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warriorsin7   0
2 hours ago
warriorsin7
2 hours ago
0 replies
9 Did I make the right choice?
Martin2001   27
N 4 hours ago by ninjaforce
If you were in 8th grade, would you rather go to MOP or mc nats? I chose to study the former more and got in so was wondering if that was valid given that I'll never make mc nats.
27 replies
Martin2001
Apr 29, 2025
ninjaforce
4 hours ago
I'm trying to find a good math comp...
ysn613   5
N 5 hours ago by MathPerson12321
Okay, so I'm in sixth grade. I have been doing AMC 8 since fourth grade, but not anything else. I was wondering what other "good" math competitions there are that I am the right age for.

I'm also looking for prep tips for math competitions, because when I (mock)ace 2000-2010 AMC 8 and then get a 19 on the real thing when I was definitely able to solve everything, I feel like what I'm doing isn't really working. Anyone got any ideas? Thanks!
5 replies
ysn613
Yesterday at 4:12 PM
MathPerson12321
5 hours ago
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   64
N Today at 2:59 PM by WhitePhoenix
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary


Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


64 replies
audio-on
Jan 26, 2025
WhitePhoenix
Today at 2:59 PM
MOP Emails Out! (not clickbait)
Mathandski   101
N Today at 1:01 PM by pingpongmerrily
What an emotional roller coaster the past 34 days have been.

Congrats to all that qualified!
101 replies
Mathandski
Apr 22, 2025
pingpongmerrily
Today at 1:01 PM
How many approaches you got? (A lot)
IAmTheHazard   86
N Today at 8:27 AM by User141208
Source: USAMO 2023/2
Let $\mathbb{R}^+$ be the set of positive real numbers. Find all functions $f \colon \mathbb{R}^+ \to \mathbb{R}^+$ such that, for all $x,y \in \mathbb{R}^+$,
$$f(xy+f(x))=xf(y)+2.$$
86 replies
IAmTheHazard
Mar 23, 2023
User141208
Today at 8:27 AM
Berkeley mini Math Tournament Online 2025 - June 7
BerkeleyMathTournament   0
Today at 7:38 AM
Berkeley mini Math Tournament is a math competition hosted for middle school students once a year. Students compete in multiple rounds: individual round, team round, puzzle round, and relay round.

BmMT 2025 Online will be held on June 7th, and registration is OPEN! Registration is $8 per student. Our website https://berkeley.mt/events/bmmt-2025-online/ has more details about the event, past tests to practice with, and frequently asked questions. We look forward to building community and inspiring students as they explore the world of math!

3 out of 4 of the rounds are completed with a team, so it’s a great opportunity for students to work together. Beyond getting more comfortable with math and becoming better problem solvers, our team is preparing some fun post-competition activities!

Registration is open to students in grades 8 or below. You do not have to be local to the Bay Area or California to register for BmMT Online. Students may register as a team of 1, but it is beneficial to compete on a team of at least 3 due to our scoring guideline and for the experience.

We hope you consider attending, or if you are a parent or teacher, that you encourage your students to think about attending BmMT. Thank you, and once again find more details/register at our website,https://berkeley.mt.
0 replies
BerkeleyMathTournament
Today at 7:38 AM
0 replies
How to get good at comp math
fossasor   28
N Today at 6:27 AM by Konigsberg
I'm a rising ninth grader who wasn't in the school math league this year, and basically put aside comp math for a year. Unfortunately, that means that now that I'm in high school and having the epiphany about how important comp math actually is, and how much it would help my chances of getting involved in other math-related programs. In addition, I do enjoy math in general, and suspect that things like the AMCs are probably going to be some of the best practice I can get. What this all means is that I'm trying to go from mediocre to orz, 2 years after I probably should have started if I wanted to be any good.

So my question is: how do I get good at comp math?

This year, my scores on AMC 10 (and these are the highest I've ever gotten) were a 73.5 and an 82.5 (AMC 8 was 21/25, but that doesn't matter much). This is not good enough to qualify for AIME, and I probably need to raise my performance on each by at least 10 points. I've been decently good in the past at Number Theory, but I need to work on Geo and Combinatorics, and I'm trying to find the best resources to do that. My biggest flaw is probably not knowing many algorithms like Stars and Bars, and the path is clear here (learn them) but I'm still not sure which ones I need to know.

I'm aware that some of this advice is going to be something like "Practice 5 hours a day and start hardgrinding" or something along those lines. Unfortunately, I have other extracurriculars I need to balance, and for me, time is a limiting resource. My parents are somewhat frowning upon me doing a lot of comp math, which limits my time as well. I have neither the time nor motivation to do more than an hour a day, and in practice, I don't think I can be doing that consistently. As such, I would need to make that time count.

I know this is a very general question, and that aops is chock-full of detailed advice for math competitions. However, I'd appreciate it if anyone here could help me out, or show me the best resources I should use to get started. What mocks are any good, or what textbooks should I use? Where do I get the best practice with the shortest time? Is there some place I can find a list of useful formulas that have appeared in math comps before?

All advice is welcome!

28 replies
fossasor
Apr 10, 2025
Konigsberg
Today at 6:27 AM
MasterScholar North Carolina Math Camp
Ruegerbyrd   17
N Today at 4:51 AM by fake123
Is this legit? Worth the cost ($6500)? Program Fees Cover: Tuition, course materials, field trip costs, and housing and meals at Saint Mary's School.

"Themes:

1. From Number Theory and Special Relativity to Game Theory
2. Applications to Economics

Subjects Covered:

Number Theory - Group Theory - RSA Encryption - Game Theory - Estimating Pi - Complex Numbers - Quaternions - Topology of Surfaces - Introduction to Differential Geometry - Collective Decision Making - Survey of Calculus - Applications to Economics - Statistics and the Central Limit Theorem - Special Relativity"

website(?): https://www.teenlife.com/l/summer/masterscholar-north-carolina-math-camp/
17 replies
Ruegerbyrd
Yesterday at 3:15 AM
fake123
Today at 4:51 AM
Segment Product
worthawholebean   25
N Today at 4:37 AM by deduck
Source: AIME 2009II Problem 13
Let $ A$ and $ B$ be the endpoints of a semicircular arc of radius $ 2$. The arc is divided into seven congruent arcs by six equally spaced points $ C_1,C_2,\ldots,C_6$. All chords of the form $ \overline{AC_i}$ or $ \overline{BC_i}$ are drawn. Let $ n$ be the product of the lengths of these twelve chords. Find the remainder when $ n$ is divided by $ 1000$.
25 replies
worthawholebean
Apr 2, 2009
deduck
Today at 4:37 AM
Olympiad Combinatorics Book
Pascal96   126
N Dec 27, 2023 by zaahir
Hi everyone, I am currently writing a book on combinatorics for people preparing for national and international math competitions, especially the IMO and selection tests leading up to it. The book is intended to expose readers to a variety of ideas, techniques and problem solving strategies, ranging from the intuitive “greedy algorithms” in the first chapter to the powerful Probabilistic Method in chapter nine.
I am uploading chapter one here, and would appreciate your feedback and any suggestions. Over the coming weeks, I will be uploading the remaining chapters one at a time.
The only prerequisites are familiarity with basic graph theoretic concepts and terminology, algebraic inequalities, induction and the pigeonhole principle. Experience with invariants and the extremal principle is also helpful.
EDIT: CHAPTER 9 IS OUT! Since only 3 attachments are allowed per post, I have uploaded chapters 4, 5 and 6 in my comment below (10th on this page), and chapters 7, 8, and 9 further below (comment number 49 on this page).
NOTE: The solution to example 8 in chapter 1 is incorrect, and will be corrected in the final version of the book. For now, ignore this example.

Full book (uploaded by green_dog_7983): Dead Link
[Amir: new link]
126 replies
Pascal96
Aug 6, 2014
zaahir
Dec 27, 2023
Olympiad Combinatorics Book
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Pascal96
124 posts
#127 • 5 Y
Y by 606234, lneis1, Aimingformygoal, 554183, winniep008hfi
Here is the second handout I created for the training camp, on advanced combinatorial algorithms.
Attachments:
Advanced_Combinatorial_Algorithms.pdf (171kb)
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Pascal96
124 posts
#128 • 1 Y
Y by quirtt
DebayuRMO wrote:
Btw when can we expect the the new beginner friendly chapters that you were planning to write? I know you are really busy but at the same time I'm too excited about this extension so that I can start reading your book.
Thank You

I appreciate the excitement! I have a few rough drafts in the works, but creating the polished final versions takes time unfortunately. I don't want to commit to any particular date at this point. In the mean time, I hope the introductory problem set serves as some solid material for beginners to work through.
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MelonGirl
573 posts
#129 • 2 Y
Y by Pascal96, Mango247
not directly related to last few posts, but I pm-ed you about this sometime back, so I guess I'll post it here as well for anyone who's worked on the problem.
Quote:
On each square of a chessboard is a light which has two states-
on or off. A move consists of choosing a square and changing
the state of the bulbs in that square and in its neighboring
squares (squares that share a side with it). Show that starting
from any configuration we can make finitely many moves to
reach a point where all the bulbs are switched off

This is under the algorithms chapter (2). People have found ways to do this with linear algebra and brute force (similar to the row reduction method here.)

Does anyone know of a purely combinatorial algorithm approach to this problem?
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Pascal96
124 posts
#130
Y by
@MelonGirl no I'm actually not aware of a purely combinatorial solution. For a few of the exercises in the book, I did not know the original source (usually because I saw the problem on some handout at an olympiad training camp). This was one such problem, and I'd actually tried it and hadn't been able to solve it. I figured it would make sense as one of the later exercises in the algorithms chapters, so placed it there without realizing it required linear algebra.
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Physicsknight
641 posts
#131
Y by
I think the linalgb and matrix makes it easier to see the grid rather than a combinatorial approach. You can check the $4$ vectors $(1,1,1,0) \,(1,1,0,1)\,(1,0,1,1)\,(0,1,1,1) $ are independent over $\mathbb{F}_2. $.
Turn the the space of the states of the chessboard into a $64$ dimensional vector space over $\mathbb {F}_2$. The field with $2$ elements $0,1, $ with addition $\pmod{2} $.
The only gruesome task is to prove that $64$ vectors are not linearly independent.
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KAKAAB
23 posts
#132
Y by
Pascal96 wrote:
DebayuRMO wrote:
Btw when can we expect the the new beginner friendly chapters that you were planning to write? I know you are really busy but at the same time I'm too excited about this extension so that I can start reading your book.
Thank You

I appreciate the excitement! I have a few rough drafts in the works, but creating the polished final versions takes time unfortunately. I don't want to commit to any particular date at this point. In the mean time, I hope the introductory problem set serves as some solid material for beginners to work through.

eagerly waiting for it :D
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TheMath_boy
1235 posts
#134
Y by
the drop box link for thefull pdf isn't working
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HoRI_DA_GRe8
597 posts
#135
Y by
Pascal96 wrote:
Hi everyone, I am currently writing a book on combinatorics for people preparing for national and international math competitions, especially the IMO and selection tests leading up to it. The book is intended to expose readers to a variety of ideas, techniques and problem solving strategies, ranging from the intuitive “greedy algorithms” in the first chapter to the powerful Probabilistic Method in chapter nine.
I am uploading chapter one here, and would appreciate your feedback and any suggestions. Over the coming weeks, I will be uploading the remaining chapters one at a time.
The only prerequisites are familiarity with basic graph theoretic concepts and terminology, algebraic inequalities, induction and the pigeonhole principle. Experience with invariants and the extremal principle is also helpful.
EDIT: CHAPTER 9 IS OUT! Since only 3 attachments are allowed per post, I have uploaded chapters 4, 5 and 6 in my comment below (10th on this page), and chapters 7, 8, and 9 further below (comment number 49 on this page).
NOTE: The solution to example 8 in chapter 1 is incorrect, and will be corrected in the final version of the book. For now, ignore this example.

Full book (uploaded by green_dog_7983): Dead Link
[Amir: new link]

Is there any hints/solution key here??
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IceWolf10
1577 posts
#136
Y by
no but there's a discussion forum
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dgrozev
2463 posts
#137
Y by
MelonGirl wrote:
not directly related to last few posts, but I pm-ed you about this sometime back, so I guess I'll post it here as well for anyone who's worked on the problem.
Quote:
On each square of a chessboard is a light which has two states-
on or off. A move consists of choosing a square and changing
the state of the bulbs in that square and in its neighboring
squares (squares that share a side with it). Show that starting
from any configuration we can make finitely many moves to
reach a point where all the bulbs are switched off

This is under the algorithms chapter (2). People have found ways to do this with linear algebra and brute force (similar to the row reduction method here.)

Does anyone know of a purely combinatorial algorithm approach to this problem?
Let the cells of the chessboard be vertices of a graph $G$. Connect any two neighboring vertices (squares). So, you can change the binary state (0,1) of any vertex and all of its neighbors. It does not matter what a graph $G$ is. For any simple graph the same claim holds. It was posted already here, in this forum. Here is a solution using linear algebra. There is a T. Gallai's result saying that the vertices of any graph can be partitioned into two sets $V_1,V_2$ such that the subgraphs induced on $V_1$ and $V_2$ have all vertices of even degrees. It's possible the above problem to be proved as a corollary of Gallai's theorem. In this blog post, the converse approach is shown.
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Karmanka
3 posts
#138 • 3 Y
Y by Mango247, Mango247, Mango247
Is it a mistake in task 5 [Czech and Slovak Republics 1997] after 1st Chapter?
Shouldn't there be only (2n+1)-gon or am I missing something (pls, explain then)?
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StefanSebez
53 posts
#139 • 4 Y
Y by adorefunctionalequation, Mango247, Mango247, Mango247
Karmanka wrote:
Is it a mistake in task 5 [Czech and Slovak Republics 1997] after 1st Chapter?
Shouldn't there be only (2n+1)-gon or am I missing something (pls, explain then)?

Yes, n should be an odd integer
Also here is that problem on aops
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Helixglich
113 posts
#140 • 2 Y
Y by adorefunctionalequation, theSpider
That book is a good one. Fairly friendly to newcomers too :blush:
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Phusy
2 posts
#141
Y by
Thanks alot. I love your style. Wish all the good thing for you <3
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zaahir
6 posts
#142
Y by
When can we expect the beginner version @Pascal96 ?
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