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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Today at 3:18 PM
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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
Today at 3:18 PM
0 replies
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k a My Retirement & New Leadership at AoPS
rrusczyk   1571
N Mar 26, 2025 by SmartGroot
I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE
1571 replies
+1 w
rrusczyk
Mar 24, 2025
SmartGroot
Mar 26, 2025
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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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MOP Cutoffs Out?
Mathandski   28
N 37 minutes ago by Yrock
MAA has just emailed a press release announcing the formula they will be using this year to come up with the MOP cutoff that applies to you! Here's the process:

1. Multiply your age by $1434$, let $n$ be the result.

2. Calculate $\varphi(n)$, where $\varphi$ is the Euler's totient theorem, which calculates the number of integers less than $n$ relatively prime to $n$.

3. Multiply your result by $1434$ again because why not, let the result be $m$.

4. Define the Fibonacci sequence $F_0 = 1, F_1 = 1, F_n = F_{n-1} + F_{n-2}$ for $n \ge 2$. Let $r$ be the remainder $F_m$ leaves when you divide it by $69$.

5. Let $x$ be your predicted USA(J)MO score.

6. You will be invited if your score is at least $\lfloor \frac{x + \sqrt[r]{r^2} + r \ln(r)}{r} \rfloor$.

7. Note that there may be additional age restrictions for non-high schoolers.

See here for MAA's original news message.

.

.

.


Edit (4/2/2025): This was an April Fool's post.
Here's the punchline
28 replies
+1 w
Mathandski
Yesterday at 11:02 PM
Yrock
37 minutes ago
J
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9 Which math contest is your favorite?
mdk2013   52
N an hour ago by mdk2013
links for details on each comp

i think thats all the major ones, comment if you have any more that i forgot to include

upvote if you're like me and you think MATHCOUNTS is obv better!

EDIT: i forgot ARML and JBMO, comment if you like those
52 replies
mdk2013
Mar 30, 2025
mdk2013
an hour ago
J
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The greatest length of a sequence that satisfies a special condition
EmersonSoriano   0
an hour ago
Source: 2018 Peru TST Cono Sur P9
Find the largest possible value of the positive integer $N$ given that there exist positive integers $a_1, a_2, \dots, a_N$ satisfying
$$ a_n = \sqrt{(a_{n-1})^2 + 2018 \, a_{n-2}}\:, \quad \text{for } n = 3,4,\dots,N. $$
0 replies
EmersonSoriano
an hour ago
0 replies
J
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Olympiad Geometry problem-second time posting
kjhgyuio   5
N an hour ago by kjhgyuio
Source: smo problem
In trapezium ABCD,AD is parallel to BC and points E and F are midpoints of AB and DC respectively. If
Area of AEFD/Area of EBCF =√3 + 1/3-√3 and the area of triangle ABD is √3 .find the area of trapezium ABCD
5 replies
kjhgyuio
Today at 1:03 AM
kjhgyuio
an hour ago
J
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Summing the GCD of a number and the divisors of another.
EmersonSoriano   0
an hour ago
Source: 2018 Peru TST Cono Sur P8
For each pair of positive integers $m$ and $n$, we define $f_m(n)$ as follows:
$$ f_m(n) = \gcd(n, d_1) + \gcd(n, d_2) + \cdots + \gcd(n, d_k), $$where $1 = d_1 < d_2 < \cdots < d_k = m$ are all the positive divisors of $m$. For example,
$f_4(6) = \gcd(6,1) + \gcd(6,2) + \gcd(6,4) = 5$.

$a)\:$ Find all positive integers $n$ such that $f_{2017}(n) = f_n(2017)$.

$b)\:$ Find all positive integers $n$ such that $f_6(n) = f_n(6)$.
0 replies
EmersonSoriano
an hour ago
0 replies
J
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Sum of whose elements is divisible by p
nntrkien   42
N an hour ago by cubres
Source: IMO 1995, Problem 6, Day 2, IMO Shortlist 1995, N6
Let $ p$ be an odd prime number. How many $ p$-element subsets $ A$ of $ \{1,2,\dots,2p\}$ are there, the sum of whose elements is divisible by $ p$?
42 replies
nntrkien
Aug 8, 2004
cubres
an hour ago
J
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kind of well known?
dotscom26   3
N an hour ago by Svenskerhaor
Source: MBL
Let $ y_1, y_2, ..., y_{2025}$ be real numbers satisfying
$ y_1^2 + y_2^2 + \cdots + y_{2025}^2 = 1. $
Find the maximum value of
$ |y_1 - y_2| + |y_2 - y_3| + \cdots + |y_{2025} - y_1|. $

I have seen many problems with the same structure, Id really appreciate if someone could explain which approach is suitable here
3 replies
dotscom26
Yesterday at 4:11 AM
Svenskerhaor
an hour ago
J
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Locus of a point on the side of a square
EmersonSoriano   0
an hour ago
Source: 2018 Peru TST Cono Sur P7
Let $ABCD$ be a fixed square and $K$ a variable point on segment $AD$. The square $KLMN$ is constructed such that $B$ is on segment $LM$ and $C$ is on segment $MN$. Let $T$ be the intersection point of lines $LA$ and $ND$. Find the locus of $T$ as $K$ varies along segment $AD$.
0 replies
EmersonSoriano
an hour ago
0 replies
J
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Chess queens on a cylindrical board
EmersonSoriano   0
an hour ago
Source: 2018 Peru TST Cono Sur P6
Let $n$ be a positive integer. In an $n \times n$ board, two opposite sides have been joined, forming a cylinder. Determine whether it is possible to place $n$ queens on the board such that no two threaten each other when:

$a)\:$ $n=14$.

$b)\:$ $n=15$.
0 replies
EmersonSoriano
an hour ago
0 replies
J
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2015 solutions for quotient function!
raxu   48
N an hour ago by zuat.e
Source: TSTST 2015 Problem 5
Let $\varphi(n)$ denote the number of positive integers less than $n$ that are relatively prime to $n$. Prove that there exists a positive integer $m$ for which the equation $\varphi(n)=m$ has at least $2015$ solutions in $n$.

Proposed by Iurie Boreico
48 replies
raxu
Jun 26, 2015
zuat.e
an hour ago
J
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GCD of x^2-y, y^2-z and z^2-x
EmersonSoriano   0
2 hours ago
Source: 2018 Peru TST Cono Sur P5
Find all positive integers $d$ that can be written in the form
$$ d = \gcd(|x^2 - y| , |y^2 - z| , |z^2 - x|), $$where $x, y, z$ are pairwise coprime positive integers such that $x^2 \neq y$, $y^2 \neq z$, and $z^2 \neq x$.
0 replies
EmersonSoriano
2 hours ago
0 replies
J
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calculate the perimeter of triangle MNP
PennyLane_31   1
N 2 hours ago by TheBaiano
Source: 2024 5th OMpD L2 P2 - Brazil - Olimpíada Matemáticos por Diversão
Let $ABCD$ be a convex quadrilateral, and $M$, $N$, and $P$ be the midpoints of diagonals $AC$ and $BD$, and side $AD$, respectively. Also, suppose that $\angle{ABC} + \angle{DCB} = 90$ and that $AB = 6$, $CD = 8$. Calculate the perimeter of triangle $MNP$.
1 reply
PennyLane_31
Oct 16, 2024
TheBaiano
2 hours ago
J
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Moving P(o)in(t)s
bobthegod78   69
N 3 hours ago by akliu
Source: USAJMO 2021/4
Carina has three pins, labeled $A, B$, and $C$, respectively, located at the origin of the coordinate plane. In a move, Carina may move a pin to an adjacent lattice point at distance $1$ away. What is the least number of moves that Carina can make in order for triangle $ABC$ to have area 2021?

(A lattice point is a point $(x, y)$ in the coordinate plane where $x$ and $y$ are both integers, not necessarily positive.)
69 replies
bobthegod78
Apr 15, 2021
akliu
3 hours ago
J
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Double dose of cyanide on day 2
brianzjk   30
N 3 hours ago by akliu
Source: USAMO 2023/5
Let $n\geq3$ be an integer. We say that an arrangement of the numbers $1$, $2$, $\dots$, $n^2$ in a $n \times n$ table is row-valid if the numbers in each row can be permuted to form an arithmetic progression, and column-valid if the numbers in each column can be permuted to form an arithmetic progression. For what values of $n$ is it possible to transform any row-valid arrangement into a column-valid arrangement by permuting the numbers in each row?
30 replies
brianzjk
Mar 23, 2023
akliu
3 hours ago
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J
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Correlation between USAMO and CMO qualification
rantaccountcs   3
N Mar 30, 2025 by BS2012
What is the correlation between cmo qualification and usamo qualification? What proportion of Canadian usamo qualifiers are cmo qualifiers and what proportion of cmo qualifiers are usamo qualifiers?
3 replies
rantaccountcs
Nov 2, 2023
BS2012
Mar 30, 2025
J
Correlation between USAMO and CMO qualification
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rantaccountcs
156 posts
rantaccountcs
#1 h  Nov 2, 2023, 7:56 PM
Y by
What is the correlation between cmo qualification and usamo qualification? What proportion of Canadian usamo qualifiers are cmo qualifiers and what proportion of cmo qualifiers are usamo qualifiers?
Z K Y
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David_Kim_0202
383 posts
David_Kim_0202
#2 h  Nov 3, 2023, 3:47 AM
Y by
can usa people take canadian math competitions?
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mrtheory
2 posts
mrtheory
#3 h  Mar 30, 2025, 6:03 PM
Y by
David_Kim_0202 wrote:
can usa people take canadian math competitions?

yes
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BS2012
967 posts
BS2012
#4 h  Mar 30, 2025, 6:14 PM
Y by
mrtheory wrote:
David_Kim_0202 wrote:
can usa people take canadian math competitions?

yes

Really?
https://cms.math.ca/competitions/cmo/#CMOeligibility wrote:
In order to be an official participant, all competitors:

must be a Canadian Citizen or Permanent Resident of Canada (but not necessarily residing in Canada currently),

must not have formally enrolled at a university or any other equivalent post-secondary institution and must not yet have graduated from high school (or equivalent),

must be currently attending school full-time since the start of the current school year,

must be less than 20 years old as of June 30 of the year of the Competition.

Additionally, the CJMO requires that competitors must be in grade ten or earlier.
(https://cms.math.ca/competitions/cmo/#CMOeligibility)
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