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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)!

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[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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Harmonic Mean
Happytycho   3
N 8 minutes ago by tilya_TASh
Source: Problem #2 2016 AMC 12B
The harmonic mean of two numbers can be calculated as twice their product divided by their sum. The harmonic mean of $1$ and $2016$ is closest to which integer?

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 45 \qquad \textbf{(C)}\ 504 \qquad \textbf{(D)}\ 1008 \qquad \textbf{(E)}\ 2015 $
3 replies
+2 w
Happytycho
Feb 21, 2016
tilya_TASh
8 minutes ago
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Jane street swag package? USA(J)MO
arfekete   31
N 3 hours ago by vsarg
Hey! People are starting to get their swag packages from Jane Street for qualifying for USA(J)MO, and after some initial discussion on what we got, people are getting different things. Out of curiosity, I was wondering how they decide who gets what.
Please enter the following info:

- USAMO or USAJMO
- Grade
- Score
- Award/Medal/HM
- MOP (yes or no, if yes then color)
- List of items you got in your package

I will reply with my info as an example.
31 replies
arfekete
May 7, 2025
vsarg
3 hours ago
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Suggestions for preparing for AMC 12
peppermint_cat   2
N 3 hours ago by peppermint_cat
So, I have decided to attempt taking the AMC 12 this fall. I don't have any experience with math competitions, and I thought that here might be a good place to see if anyone who has taken the AMC 12 (or done any other math competitions) has any suggestions on what to expect, how to prepare, etc. Thank you!
2 replies
peppermint_cat
4 hours ago
peppermint_cat
3 hours ago
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[MAIN ROUND STARTS MAY 17] OMMC Year 5
DottedCaculator   61
N 4 hours ago by fuzimiao2013
Hello to all creative problem solvers,

Do you want to work on a fun, untimed team math competition with amazing questions by MOPpers and IMO & EGMO medalists? $\phantom{You lost the game.}$
Do you want to have a chance to win thousands in cash and raffle prizes (no matter your skill level)?

Check out the fifth annual iteration of the

Online Monmouth Math Competition!

Online Monmouth Math Competition, or OMMC, is a 501c3 accredited nonprofit organization managed by adults, college students, and high schoolers which aims to give talented high school and middle school students an exciting way to develop their skills in mathematics.

Our website: https://www.ommcofficial.org/
Our Discord (6000+ members): https://tinyurl.com/joinommc
Test portal: https://ommc-test-portal.vercel.app/

This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read carefully and thoroughly. Join our Discord or monitor this thread for updates and test releases.

How hard is it?

We plan to raffle out a TON of prizes over all competitors regardless of performance. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!

How are the problems?

You can check out our past problems and sample problems here:
https://www.ommcofficial.org/sample
https://www.ommcofficial.org/2022-documents
https://www.ommcofficial.org/2023-documents
https://www.ommcofficial.org/ommc-amc

How will the test be held?/How do I sign up?

Solo teams?

Test Policy

Timeline:
Main Round: May 17th - May 24th
Test Portal Released. The Main Round of the contest is held. The Main Round consists of 25 questions that each have a numerical answer. Teams will have the entire time interval to work on the questions. They can submit any time during the interval. Teams are free to edit their submissions before the period ends, even after they submit.

Final Round: May 26th - May 28th
The top placing teams will qualify for this invitational round (5-10 questions). The final round consists of 5-10 proof questions. Teams again will have the entire time interval to work on these questions and can submit their proofs any time during this interval. Teams are free to edit their submissions before the period ends, even after they submit.

Conclusion of Competition: Early June
Solutions will be released, winners announced, and prizes sent out to winners.

Scoring:

Prizes:

I have more questions. Whom do I ask?

We hope for your participation, and good luck!

OMMC staff

OMMC’S 2025 EVENTS ARE SPONSORED BY:

[list]
[*]Nontrivial Fellowship
[*]Citadel
[*]SPARC
[*]Jane Street
[*]And counting!
[/list]

61 replies
DottedCaculator
Apr 26, 2025
fuzimiao2013
4 hours ago
J
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Minimum number of points
Ecrin_eren   2
N Yesterday at 8:32 PM by Shan3t
There are 18 teams in a football league. Each team plays against every other team twice in a season—once at home and once away. A win gives 3 points, a draw gives 1 point, and a loss gives 0 points. One team became the champion by earning more points than every other team. What is the minimum number of points this team could have?

2 replies
Ecrin_eren
Yesterday at 4:09 PM
Shan3t
Yesterday at 8:32 PM
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Weird locus problem
Sedro   7
N Yesterday at 8:00 PM by ReticulatedPython
Points $A$ and $B$ are in the coordinate plane such that $AB=2$. Let $\mathcal{H}$ denote the locus of all points $P$ in the coordinate plane satisfying $PA\cdot PB=2$, and let $M$ be the midpoint of $AB$. Points $X$ and $Y$ are on $\mathcal{H}$ such that $\angle XMY = 45^\circ$ and $MX\cdot MY=\sqrt{2}$. The value of $MX^4 + MY^4$ can be expressed in the form $\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
7 replies
Sedro
May 11, 2025
ReticulatedPython
Yesterday at 8:00 PM
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2024 Mock AIME 1 ** p15 (cheaters' trap) - 128 | n^{\sigma (n)} - \sigma(n^n)
parmenides51   3
N Yesterday at 6:17 PM by Sedro
Let $N$ be the number of positive integers $n$ such that $n$ divides $2024^{2024}$ and $128$ divides
$$n^{\sigma (n)} - \sigma(n^n)$$where $\sigma (n)$ denotes the number of positive integers that divide $n$, including $1$ and $n$. Find the remainder when $N$ is divided by $1000$.
3 replies
parmenides51
Jan 29, 2025
Sedro
Yesterday at 6:17 PM
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IOQM P23 2024
SomeonecoolLovesMaths   3
N Yesterday at 4:53 PM by lakshya2009
Consider the fourteen numbers, $1^4,2^4,...,14^4$. The smallest natural numebr $n$ such that they leave distinct remainders when divided by $n$ is:
3 replies
SomeonecoolLovesMaths
Sep 8, 2024
lakshya2009
Yesterday at 4:53 PM
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Inequalities
sqing   2
N Yesterday at 4:05 PM by MITDragon
Let $ 0\leq x,y,z\leq 2. $ Prove that
$$-48\leq (x-yz)( 3y-zx)(z-xy)\leq 9$$$$-144\leq (3x-yz)(y-zx)(3z-xy)\leq\frac{81}{64}$$$$-144\leq (3x-yz)(2y-zx)(3z-xy)\leq\frac{81}{16}$$
2 replies
sqing
May 9, 2025
MITDragon
Yesterday at 4:05 PM
J
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Pells equation
Entrepreneur   0
Yesterday at 3:56 PM
A Pells Equation is defined as follows $$x^2-1=ky^2.$$Where $x,y$ are positive integers and $k$ is a non-square positive integer. If $(x_n,y_n)$ denotes the n-th set of solution to the equation with $(x_0,y_0)=(1,0).$ Then, prove that $$x_{n+1}x_n-ky_{n+1}y_n=x_1,$$$$x_n\pm y_n\sqrt k=(x_1\pm y_1\sqrt k)^n.$$
0 replies
Entrepreneur
Yesterday at 3:56 PM
0 replies
J
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Incircle concurrency
niwobin   1
N Yesterday at 2:42 PM by niwobin
Triangle ABC with incenter I, incircle is tangent to BC, AC, and AB at D, E and F respectively.
DT is a diameter for the incircle, and AT meets the incircle again at point H.
Let DH and EF intersect at point J. Prove: AJ//BC.
1 reply
niwobin
May 11, 2025
niwobin
Yesterday at 2:42 PM
J
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Inequalities
sqing   3
N Yesterday at 2:29 PM by rachelcassano
Let $ a,b,c>0 $ . Prove that
$$\frac{a+5b}{b+c}+\frac{b+5c}{c+a}+\frac{c+5a}{a+b}\geq 9$$$$ \frac{2a+11b}{b+c}+\frac{2b+11c}{c+a}+\frac{2c+11a}{a+b}\geq \frac{39}{2}$$$$ \frac{25a+147b}{b+c}+\frac{25b+147c}{c+a}+\frac{25c+147a}{a+b} \geq258$$
3 replies
sqing
May 14, 2025
rachelcassano
Yesterday at 2:29 PM
J
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The centroid of ABC lies on ME [2023 Abel, Problem 1b]
Amir Hossein   3
N Yesterday at 1:45 PM by Captainscrubz
In the triangle $ABC$, points $D$ and $E$ lie on the side $BC$, with $CE = BD$. Also, $M$ is the midpoint of $AD$. Show that the centroid of $ABC$ lies on $ME$.
3 replies
Amir Hossein
Mar 12, 2024
Captainscrubz
Yesterday at 1:45 PM
J
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2021 SMT Guts Round 5 p17-20 - Stanford Math Tournament
parmenides51   5
N Yesterday at 8:00 AM by MATHS_ENTUSIAST
p17. Let the roots of the polynomial $f(x) = 3x^3 + 2x^2 + x + 8 = 0$ be $p, q$, and $r$. What is the sum $\frac{1}{p} +\frac{1}{q} +\frac{1}{r}$ ?


p18. Two students are playing a game. They take a deck of five cards numbered $1$ through $5$, shuffle them, and then place them in a stack facedown, turning over the top card next to the stack. They then take turns either drawing the card at the top of the stack into their hand, showing the drawn card to the other player, or drawing the card that is faceup, replacing it with the card on the top of the pile. This is repeated until all cards are drawn, and the player with the largest sum for their cards wins. What is the probability that the player who goes second wins, assuming optimal play?


p19. Compute the sum of all primes $p$ such that $2^p + p^2$ is also prime.


p20. In how many ways can one color the $8$ vertices of an octagon each red, black, and white, such that no two adjacent sides are the same color?


PS. You should use hide for answers. Collected here.
5 replies
parmenides51
Feb 11, 2022
MATHS_ENTUSIAST
Yesterday at 8:00 AM
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Question
HopefullyMcNats2025   19
N Apr 29, 2025 by MC_ADe
Is it more difficult to make MOP or make usajmo, usapho, and usabo
19 replies
HopefullyMcNats2025
Apr 7, 2025
MC_ADe
Apr 29, 2025
J
Question
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Reveal topic tags
USA(J)MO
USAPhO
usabo
AMC
USAJMO
MOP
L
G H BBookmark kLocked kLocked NReply
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#1 h  Apr 7, 2025, 2:00 AM
Y by
Is it more difficult to make MOP or make usajmo, usapho, and usabo
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#2 h  Apr 7, 2025, 2:02 AM
Y by
Btw Usabo and usapho no one cares, I mean usapho and usabo camps
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ConfidentKoala4
611 posts
ConfidentKoala4
#3 h  Apr 7, 2025, 2:07 AM
Y by
all hard, usabo prolly easiest
mop prolly hardest
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#4 h  Apr 7, 2025, 2:12 AM
Y by
Thanks man
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xHypotenuse
783 posts
xHypotenuse
#5 h  Apr 7, 2025, 4:44 PM • 3 Y
Y by happyhippos, aidan0626, Elephant200
No one cares about USABO/USAPhO is wild
This post has been edited 1 time. Last edited by xHypotenuse, Apr 7, 2025, 7:41 PM
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Ruegerbyrd
1094 posts
Ruegerbyrd
#6 h  Apr 7, 2025, 9:09 PM
Y by
MOP, USA(J)MO, usapho, usabo
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MC_ADe
183 posts
MC_ADe
#7 h  Apr 7, 2025, 9:16 PM
Y by
u should talk about camping in these respective things instead cuz MOP is literally camping so u need to like say phys camp or bio camp not jst usapho or usabo
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TetraFish
1088 posts
TetraFish
#8 h  Apr 8, 2025, 12:47 AM
Y by
I think he means MOP vs making that stage in all 3 of them combined.
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LockingIN2026
5 posts
LockingIN2026
#9 h  Apr 8, 2025, 1:13 AM
Y by
TetraFish wrote:
I think he means MOP vs making that stage in all 3 of them combined.

prob the latter
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elasticwealth
342 posts
elasticwealth
#10 h  Apr 8, 2025, 1:17 PM • 1 Y
Y by Sunhaops
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME
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NoSignOfTheta
1744 posts
NoSignOfTheta
#11 h  Apr 8, 2025, 1:25 PM
Y by
MC_ADe wrote:
u should talk about camping in these respective things instead cuz MOP is literally camping so u need to like say phys camp or bio camp not jst usapho or usabo
HopefullyMcNats2025 wrote:
Btw Usabo and usapho no one cares, I mean usapho and usabo camps
Z K Y
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sadas123
1306 posts
sadas123
#13 h  Apr 8, 2025, 8:37 PM
Y by
elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

That is somewhat of the list.
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happyhippos
2199 posts
happyhippos
#14 h  Apr 8, 2025, 8:59 PM
Y by
HopefullyMcNats2025 wrote:
Btw Usabo and usapho no one cares, I mean usapho and usabo camps

That's an interesting thing to say, considering USAPhO-style physics is much more relevant to actually useful real-life things than USAMO-style math.
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mdk2013
642 posts
mdk2013
#15 h  Apr 8, 2025, 9:08 PM
Y by
fake123 wrote:
elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

wdym qualifying for AMC 8 is harder

:ewpu: wut
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Jack_w
109 posts
Jack_w
#16 h  Apr 8, 2025, 9:55 PM
Y by
TetraFish wrote:
I think he means MOP vs making that stage in all 3 of them combined.

MOP harder
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nsking_1209
173 posts
nsking_1209
#17 h  Apr 9, 2025, 2:42 AM
Y by
MOP > usabo camp > usapho camp > usaco camp > usajmo
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Sunhaops
8 posts
Sunhaops
#18 h  Apr 29, 2025, 6:53 PM
Y by
elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

well said, only before AIME should be >> instead of >
This post has been edited 1 time. Last edited by Sunhaops, Apr 29, 2025, 6:54 PM
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xHypotenuse
783 posts
xHypotenuse
#19 h  Apr 29, 2025, 7:37 PM
Y by
Not really, usapho qual isn't severely difficult compared to aime.

Also, I think usapho camp is around equal or harder than usabo camp for sure
This post has been edited 1 time. Last edited by xHypotenuse, Apr 29, 2025, 7:38 PM
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Lijin
225 posts
Lijin
#20 h  Apr 29, 2025, 10:19 PM
Y by
I thought you had to make USA(J)MO first to make MOP?
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MC_ADe
183 posts
MC_ADe
#21 h  Apr 29, 2025, 10:29 PM
Y by
by usabo do u mean semifinals, camp or what
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