
Good: Switching between threads quickly shows blank page.

The report
Use this format to report bugs. Be as specific as possible. If you don't know the answer exactly, give us as much information as you know. Attaching a screenshot is helpful if you can take one.

Summary of the problem:
Page URL:
Steps to reproduce:
1.
2.
3.
...
Expected behavior:
Frequency:
Operating system(s):
Browser(s), including version:
Additional information:


If your computer or tablet is school issued, please indicate this under Additional information.

Example
Summary of the problem: When I click back and forth between two threads in the site support section, the content of the threads no longer show up. (See attached screenshot.)
Page URL: http://artofproblemsolving.com/community/c10_site_support
Steps to reproduce:
1. Go to the Site Support forum.
2. Click on any thread.
3. Click quickly on a different thread.
Expected behavior: To see the second thread.
Frequency: Every time
Operating system: Mac OS X
Browser: Chrome and Firefox
Additional information: Only happens in the Site Support forum. My tablet is school issued, but I have the problem at both school and home.

How to take a screenshot
Mac OS X: If you type ⌘+Shift+4, you'll get a "crosshairs" that lets you take a custom screenshot size. Just click and drag to select the area you want to take a picture of. If you type ⌘+Shift+4+space, you can take a screenshot of a specific window. All screenshots will show up on your desktop.

Windows: Hit the Windows logo key+PrtScn, and a screenshot of your entire screen. Alternatively, you can hit Alt+PrtScn to take a screenshot of the currently selected window. All screenshots are saved to the Pictures → Screenshots folder.

Advanced
If you're a bit more comfortable with how browsers work, you can also show us what happens in the JavaScript console.

In Chrome, type CTRL+Shift+J (Windows, Linux) or ⌘+Option+J (Mac).
In Firefox, type CTRL+Shift+K (Windows, Linux) or ⌘+Option+K (Mac).
In Internet Explorer, it's the F12 key.
In Safari, first enable the Develop menu: Preferences → Advanced, click "Show Develop menu in menu bar." Then either go to Develop → Show Error console or type Option+⌘+C.

It'll look something like this:
IMAGE
3 replies
slester
Apr 9, 2015
LauraZed
May 4, 2019
k i Community Safety
dcouchman   0
Jan 18, 2018
If you find content on the AoPS Community that makes you concerned for a user's health or safety, please alert AoPS Administrators using the report button (Z) or by emailing sheriff@aops.com . You should provide a description of the content and a link in your message. If it's an emergency, call 911 or whatever the local emergency services are in your country.

Please also use those steps to alert us if bullying behavior is being directed at you or another user. Content that is "unlawful, harmful, threatening, abusive, harassing, tortuous, defamatory, vulgar, obscene, libelous, invasive of another's privacy, hateful, or racially, ethnically or otherwise objectionable" (AoPS Terms of Service 5.d) or that otherwise bullies people is not tolerated on AoPS, and accounts that post such content may be terminated or suspended.
0 replies
dcouchman
Jan 18, 2018
0 replies
Moving stones on an infinite row
miiirz30   0
6 minutes ago
Source: 2025 Euler Olympiad, Round 2
We are given an infinite row of cells extending infinitely in both directions. Some cells contain one or more stones. The total number of stones is finite. At each move, the player performs one of the following three operations:

1. Take three stones from some cell, and add one stone to the cells located one cell to the left and one cell to the right, each skipping one cell in between.

2. Take two stones from some cell, and add one stone to the cell one cell to the left, skipping one cell and one stone to the adjacent cell to the right.

3. Take one stone from each of two adjacent cells, and add one stone to the cell to the right of these two cells.

The process ends when no moves are possible. Prove that the process always terminates and the final distribution of stones does not depend on the choices of moves made by the player.

IMAGE

Proposed by Luka Tsulaia, Georgia
0 replies
miiirz30
6 minutes ago
0 replies
Cauchy and multiplicative function over a field extension
miiirz30   0
19 minutes ago
Source: 2025 Euler Olympiad, Round 2
Find all functions $f : \mathbb{Q}[\sqrt{2}] \to \mathbb{Q}[\sqrt{2}]$ such that for all $x, y \in \mathbb{Q}[\sqrt{2}]$,
$$
f(xy) = f(x)f(y) \quad \text{and} \quad f(x + y) = f(x) + f(y),
$$where $\mathbb{Q}[\sqrt{2}] = \{ a + b\sqrt{2} \mid a, b \in \mathbb{Q} \}$.

Proposed by Stijn Cambie, Belgium
0 replies
miiirz30
19 minutes ago
0 replies
Alice, Bob and 6 boxes
Anulick   1
N 25 minutes ago by RPCX
Source: SMMC 2024, B1
Alice has six boxes labelled 1 through 6. She secretly chooses exactly two of the boxes and places a coin inside each. Bob is trying to guess which two boxes contain the coins. Each time Bob guesses, he does so by tapping exactly two of the boxes. Alice then responds by telling him the total number of coins inside the two boxes that he tapped. Bob successfully finds the two coins when Alice responds with the number 2.

What is the smallest positive integer $n$ such that Bob can always find the two coins in at most $n$ guesses?
1 reply
Anulick
Oct 12, 2024
RPCX
25 minutes ago
functional inequality with equality
miiirz30   0
27 minutes ago
Source: 2025 Euler Olympiad, Round 2
Find all functions \( f : \mathbb{R} \to \mathbb{R} \) such that the following two conditions hold:

1. For all real numbers $a$ and $b$ satisfying $a^2 + b^2 = 1$, We have $f(x) + f(y) \geq f(ax + by)$ for all real numbers $x, y$.

2. For all real numbers $x$ and $y$, there exist real numbers $a$ and $b$, such that $a^2 + b^2 = 1$ and $f(x) + f(y) = f(ax + by)$.

Proposed by Zaza Melikidze, Georgia
0 replies
miiirz30
27 minutes ago
0 replies
k alcumus going crazy?
LittleSnake____   61
N May 19, 2025 by jlacosta
all of a sudden, the alcumus forum has gotten completely exploded by gamebot's posts.

https://artofproblemsolving.com/community/c63h3570498_alcumus_going_crazy
61 replies
LittleSnake____
May 18, 2025
jlacosta
May 19, 2025
k New user not allowed to use LaTeX
Cats_on_a_computer   8
N May 19, 2025 by Cats_on_a_computer
Do I seriously have to post everyday for 14 days for me not to be considered a “new user? I didn’t even upload any images, I just used LaTeX. How am I supposed to write anything without LaTeX?
8 replies
Cats_on_a_computer
May 18, 2025
Cats_on_a_computer
May 19, 2025
k Duplicate Gamebot
cz1917   3
N May 19, 2025 by aiops
The same problem of Alcumus is posted twice by Gamebot. They even have different links:
First Link
Second Link
3 replies
cz1917
May 19, 2025
aiops
May 19, 2025
k Time travel
centslordm   11
N May 19, 2025 by stjwyl
IMAGE
11 replies
centslordm
May 18, 2025
stjwyl
May 19, 2025
k ALCUMUS IS BROKEN AGAIN!!!!
Neilmarar2022   1
N May 18, 2025 by Neilmarar2022
Game Bot is going crazy again... there is an insane number of posts in the last minute
1 reply
Neilmarar2022
May 18, 2025
Neilmarar2022
May 18, 2025
k Gamebot Problem
zhenghua   4
N May 18, 2025 by MathPerson12321
Summary of the problem: Multiple topics of the same problem are on the feed.
Page URL: Global Feed
Steps to reproduce:
1. Open the global feed
2. There are a lot of topics of the same problem.
Expected behavior: Should only be one topic.
Frequency: 100%
Operating system(s): Windows 10
Browser(s), including version: Google (don't know which version)
Additional information: None
4 replies
zhenghua
May 18, 2025
MathPerson12321
May 18, 2025
k My problem with AoPS account
BBNoDollar   2
N May 18, 2025 by SpeedCuber7
Hello ! Sorry because this is not a math problem. I wanted to post an image with a math problem, but it says I can t add photos because my account is too new. I joined in 2 May 2025, so my account is more than 2 weeks old. How do I find a solution? Thanks!
2 replies
BBNoDollar
May 18, 2025
SpeedCuber7
May 18, 2025
k profile pictures
happymoose666   1
N May 15, 2025 by RollingPanda4616
I'm pretty sure this question was raised before but why are their two different avatars?
1 reply
happymoose666
May 15, 2025
RollingPanda4616
May 15, 2025
k Glitch or Bug?
awesometriangles   5
N May 14, 2025 by Craftybutterfly
I was asking for some $\LaTeX$ help in one of my classrooms, and one of the Halpers posted. Is this a glitch or a bug(see screenshot)?


It seems as though I can edit their post...
5 replies
awesometriangles
May 14, 2025
Craftybutterfly
May 14, 2025
k Deleting collections
Sadigly   1
N May 12, 2025 by jlacosta
How to delete some collections? I accidently created 2 same collections, and one of them is useless
1 reply
Sadigly
May 11, 2025
jlacosta
May 12, 2025
Do not try to bash on beautiful geometry
ItzsleepyXD   9
N May 2, 2025 by Captainscrubz
Source: Own , Mock Thailand Mathematic Olympiad P9
Let $ABC$be triangle with point $D,E$ and $F$ on $BC,AB,CA$
such that $BE=CF$ and $E,F$ are on the same side of $BC$
Let $M$ be midpoint of segment $BC$ and $N$ be midpoint of segment $EF$
Let $G$ be intersection of $BF$ with $CE$ and $\dfrac{BD}{DC}=\dfrac{AC}{AB}$
Prove that $MN\parallel DG$
9 replies
ItzsleepyXD
Apr 30, 2025
Captainscrubz
May 2, 2025
Do not try to bash on beautiful geometry
G H J
Source: Own , Mock Thailand Mathematic Olympiad P9
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ItzsleepyXD
147 posts
#1 • 1 Y
Y by Dasfailure
Let $ABC$be triangle with point $D,E$ and $F$ on $BC,AB,CA$
such that $BE=CF$ and $E,F$ are on the same side of $BC$
Let $M$ be midpoint of segment $BC$ and $N$ be midpoint of segment $EF$
Let $G$ be intersection of $BF$ with $CE$ and $\dfrac{BD}{DC}=\dfrac{AC}{AB}$
Prove that $MN\parallel DG$
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moony_
22 posts
#2
Y by
ddit for AEGF and point D: pairs (DE, DF), (DA, DG), (DB, DC) are in involution. Now move this lines to point A in parallel: (AK, AI), (AL, AD), (Ainf, Ainf) and we wanna proof that AL is bissector of angle BAC. Now we move this involution on line BC: (K, I), (L, D), (inf, inf).
CI/CD = CA/CF => CI/BK = BE/CF * CA/BA * CD/BD = 1 => CI = BK => this involution is symmetry by point M => D and L are symmetrical by M => BL/CL = BA/CA => BL - bissector of angle BAC => DG || AL || MN => DG || MN

soooo nice geo ^_^
Attachments:
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moony_
22 posts
#3
Y by
ItzsleepyXD wrote:
Let $ABC$be triangle with point $D,E$ and $F$ on $BC,AB,CA$
such that $BE=CF$ and $E,F$ are on the same side of $BC$
Let $M$ be midpoint of segment $BC$ and $N$ be midpoint of segment $EF$
Let $G$ be intersection of $BF$ with $CE$ and $\dfrac{BD}{DC}=\dfrac{AC}{AB}$
Prove that $MN\parallel DG$


another solution:
Let ABA'C - parallelogram
BD/DC = CA/BA = BA'/CA' => A'D - bissector of angle BA'C.
G, D, A' collinear cuz parallelogram bissector lemma
GD || bissector of angle BAC || MN => GD || MN

you can proove parallelogram bissector lemma by using pappus theorem for lines AB and AC and points E, B, inf and F, C, inf on them

it may be easier than first one... hahaha

upd: point names on pic are wrong, sry
Attachments:
This post has been edited 2 times. Last edited by moony_, Apr 30, 2025, 12:38 PM
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FarrukhBurzu
6 posts
#4
Y by
Is $BE=CF$ true for D E F symmetrically ?
This post has been edited 1 time. Last edited by FarrukhBurzu, Apr 30, 2025, 7:59 PM
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Tkn
33 posts
#6
Y by
[asy]
size(9cm);
defaultpen(fontsize(11pt));
    
pair A = (-0.25,2);
pair B = (-1,0);
pair C = (2,0);

path C1 = circle(B,1);
path C2 = circle(C,1);

pair E1 = intersectionpoint(C1, A--B);
pair F = intersectionpoint(C2, A--C);

pair M = (E1+F)/2;
pair N1 = (B+C)/2;

pair P = 2N1-A;
pair Q = 2M-A;

pair R = extension(Q,F,B,P);
pair S1 = extension(E1,Q,C,P);
pair T = extension(B,F,C,E1);
pair D = extension(T,P,B,C);
pair U = extension(F,Q,C,E1);

draw(A--B--C--cycle, black);
draw(E1--Q--F, black);
draw(B--P--C, black);
draw(R--Q--S1, black+dashed);
draw(E1--F, black);
draw(B--F,blue);
draw(C--E1,blue);
draw(T--P, blue+dashed);
draw(M--N1, red+dashed);

        
dot(A);
dot(B);
dot(C);
dot(E1);
dot(F);
dot(P);
dot(Q);
dot(R);
dot(S1);
dot(M,red);
dot(N1,red);
dot(T,blue);
dot(D);

label("$A$", A, N, black);
label("$B$", B, SW, black);
label("$C$", C, E, black);
label("$E$", E1, NW, black);
label("$F$", F, NE, black);
label("$Q$", Q, 1.3W+0.5S, black);
label("$P$", P, S, black);
label("$R$", R, SW, black);
label("$S$", S1, SE, black);
label("$N$", N1, SW, black);
label("$M$", M, N, black);
label("$G$", T, S+0.5W, black);
label("$D$", D, NE, black);
[/asy]

Let $P$ and $Q$ denote the reflection of $A$ across $N$ and $M$, respectively.
Let $R=\overleftrightarrow{FQ}\cap\overleftrightarrow{BP}$, and $S=\overleftrightarrow{EQ}\cap \overleftrightarrow{CP}$
Note that $AM=MQ$, and $AN=NP$. It implies that $AEQF$, and $ABPC$ are parallelograms.
Since $BE=CF$, we have $QS=RP=RQ=PS$. This indicates that $PRQS$ is a rhombus. Furthermore, the line $\overleftrightarrow{PQ}$ must bisect $\angle{BPC}$.
By the given ratio condition of the point $D$:
$$\frac{BD}{CD}=\frac{AC}{AB}=\frac{BP}{CP},$$so, $D$ lies on the angle bisector of $\angle{BPC}$; that is $D\in \overleftrightarrow{PQ}$.
Next, it suffices to show that $G$ also lies on $\overleftrightarrow{PQ}$, and it could be proceed using Menelaus' theorem on $\triangle{ABF}$ and the line $\overleftrightarrow{EGC}$:
\begin{align*}
    1&=\frac{BE}{AE}\cdot \frac{AC}{CF}\cdot \frac{FG}{GB}\\
    &=\frac{AE}{BE}\cdot \frac{CF}{AC}\cdot \frac{GB}{FG}\\
    &=\frac{FQ}{QR}\cdot \frac{RP}{BP}\cdot \frac{GB}{GF}.
\end{align*}The converse of Menelaus' theorem also holds for $\triangle{FBR}$, so $G\in \overleftrightarrow{PQ}$.
The last step is to observe that $A$ is the homothetic center sending $\overline{MN}\mapsto \overline{QP}$. Therefore, $\overleftrightarrow{PQ}\parallel\overleftrightarrow{MN}$.
In conclusion $\overleftrightarrow{MN}\parallel\overleftrightarrow{GD}$ as desired.
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cj13609517288
1922 posts
#7
Y by
Swap the names of $E$ and $F$.

Move $E$ linearly along $AC$, then $F$ moves linearly along $AB$ and $N$ moves linearly. Assume WLOG $AB<AC$, then let the value of $E$ when $F=A$ be $P$. Then when $F=B$ and $F=A$ we get that $N$ lies on the line through $M$ and the midpoint of $AP$. A homothety of scale factor $2$ from $A$ takes this line through $D$ parallel to the $A$-angle bisector. A simple bary (or MMP) argument shows that $G$ moves on a line (since it's degree $1+1-1=1$). When $E=P$ we get $G=P$ which does lie on the desired line. When $E=A$ we get $G=DP\cap AB$ which does lie on the desired line. $\blacksquare$
This post has been edited 1 time. Last edited by cj13609517288, May 1, 2025, 3:55 PM
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DottedCaculator
7357 posts
#8
Y by
Beautiful problem with a beautiful solution!

Let $D=(0:c:b)$, $E=(t:c-t:0)$, and $F=(t:0:b-t)$. Then, $M=(0:1:1)$ and $N=((b+c)t:b(c-t):c(b-t))$, so $MN$ has direction $(b+c:-b:-c)$. In addition, $G=(t:c-t:b-t)$, so $DG$ also has direction $(t(b+c):(c-t)(b+c)-c(b+c-t):(b-t)(b+c)-b(b+c-t))=(t(b+c):-bt:-ct)=(b+c:-b:-c)$. Therefore, $MN$ and $DG$ are parallel.
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Assassino9931
1362 posts
#9
Y by
In this config it is also well known (follows through the midpoint of $BF$ or $CE$) that $MN$ is parallel to the angle bisector of $\angle BAC$.
In fact, the foot of this bisector is isotomic with $D$ by the angle bisector property.
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Ianis
415 posts
#10
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Assassino9931 wrote:
In this config it is also well known (follows through the midpoint of $BF$ or $CE$) that $MN$ is parallel to the angle bisector of $\angle BAC$.
In fact, the foot of this bisector is isotomic with $D$ by the angle bisector property.

Indeed! And hence it suffices to prove that if $G'$ is the reflection of $G$ wart to $M$ then $G'$ lies on the angle bisector of $\angle BAC$, for which it suffices to prove that the distances from $G'$ to $CA$ and $AB$ are equal. Since $CF=BE$ it suffices to prove that $[G'CF]=[G'EB]$. Now, observe that$$[G'CF]=[G'CB]=[G'EB],$$because $BF\parallel BG\parallel CG'$ and $CE\parallel CG\parallel BF'$. Done.

Credits go to @magnusarg for this solution.
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Captainscrubz
78 posts
#11
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Let $P$ be the arc midpoint of $BAC$
Let an arbitrary circle from $P$ and $A$ intersect $AB$ and $AC$ at $E'$ and $F'$ respectively.
As $P$ will be the center of spiral similarity that sends $E'F'\rightarrow BC$
$\implies \angle E'PB=\angle F'PC$ and $E'P=F'P, BP=PC \implies E'B=F'C$
$\therefore E'\equiv E$ and $F'\equiv F$
If $AB<AC$ then let $H=MN\cap AC$
see that as $P$ is the center of spiral similarity that sends $NF\rightarrow MC$ and a fixed point $\implies PHMC$ is cyclic$\implies H$ is a fixed point
and $\angle NHF=\angle NPF=\angle \frac{A}{2} \implies MN \parallel A\text{ angle bisector}$
Now after the introduction of point $A'$ such that $ABA'C$ is a parallelogram the problem reduces to-
Quote:
Let $G$ be a point on the angle bisector of $A$ and let $l_1$ and $l_2$ be lines from $B$ and $C$ such that $l_1$ and $l_2$ is parallel to $AC$ and $AB$. Let $E=CG\cap l_1$ and $F=BG\cap l_2$. Prove $BE=CF$.
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