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Contests & Programs
AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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d_k-eja Vu
ihatemath123 50
N
3 hours ago
by MathematicalArceus
Source: 2024 USAMO Problem 1
Find all integers
such that the following property holds: if we list the divisors of
in increasing order as
, then we have
![\[ d_2 - d_1 \leq d_3 - d_2 \leq \dots \leq d_k - d_{k-1}. \]](//latex.artofproblemsolving.com/a/d/c/adc94af88b3579164aabba51bd021442133e364a.png)
Proposed by Luke Robitaille.



![\[ d_2 - d_1 \leq d_3 - d_2 \leq \dots \leq d_k - d_{k-1}. \]](http://latex.artofproblemsolving.com/a/d/c/adc94af88b3579164aabba51bd021442133e364a.png)
Proposed by Luke Robitaille.
50 replies
Essentially, how to get good at olympiad math?
gulab_jamun 3
N
3 hours ago
by sus_rbo
Ok, so I'm posting this as an anynonymous user cuz I don't want to get flamed by anyone I know for my goals but I really do want to improve on my math skill.
Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!
Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!
3 replies
No math to big math in 42 days
observer04 3
N
Today at 1:57 PM
by maxamc
CAN IT BE DONE
usajmo
usajmo
3 replies
[TEST RELEASED] OMMC Year 5
DottedCaculator 73
N
Today at 5:31 AM
by Ruegerbyrd
Test portal: https://ommc-test-portal-2025.vercel.app/
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?
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
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]
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?

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
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 designed OMMC to be accessible to beginners but also challenging to experts. Earlier questions on the main round will be around the difficulty of easy questions from the AMC 8 and AMC 10/12, and later questions will be at the difficulty of the hardest questions from the AIME. Our most skilled teams are invited to compete in an invitational final round consisting of difficult proof questions. We hope that teams will have fun and think deeply about the problems on the test, no matter their skill level.
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?
Only the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds upon hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have attended MOP, participated in MIT-PRIMES, RSI, SPARC, won medals at EGMO, IMO, RMM, etc. Our staff members have contributed to countless student-led math organizations and competitions in the past and we all have a high degree of mathematical experience under our belts. We believe OMMC Year 5 contains some of our best work thus far.
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?
We highly recommend competitors join our Community Discord for the latest updates on the competition, as well as for finding team members to team up with. Each team is between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger. You won’t have to sign up right now. Look out for a test portal link by which teams can register and access the test. Teams will put in their registration information as they submit the test.
However, we do encourage you to “sign up” on this thread, just like how you might with a mock contest. This isn’t required to take the test nor does it force you to take the test. But it’s a great way to show support and bump the thread to the top of the forums, so we appreciate it. (Also a great way to find teammates!)
However, we do encourage you to “sign up” on this thread, just like how you might with a mock contest. This isn’t required to take the test nor does it force you to take the test. But it’s a great way to show support and bump the thread to the top of the forums, so we appreciate it. (Also a great way to find teammates!)
Solo teams?
Solo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people.
Test Policy
Our test will be held completely online and untimed. We do not allow the use of anything other than writing utensils, scratch paper, compass, ruler/straightedge, and a single four function calculator (addition, subtraction, multiplication, division).
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:
For the main round, there are 25 computational (number answer questions). Each of the 25 questions will be worth 2 points, for a total of 50 points. Ties are broken by the last (highest numbered) question that one team solved and the other team didn’t, MATHCOUNTS-style. The team that solved this question would be given preference. For example, if teams A and B both have scores of 24, but Team A got question 20 wrong and Team B got question 25 wrong, then team A will be given preference over team B because team A solved question 25.
The top ~10-15 teams will move onto the final round, where there are 5-10 proof questions. Each of the questions is worth a different number of points (the specific weighting will be given to each of the finalist teams). The Olympiad round in total will be worth 50 points. A team’s total OMMC index will be the sum of the main round score and the final round score (out of 50+50=100), and teams will be ranked on their OMMC index (if there are ties, they will be broken by the aforementioned main round tie breaking system).
The top ~10-15 teams will move onto the final round, where there are 5-10 proof questions. Each of the questions is worth a different number of points (the specific weighting will be given to each of the finalist teams). The Olympiad round in total will be worth 50 points. A team’s total OMMC index will be the sum of the main round score and the final round score (out of 50+50=100), and teams will be ranked on their OMMC index (if there are ties, they will be broken by the aforementioned main round tie breaking system).
Prizes:
Prize List So Far:
- TBD
In past years we’ve received $5000+ in prizes. Stay tuned for more details, but we intend to give prizes to all teams on the leaderboard, as well as raffle out a TON of prizes over all competitors. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!
- TBD
In past years we’ve received $5000+ in prizes. Stay tuned for more details, but we intend to give prizes to all teams on the leaderboard, as well as raffle out a TON of prizes over all competitors. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!
I have more questions. Whom do I ask?
We respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.
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]
73 replies

usamOOK geometry
KevinYang2.71 107
N
Today at 3:39 AM
by RedFireTruck
Source: USAMO 2025/4, USAJMO 2025/5
Let
be the orthocenter of acute triangle
, let
be the foot of the altitude from
to
, and let
be the reflection of
across
. Suppose that the circumcircle of triangle
intersects line
at two distinct points
and
. Prove that
is the midpoint of
.














107 replies
what the yap
KevinYang2.71 30
N
Today at 3:28 AM
by RedFireTruck
Source: USAMO 2025/3
Alice the architect and Bob the builder play a game. First, Alice chooses two points
and
in the plane and a subset
of the plane, which are announced to Bob. Next, Bob marks infinitely many points in the plane, designating each a city. He may not place two cities within distance at most one unit of each other, and no three cities he places may be collinear. Finally, roads are constructed between the cities as follows: for each pair
of cities, they are connected with a road along the line segment
if and only if the following condition holds:
[center]For every city
distinct from
and
, there exists
such[/center]
[center]that
is directly similar to either
or
.[/center]
Alice wins the game if (i) the resulting roads allow for travel between any pair of cities via a finite sequence of roads and (ii) no two roads cross. Otherwise, Bob wins. Determine, with proof, which player has a winning strategy.
Note:
is directly similar to
if there exists a sequence of rotations, translations, and dilations sending
to
,
to
, and
to
.





[center]For every city




[center]that



Alice wins the game if (i) the resulting roads allow for travel between any pair of cities via a finite sequence of roads and (ii) no two roads cross. Otherwise, Bob wins. Determine, with proof, which player has a winning strategy.
Note:








30 replies
Prove a polynomial has a nonreal root
KevinYang2.71 47
N
Today at 3:15 AM
by RedFireTruck
Source: USAMO 2025/2
Let
and
be positive integers with
. Let
be a polynomial of degree
with real coefficients, nonzero constant term, and no repeated roots. Suppose that for any real numbers
such that the polynomial
divides
, the product
is zero. Prove that
has a nonreal root.










47 replies


Question about AMC 10
MathNerdRabbit103 17
N
Today at 12:52 AM
by Zusen
Hi,
Can anybody predict a good score that I can get on the AMC 10 this November by only being good at counting and probability, number theory, and algebra? I know some geometry because I took it in school though, but it isn’t competition math so it probably doesn’t count.
Thanks.
Can anybody predict a good score that I can get on the AMC 10 this November by only being good at counting and probability, number theory, and algebra? I know some geometry because I took it in school though, but it isn’t competition math so it probably doesn’t count.
Thanks.
17 replies
Jane street swag package? USA(J)MO
arfekete 38
N
Today at 12:34 AM
by Learning11
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.
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.
38 replies

prime spam
fruitmonster97 36
N
Yesterday at 2:44 PM
by ZMB038
Source: 2024 AMC 10A #3
What is the sum of the digits of the smallest prime that can be written as a sum of
distinct primes?


36 replies
