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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
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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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Circle in a Parallelogram
djmathman   55
N 6 minutes ago by Ilikeminecraft
Source: 2022 AIME I #11
Let $ABCD$ be a parallelogram with $\angle BAD < 90^{\circ}$. A circle tangent to sides $\overline{DA}$, $\overline{AB}$, and $\overline{BC}$ intersects diagonal $\overline{AC}$ at points $P$ and $Q$ with $AP < AQ$, as shown. Suppose that $AP = 3$, $PQ = 9$, and $QC = 16$. Then the area of $ABCD$ can be expressed in the form $m\sqrt n$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$.

IMAGE
55 replies
djmathman
Feb 9, 2022
Ilikeminecraft
6 minutes ago
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Maximum reach of splitting tokens
MathMystic33   0
9 minutes ago
Source: Macedonian Mathematical Olympiad 2025 Problem 3
On a horizontally placed number line, a pile of \( t_i > 0 \) tokens is placed on each number \( i \in \{1, 2, \ldots, s\} \). As long as at least one pile contains at least two tokens, we repeat the following procedure: we choose such a pile (say, it consists of \( k \geq 2 \) tokens), and move the top token from the selected pile \( k - 1 \) unit positions to the right along the number line. What is the largest natural number \( N \) on which a token can be placed? (Express \( N \) as a function of \( (t_i;\ i = 1, \ldots, s) \).)
0 replies
+1 w
MathMystic33
9 minutes ago
0 replies
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Inequality with rational function
MathMystic33   0
11 minutes ago
Source: Macedonian Mathematical Olympiad 2025 Problem 2
Let \( n > 2 \) be an integer, \( k > 1 \) a real number, and \( x_1, x_2, \ldots, x_n \) be positive real numbers such that \( x_1 \cdot x_2 \cdots x_n = 1 \). Prove that:

\[ \frac{1 + x_1^k}{1 + x_2} + \frac{1 + x_2^k}{1 + x_3} + \cdots + \frac{1 + x_n^k}{1 + x_1} \geq n. \]
When does equality hold?
0 replies
MathMystic33
11 minutes ago
0 replies
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Circumcircle of MUV tangent to two circles at once
MathMystic33   0
13 minutes ago
Source: Macedonian Mathematical Olympiad 2025 Problem 1
Given is an acute triangle \( \triangle ABC \) with \( AB < AC \). Let \( M \) be the midpoint of side \( BC \), and let \( X \) and \( Y \) be points on segments \( BM \) and \( CM \), respectively, such that \( BX = CY \). Let \( \omega_1 \) be the circumcircle of \( \triangle ABX \), and \( \omega_2 \) the circumcircle of \( \triangle ACY \). The common tangent \( t \) to \( \omega_1 \) and \( \omega_2 \), which lies closer to point \( A \), touches \( \omega_1 \) and \( \omega_2 \) at points \( P \) and \( Q \), respectively. Let the line \( MP \) intersect \( \omega_1 \) again at \( U \), and the line \( MQ \) intersect \( \omega_2 \) again at \( V \). Prove that the circumcircle of triangle \( \triangle MUV \) is tangent to both \( \omega_1 \) and \( \omega_2 \).
0 replies
MathMystic33
13 minutes ago
0 replies
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Aime 2 2025 problem 10
Rook567   0
16 minutes ago
Looking the solution 2, why are there 9 cases when no person is sitting next to another person? Wouldn’t there be just two, all even numbered or all odd numbered chairs?
0 replies
1 viewing
Rook567
16 minutes ago
0 replies
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USAMO 2003 Problem 5
MithsApprentice   93
N 17 minutes ago by endless_abyss
Let $ a$, $ b$, $ c$ be positive real numbers. Prove that
\[ \dfrac{(2a + b + c)^2}{2a^2 + (b + c)^2} + \dfrac{(2b + c + a)^2}{2b^2 + (c + a)^2} + \dfrac{(2c + a + b)^2}{2c^2 + (a + b)^2} \le 8. \]
93 replies
MithsApprentice
Sep 27, 2005
endless_abyss
17 minutes ago
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I got stuck in this combinatorics
artjustinhere237   1
N 35 minutes ago by maromex
Let $S = \{1, 2, 3, \ldots, k\}$, where $k \geq 4$ is a positive integer.
Prove that there exists a subset of $S$ with exactly $k - 2$ elements such that the sum of its elements is a prime number.
1 reply
artjustinhere237
an hour ago
maromex
35 minutes ago
J
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Solve the equation x^3y^2(2y - x) = x^2y^4-36
Eukleidis   9
N 36 minutes ago by MITDragon
Source: Greek Mathematical Olympiad 2011 - P1
Solve in integers the equation
\[{x^3}{y^2}\left( {2y - x} \right) = {x^2}{y^4} - 36\]
9 replies
Eukleidis
May 13, 2011
MITDragon
36 minutes ago
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[Signups Now!] - Inaugural Academy Math Tournament
elements2015   1
N 37 minutes ago by Ruegerbyrd
Hello!

Pace Academy, from Atlanta, Georgia, is thrilled to host our Inaugural Academy Math Tournament online through Saturday, May 31.

AOPS students are welcome to participate online, as teams or as individuals (results will be reported separately for AOPS and Georgia competitors). The difficulty of the competition ranges from early AMC to mid-late AIME, and is 2 hours long with multiple sections. The format is explained in more detail below. If you just want to sign up, here's the link:

https://forms.gle/ih548axqQ9qLz3pk7

If participating as a team, each competitor must sign up individually and coordinate team names!

Detailed information below:

Divisions & Teams
[list]
[*] Junior Varsity: Students in 10th grade or below who are enrolled in Algebra 2 or below.
[*] Varsity: All other students.
[*] Teams of up to four students compete together in the same division.
[list]
[*] (If you have two JV‑eligible and two Varsity‑eligible students, you may enter either two teams of two or one four‑student team in Varsity.)
[*] You may enter multiple teams from your school in either division.
[*] Teams need not compete at the same time. Each individual will complete the test alone, and team scores will be the sum of individual scores.
[/list]
[/list]
Competition Format
Both sections—Sprint and Challenge—will be administered consecutively in a single, individually completed 120-minute test. Students may allocate time between the sections however they wish to.

[list=1]
[*] Sprint Section
[list]
[*] 25 multiple‑choice questions (five choices each)
[*] recommended 2 minutes per question
[*] 6 points per correct answer; no penalty for guessing
[/list]

[*] Challenge Section
[list]
[*] 18 open‑ended questions
[*] answers are integers between 1 and 10,000
[*] recommended 3 or 4 minutes per question
[*] 8 points each
[/list]
[/list]
You may use blank scratch/graph paper, rulers, compasses, protractors, and erasers. No calculators are allowed on this examination.

Awards & Scoring
[list]
[*] There are no cash prizes.
[*] Team Awards: Based on the sum of individual scores (four‑student teams have the advantage). Top 8 teams in each division will be recognized.
[*] Individual Awards: Top 8 individuals in each division, determined by combined Sprint + Challenge scores, will receive recognition.
[/list]
How to Sign Up
Please have EACH STUDENT INDIVIDUALLY reserve a 120-minute window for your team's online test in THIS GOOGLE FORM:
https://forms.gle/ih548axqQ9qLz3pk7
EACH STUDENT MUST REPLY INDIVIDUALLY TO THE GOOGLE FORM.
You may select any slot from now through May 31, weekdays or weekends. You will receive an email with the questions and a form for answers at the time you receive the competition. There will be a 15-minute grace period for entering answers after the competition.
1 reply
elements2015
Yesterday at 8:13 PM
Ruegerbyrd
37 minutes ago
J
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Goals for 2025-2026
Airbus320-214   108
N 38 minutes ago by Ruegerbyrd
Please write down your goal/goals for competitions here for 2025-2026.
108 replies
Airbus320-214
May 11, 2025
Ruegerbyrd
38 minutes ago
J
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c^a + a = 2^b
Havu   2
N 40 minutes ago by dromemsilly
Find $a, b, c\in\mathbb{Z}^+$ such that $a,b,c$ coprime, $a + b = 2c$ and $c^a + a = 2^b$.
2 replies
Havu
May 10, 2025
dromemsilly
40 minutes ago
J
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They copied their problem!
pokmui9909   11
N an hour ago by cursed_tangent1434
Source: FKMO 2025 P1
Sequence $a_1, a_2, a_3, \cdots$ satisfies the following condition.

(Condition) For all positive integer $n$, $\sum_{k=1}^{n}\frac{1}{2}\left(1 - (-1)^{\left[\frac{n}{k}\right]}\right)a_k=1$ holds.

For a positive integer $m = 1001 \cdot 2^{2025}$, compute $a_m$.
11 replies
pokmui9909
Mar 29, 2025
cursed_tangent1434
an hour ago
J
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Trigonometric Product
Henryfamz   0
an hour ago
Compute $$\prod_{n=1}^{45}\sin(2n-1)$$
0 replies
Henryfamz
an hour ago
0 replies
J
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Gives typical russian combinatorics vibes
Sadigly   1
N an hour ago by Sadigly
Source: Azerbaijan Senior MO 2025 P3
You are given a positive integer $n$. $n^2$ amount of people stand on coordinates $(x;y)$ where $x,y\in\{0;1;2;...;n-1\}$. Every person got a water cup and two people are considered to be neighbour if the distance between them is $1$. At the first minute, the person standing on coordinates $(0;0)$ got $1$ litres of water, and the other $n^2-1$ people's water cup is empty. Every minute, two neighbouring people are chosen that does not have the same amount of water in their water cups, and they equalize the amount of water in their water cups.

Prove that, no matter what, the person standing on the coordinates $(x;y)$ will not have more than $\frac1{x+y+1}$ litres of water.
1 reply
1 viewing
Sadigly
May 8, 2025
Sadigly
an hour ago
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J
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k RIP BS2012
gavinhaominwang   22
N Apr 23, 2025 by torch
Rip BS2012, I hope you come back next year stronger and prove everyone wrong.
22 replies
gavinhaominwang
Apr 23, 2025
torch
Apr 23, 2025
J
RIP BS2012
G H J
Reveal topic tags
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G H BBookmark kLocked kLocked NReply
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gavinhaominwang
92 posts
gavinhaominwang
#1 h  Apr 23, 2025, 12:32 AM • 4 Y
Y by PikaPika999, bwu_2022, scannose, bjump
Rip BS2012, I hope you come back next year stronger and prove everyone wrong.
Z Y
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maxamc
577 posts
maxamc
#2 h  Apr 23, 2025, 12:33 AM • 1 Y
Y by PikaPika999
Also rip hashbrown2009
Z Y
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Andyluo
965 posts
Andyluo
#3 h  Apr 23, 2025, 2:43 AM • 4 Y
Y by Mathandski, bjump, megarnie, KevinYang2.71
RIP Bjump, you got this next year tho fr
Z Y
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mathkiddus
242 posts
mathkiddus
#4 h  Apr 23, 2025, 2:55 AM • 2 Y
Y by mathfan2020, bjump
also RIP dogeA,
Z Y
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vincentwant
1417 posts
vincentwant
#5 h  Apr 23, 2025, 3:36 AM • 3 Y
Y by mathfan2020, Ilikeminecraft, bjump
RIP a_smart_alecks
Z Y
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ThoughtfulGorilla10
27 posts
ThoughtfulGorilla10
#6 h  Apr 23, 2025, 3:40 AM
Y by
What do i do here
Z Y
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mathfan2020
351 posts
mathfan2020
#7 h  Apr 23, 2025, 3:56 AM • 1 Y
Y by bjump
RIP PenguinMoosey
Z Y
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PEKKA
1848 posts
PEKKA
#8 h  Apr 23, 2025, 4:23 AM • 1 Y
Y by bjump
RIP llmmddtt1
Z Y
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zhoujef000
318 posts
zhoujef000
#9 h  Apr 23, 2025, 4:26 AM • 4 Y
Y by bjump, megarnie, mathfan2020, KnowingAnt
RIP KnowingAnt
Z Y
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Alpaca31415
12 posts
Alpaca31415
#10 h  Apr 23, 2025, 4:41 AM • 1 Y
Y by bjump
rip me fr I suck
Z Y
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Ilikeminecraft
643 posts
Ilikeminecraft
#11 h  Apr 23, 2025, 4:55 AM • 2 Y
Y by bjump, mathfan2020
rip impromptuA
Z Y
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deduck
238 posts
deduck
#12 h  Apr 23, 2025, 5:24 AM • 4 Y
Y by bjump, bachkieu, mathfan2020, ninjaforce
rip math4life2020
Z Y
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KevinYang2.71
427 posts
KevinYang2.71
#13 h  Apr 23, 2025, 6:40 AM • 4 Y
Y by Mathandski, bjump, megarnie, deduck
rip deduck
Z Y
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MathRook7817
734 posts
MathRook7817
#14 h  Apr 23, 2025, 2:16 PM
Y by
RIP MathRook7817
Z Y
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NoSignOfTheta
1744 posts
NoSignOfTheta
#15 h  Apr 23, 2025, 2:23 PM
Y by
RIP aopsonline2020888
Z Y
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ethan2011
320 posts
ethan2011
#16 h  Apr 23, 2025, 2:28 PM • 1 Y
Y by mathfan2020
RIP mathfan2020
Z Y
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TiguhBabeHwo
479 posts
TiguhBabeHwo
#17 h  Apr 23, 2025, 2:50 PM • 1 Y
Y by mathfan2020
RIP ethan2011
Z Y
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MathPerson12321
3778 posts
MathPerson12321
#18 h  Apr 23, 2025, 2:53 PM
Y by
rip everyone but we dont need a separate thread for this
/req lock

you all will make it next yr!
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bachkieu
137 posts
bachkieu
#19 h  Apr 23, 2025, 3:01 PM
Y by
rip tiguhbabehwo 232
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Mathdreams
1472 posts
Mathdreams
#20 h  Apr 23, 2025, 3:13 PM • 1 Y
Y by bjump
RIP bjump :(
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dragoon
1948 posts
dragoon
#21 h  Apr 23, 2025, 3:14 PM • 1 Y
Y by bjump
rip bjump :( :(
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MathRook7817
734 posts
MathRook7817
#22 h  Apr 23, 2025, 3:22 PM
Y by
RIP everyone who didnt make JMO (me)
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torch
1014 posts
torch
#23 h  Apr 23, 2025, 3:23 PM • 2 Y
Y by bjump, KevinYang2.71
rip bjump :(
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