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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/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
Mar 2, 2025
0 replies
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
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
Problem 4
blug   0
23 minutes ago
Source: Polish Junior Math Olympiad Finals 2025
In a rhombus $ABCD$, angle $\angle ABC=100^{\circ}$. Point $P$ lies on $CD$ such that $\angle PBC=20^{\circ}$. Line parallel to $AD$ passing trough $P$ intersects $AC$ at $Q$. Prove that $BP=AQ$.
0 replies
blug
23 minutes ago
0 replies
Problem 3
blug   0
26 minutes ago
Source: Polish Junior Math Olympiad Finals 2025
Find all primes $(p, q, r)$ such that
$$pq+4=r^4.$$
0 replies
blug
26 minutes ago
0 replies
Problem 2
blug   0
27 minutes ago
Source: Polish Junior Math Olympiad Finals 2025
A party is attended by boys and girls. Each person attending the party knows exactly 3 boys and exactly 7 girls among the other people. Prove that the number of all the people attending the party is divisible by 20.
0 replies
blug
27 minutes ago
0 replies
Problem 1
blug   0
28 minutes ago
Source: Polish Junior Math Olympiad Finals 2025
Do there exists a tetrahedron, in which the lenghts of the edges are six different integers such that their sum is 25?
0 replies
blug
28 minutes ago
0 replies
A two-variable & non-homogenous inequality that seems hard to me
MyLifeMyChoice   3
N 36 minutes ago by Radin_
Source: Developing from a larger, three-variable one
For $a,b>0$, prove/disprove the following claim: :maybe:

$a^3b^3+\frac{1}{a^3}+\frac{1}{b^3}+3\stackrel{?}{\ge}a^2b+b^2a+\frac{1}{a^2b}+\frac{1}{b^2a}+\frac{a}{b}+\frac{b}{a}$
3 replies
MyLifeMyChoice
Mar 13, 2025
Radin_
36 minutes ago
exponential diophantine with factorials
skellyrah   4
N an hour ago by InftyByond
find all non negative integers (x,y) such that $$ x! + y! = 2025^x + xy$$
4 replies
skellyrah
Feb 24, 2025
InftyByond
an hour ago
Point satisfies triple property
62861   35
N an hour ago by Sanjana42
Source: USA Winter Team Selection Test #2 for IMO 2018, Problem 2
Let $ABCD$ be a convex cyclic quadrilateral which is not a kite, but whose diagonals are perpendicular and meet at $H$. Denote by $M$ and $N$ the midpoints of $\overline{BC}$ and $\overline{CD}$. Rays $MH$ and $NH$ meet $\overline{AD}$ and $\overline{AB}$ at $S$ and $T$, respectively. Prove that there exists a point $E$, lying outside quadrilateral $ABCD$, such that
[list]
[*] ray $EH$ bisects both angles $\angle BES$, $\angle TED$, and
[*] $\angle BEN = \angle MED$.
[/list]

Proposed by Evan Chen
35 replies
62861
Jan 22, 2018
Sanjana42
an hour ago
Prove concyclic and tangency
syk0526   40
N an hour ago by Ilikeminecraft
Source: Japan Olympiad Finals 2014, #4
Let $ \Gamma $ be the circumcircle of triangle $ABC$, and let $l$ be the tangent line of $\Gamma $ passing $A$. Let $ D, E $ be the points each on side $AB, AC$ such that $ BD : DA= AE : EC $. Line $ DE $ meets $\Gamma $ at points $ F, G $. The line parallel to $AC$ passing $ D $ meets $l$ at $H$, the line parallel to $AB$ passing $E$ meets $l$ at $I$. Prove that there exists a circle passing four points $ F, G, H, I $ and tangent to line $ BC$.
40 replies
syk0526
May 17, 2014
Ilikeminecraft
an hour ago
p^2+3*p*q+q^2
mathbetter   0
2 hours ago
\[
\text{Find all prime numbers } (p, q) \text{ such that } p^2 + 3pq + q^2 \text{ is a fifth power of an integer.}
\]
0 replies
+1 w
mathbetter
2 hours ago
0 replies
two sequences of positive integers and inequalities
rmtf1111   49
N 2 hours ago by dolphinday
Source: EGMO 2019 P5
Let $n\ge 2$ be an integer, and let $a_1, a_2, \cdots , a_n$ be positive integers. Show that there exist positive integers $b_1, b_2, \cdots, b_n$ satisfying the following three conditions:

$\text{(A)} \ a_i\le b_i$ for $i=1, 2, \cdots , n;$

$\text{(B)} \ $ the remainders of $b_1, b_2, \cdots, b_n$ on division by $n$ are pairwise different; and

$\text{(C)} \ $ $b_1+b_2+\cdots b_n \le n\left(\frac{n-1}{2}+\left\lfloor \frac{a_1+a_2+\cdots a_n}{n}\right \rfloor \right)$

(Here, $\lfloor x \rfloor$ denotes the integer part of real number $x$, that is, the largest integer that does not exceed $x$.)
49 replies
rmtf1111
Apr 10, 2019
dolphinday
2 hours ago
AIME score for college apps
Happyllamaalways   56
N 4 hours ago by Countmath1
What good colleges do I have a chance of getting into with an 11 on AIME? (Any chances for Princeton)

Also idk if this has weight but I had the highest AIME score in my school.
56 replies
Happyllamaalways
Mar 13, 2025
Countmath1
4 hours ago
MIT Beaverworks Summer Institute
PowerOfPi_09   0
4 hours ago
Hi! I was wondering if anyone here has completed this program, and if so, which track did you choose? Do rising juniors have a chance, or is it mainly rising seniors that they accept? Also, how long did it take you to complete the prerequisites?
Thanks!
0 replies
PowerOfPi_09
4 hours ago
0 replies
Convolution of order f(n)
trumpeter   70
N 4 hours ago by HamstPan38825
Source: 2019 USAMO Problem 1
Let $\mathbb{N}$ be the set of positive integers. A function $f:\mathbb{N}\to\mathbb{N}$ satisfies the equation \[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]for all positive integers $n$. Given this information, determine all possible values of $f(1000)$.

Proposed by Evan Chen
70 replies
trumpeter
Apr 17, 2019
HamstPan38825
4 hours ago
k HOT TAKE: MIT SHOULD NOT RELEASE THEIR DECISIONS ON PI DAY
alcumusftwgrind   8
N Today at 10:13 AM by maxamc
rant lol

Imagine a poor senior waiting for their MIT decisions just to have their hopes CRUSHED on 3/14 and they can't even celebrate pi day...

and even worse, this year's pi day is special because this year is a very special number...

8 replies
alcumusftwgrind
Today at 2:11 AM
maxamc
Today at 10:13 AM
Bela and Non-Integral Values
Welp...   108
N Oct 26, 2022 by ihatemath123
Source: 2020 AMC 12B #14 / 2020 AMC 10B #16
Bela and Jenn play the following game on the closed interval $[0, n]$ of the real number line, where $n$ is a fixed integer greater than $4$. They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval $[0, n]$. Thereafter, the player whose turn it is chooses a real number that is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?

$\textbf{(A) } \text{Bela will always win.}$
$\textbf{(B) } \text{Jenn will always win.} $
$\textbf{(C) } \text{Bela will win if and only if }n \text{ is odd.}$
$\textbf{(D) } \text{Jenn will win if and only if }n \text{ is odd.} $
$\textbf{(E) } \text{Jenn will win if and only if }n > 8.$
108 replies
Welp...
Feb 6, 2020
ihatemath123
Oct 26, 2022
Bela and Non-Integral Values
G H J
G H BBookmark kLocked kLocked NReply
Source: 2020 AMC 12B #14 / 2020 AMC 10B #16
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Welp...
1400 posts
#1 • 1 Y
Y by Adventure10
Bela and Jenn play the following game on the closed interval $[0, n]$ of the real number line, where $n$ is a fixed integer greater than $4$. They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval $[0, n]$. Thereafter, the player whose turn it is chooses a real number that is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?

$\textbf{(A) } \text{Bela will always win.}$
$\textbf{(B) } \text{Jenn will always win.} $
$\textbf{(C) } \text{Bela will win if and only if }n \text{ is odd.}$
$\textbf{(D) } \text{Jenn will win if and only if }n \text{ is odd.} $
$\textbf{(E) } \text{Jenn will win if and only if }n > 8.$
This post has been edited 2 times. Last edited by Welp..., Feb 6, 2020, 6:14 PM
Reason: better title than generic
Z K Y
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Airplane50
234 posts
#2 • 1 Y
Y by Adventure10
RIP 100% trolled--the answer should be A
This post has been edited 2 times. Last edited by Airplane50, Feb 6, 2020, 6:04 PM
Z K Y
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suryaj
177 posts
#3 • 1 Y
Y by Adventure10
I need desperate confirmation on this one. I put A
Z K Y
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warriorcats
35 posts
#4 • 1 Y
Y by Adventure10
I said C... not sure about the answer though.
Z K Y
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Susanssluk
436 posts
#5 • 1 Y
Y by Adventure10
confirm A
Z K Y
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lakecomo224
3837 posts
#6 • 1 Y
Y by Adventure10
It's A but I put E :noo:
Z K Y
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mathisawesome2169
1823 posts
#7 • 17 Y
Y by Williamgolly, Mudkipswims42, pad, Epic_Dabber, Frestho, asdf334, yrnsmurf, Radio2, fifty51, programjames1, mathleticguyyy, mira74, Ultroid999OCPN, rayfish, awsomek, celestialphoenix3768, Adventure10
sol
Z K Y
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Williamgolly
3760 posts
#8 • 1 Y
Y by Adventure10
I got A yayayay
Z K Y
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flec
779 posts
#10 • 1 Y
Y by Adventure10
I think it's A. Poor Jenn........
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Lingjun
89 posts
#11 • 2 Y
Y by Adventure10, Mango247
it is A?
can someone post a solution
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Williamgolly
3760 posts
#12 • 1 Y
Y by Adventure10
So misplaced tho
Z K Y
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dasdhajskhd
110 posts
#13 • 2 Y
Y by Jerry122805, Adventure10
AMC learning to make full use of answer choices...
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Unum
183 posts
#14 • 1 Y
Y by Adventure10
hard. i used bash and poe to get a but took a long time, semi-guessed also
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USER394745
116 posts
#15 • 3 Y
Y by Lingjun, PotatoPenguin19, Adventure10
Sol:

Bela places her point in the middle. Then, wherever Jenn places, Bela mirrors him (so if Jenn places 1, Bela places n-1, etc.)

Bela always wins with this method.
This post has been edited 1 time. Last edited by USER394745, Feb 6, 2020, 6:06 PM
Reason: typo
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blueyellowgreen
327 posts
#16 • 1 Y
Y by Adventure10
I messed this up and put e because I thought they have to pick integers. I first wrote a and then erased and put e, I thought I was being clever oof.
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G
H
=
a