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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 May Highlights and 2025 AoPS Online Class Information
jlacosta   0
Yesterday at 11:16 PM
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)!

Be sure to mark your calendars for the following upcoming events:
[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
Yesterday at 11:16 PM
0 replies
purple comet discussion
ConfidentKoala4   18
N 13 minutes ago by aopslover08
when can we discuss purple comet
18 replies
ConfidentKoala4
4 hours ago
aopslover08
13 minutes ago
Mathcounts state
happymoose666   34
N 38 minutes ago by ZMB038
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure
34 replies
happymoose666
Mar 24, 2025
ZMB038
38 minutes ago
Math Kangaroo 2025 Thread
FuturePanda   3
N 41 minutes ago by Ashleyandxin
Are we allowed to discuss scores and problems yet? If so, we can start here.
3 replies
+1 w
FuturePanda
Today at 3:34 AM
Ashleyandxin
41 minutes ago
Putnam 1954 A1
sqrtX   2
N 43 minutes ago by centslordm
Source: Putnam 1954
Let $n$ be an odd integer greater than $1.$ Let $A$ be an $n\times n$ symmetric matrix such that each row and column consists of some permutation of the integers $1,2, \ldots, n.$ Show that each of the integers $1,2, \ldots, n$ must appear in the main diagonal of $A$.
2 replies
sqrtX
Jul 17, 2022
centslordm
43 minutes ago
Putnam 1953 B1
sqrtX   7
N 44 minutes ago by centslordm
Source: Putnam 1953
Is the infinite series
$$\sum_{n=1}^{\infty} \frac{1}{n^{1+\frac{1}{n}}}$$convergent?
7 replies
sqrtX
Jul 16, 2022
centslordm
44 minutes ago
1953 Putnam A2
Taco12   4
N an hour ago by centslordm
Source: 1953 Putnam A2
The complete graph with 6 points and 15 edges has each edge colored red or blue. Show that we can find 3 points such that the 3 edges joining them are the same color.
4 replies
Taco12
Aug 20, 2021
centslordm
an hour ago
Putnam 1952 B4
sqrtX   1
N an hour ago by centslordm
Source: Putnam 1952
A homogeneous solid body is made by joining a base of a circular cylinder of height $h$ and radius $r,$ and the base of a hemisphere of radius $r.$ This body is placed with the hemispherical end on a horizontal table, with the axis of the cylinder in a vertical position, and then slightly oscillated. It is intuitively evident that if $r$ is large as compared to $h$, the equilibrium will be stable; but if $r$ is small compared to $h$, the equilibrium will be unstable. What is the critical value of the ratio $r\slash h$ which enables the body to rest in neutral equilibrium in any position?
1 reply
sqrtX
Jul 7, 2022
centslordm
an hour ago
Putnam 1952 B3
centslordm   2
N an hour ago by centslordm
Develop necessary and sufficient conditions that the equation \[ \begin{vmatrix} 0 & a_1 - x & a_2 - x \\ -a_1 - x & 0 & a_3 - x \\ -a_2 - x & -a_3 - x & 0\end{vmatrix} = 0 \qquad (a_i \neq 0) \]shall have a multiple root.
2 replies
centslordm
May 30, 2022
centslordm
an hour ago
Putnam 1952 A6
centslordm   1
N an hour ago by centslordm
A man has a rectangular block of wood $m$ by $n$ by $r$ inches ($m, n,$ and $r$ are integers). He paints the entire surface of the block, cuts the block into inch cubes, and notices that exactly half the cubes are completely unpainted. Prove that the number of essentially different blocks with this property is finite. (Do not attempt to enumerate them.)
1 reply
centslordm
May 29, 2022
centslordm
an hour ago
Putnam 1952 A4
centslordm   2
N an hour ago by centslordm
The flag of the United Nations consists of a polar map of the world, with the North Pole as its center, extending to approximately $45^\circ$ South Latitude. The parallels of latitude are concentric circles with radii proportional to their co-latitudes. Australia is near the periphery of the map and is intersected by the parallel of latitude $30^\circ$ S.In the very close vicinity of this parallel how much are East and West distances exaggerated as compared to North and South distances?
2 replies
centslordm
May 29, 2022
centslordm
an hour ago
Units Digit of Monomial/Exponent
worthawholebean   20
N 4 hours ago by SomeonecoolLovesMaths
Source: AMC 12 2008A Problem 15
Let $ k=2008^2+2^{2008}$. What is the units digit of $ k^2+2^k$?

$ \textbf{(A)}\ 0 \qquad
\textbf{(B)}\ 2 \qquad
\textbf{(C)}\ 4 \qquad
\textbf{(D)}\ 6 \qquad
\textbf{(E)}\ 8$
20 replies
worthawholebean
Feb 17, 2008
SomeonecoolLovesMaths
4 hours ago
Putnam 1958 November A7
sqrtX   1
N 4 hours ago by centslordm
Source: Putnam 1958 November
Let $a$ and $b$ be relatively prime positive integers, $b$ even. For each positive integer $q$, let $p=p(q)$ be chosen so that
$$ \left| \frac{p}{q} - \frac{a}{b}  \right|$$is a minimum. Prove that
$$ \lim_{n \to \infty} \sum_{q=1 }^{n} \frac{ q\left| \frac{p}{q} - \frac{a}{b}  \right|}{n} = \frac{1}{4}.$$
1 reply
sqrtX
Jul 19, 2022
centslordm
4 hours ago
Putnam 1958 November B7
sqrtX   5
N 4 hours ago by centslordm
Source: Putnam 1958 November
Let $a_1 ,a_2 ,\ldots, a_n$ be a permutation of the integers $1,2,\ldots, n.$ Call $a_i$ a big integer if $a_i >a_j$ for all $i<j.$ Find the mean number of big integers over all permutations on the first $n$ postive integers.
5 replies
sqrtX
Jul 19, 2022
centslordm
4 hours ago
System of two matrices of the same rank
Assassino9931   3
N 5 hours ago by RobertRogo
Source: Vojtech Jarnik IMC 2025, Category II, P2
Let $A,B$ be two $n\times n$ complex matrices of the same rank, and let $k$ be a positive integer. Prove that $A^{k+1}B^k = A$ if and only if $B^{k+1}A^k = B$.
3 replies
Assassino9931
Today at 1:02 AM
RobertRogo
5 hours ago
k Sit Back and Enjoy the Problems
Binomial-theorem   230
N Jun 10, 2020 by Piano_Man123
Hi everyone! I was talking to djmathman earlier today, and we both noticed an increase in threads this contest season along the lines of “I suck at math because I didn’t do well on the AMC 10/12 test”. This unfortunate thought pattern seems to be growing a lot as people associate self-worth with contest math performance. However, while it’s true that people who often do great on math contests go on to do amazing things in mathematics, doing poorly on math contests does not make a person any less of a mathematician. Contest mathematics isn’t the “be all end all” of mathematics performance: it’s merely a gateway into getting people to think about more interesting problems.

One huge contributing factor to success in contest mathematics is having seen a lot of problems. Many contest math problems are very similar to problems on previous year’s contests, and therefore, understanding a lot of problem solving techniques is critical to success. (For instance, consider 2016 AMC 12A Problem #22 . Having seen 1987 AIME I Problem #7, a student could solve this problem almost immediately. On the other hand, a student who has never seen a problem like this before would be at a huge disadvantage, because, while they could come up with a solution on the fly, they don’t have a lot of time to do so.) Time pressure is a huge element of the AMC tests; these contests don’t always allow students to fully think about problems. When I do math problems, one of my favorite things to do is sit down with an idea and work with it for a while until I really fully grasp that concept, and the MAA does a fantastic job of starting conversations about tons of interesting things in mathematics. However, during the actual contest, competitors don’t have enough time to do so. If you can’t figure out how to solve a problem on the test, while it’s natural to feel bad initially (I’ve kicked myself many times over the “could’ve would’ve” problems), remember the main goal of doing mathematics: to understand and enjoy the problems. Read the different solutions on the forums, research a topic more which you may have been unfamiliar with, read a book. Then, next time around, not only will you nail the problem on the test, but you will also understand the underlying idea and intuition behind it.

I’m currently a senior in high school, and am almost officially finished with high school math competitions. I’ve participated in the AIME for the past 5 years along with MATHCOUNTS Nationals in 8th grade. I rarely share my scores with others on these tests for two reasons: (1) they’re usually below the first quartile of scores posted on AoPS and, most importantly, (2) I don’t compete in contest math for the sake of having a good score. I do it because I enjoy the problems, and the underlying mathematical ideas which accompany them. I’m an avid lover of Number Theory problems (shameless self promotion) and problems like 2016 AMC 12B Problem #22 excite me a lot, because this problem combined ideas about repeating decimals, order of a number, and divisibility. I didn’t solve this problem until after the test was over; however, when I did, I excitedly shared it with everyone in my school’s math club while teaching them some new things in number theory. Sharing this problem with my friends and teachers is the essence of the beauty of mathematics for me, because it lends itself well to collaboration in problem solving. When I find interesting problems like these, I often have them queued up to show to various people I encounter because I love inspiring others to have this level of inquisitiveness about a mathematical idea.

I’ve also been on the writing end of several math contests, including many Mock AMC exams on the AoPS forum, most notably the 2015 Mock AIME I. I also help write problems for the NIMO contest. My favorite thing about writing these problems is allowing competitors to think about mathematical concepts in new ways. For instance, this polynomial transformation problem taught a very important idea in algebra, which is building a polynomial out of the roots (an idea which was also featured in a similar USAMO problem before). Contributing to these discussions and having people solve my problems in many different ways is incredibly humbling for me, and is part of the beauty of contest mathematics. For more information on this, I highly recommend reading djmathman’s post here .

One of the great things about contest math is it starts these discussions. And, while tons of team contests like ARML and MATHCOUNTS try to inspire this level of collaboration and communication, it seems like it is often the missing link for many students who may be kicking themselves over a low score. Instead of thinking of a 96 on the AMC 10 as a complete failure and a wasted 2 years preparing for the exam, don’t let this score define you. Instead, learn new ideas from the problems and share them with those around you. Teaching may be a passion which is just mine, but I hope that you all can learn to truly enjoy the problems. Maybe you couldn’t solve 2016 AMC 12A Problem 23 . Read the solutions online, try to understand what’s going on in the 3d graph for this problem. Study equations like these more, and understand their graphs (this is especially important when discussing the space of matrices later down the road). If you want to go way above and beyond, maybe try to start understanding double integrals, as in va2010’s post in that thread. The main point is, this problem alone can generate tons of interesting discussions, and missing out on these are a shame. Getting a bad score isn’t a bad thing, but not learning from it surely is.

For another post in a similar vein, I highly recommend reading this post by hyperbolictangent. Although it approaches the manner from the perspective of students who are trying to prove themselves by commenting on how they underperformed on a contest, the ideas present in that post are incredibly relevant to this topic as well. (I highly recommend reading the whole thread too, as it has many different perspectives from many successful students).

Good luck on your future endeavors, and don’t forget to sit back and enjoy the problems!
230 replies
Binomial-theorem
Mar 13, 2016
Piano_Man123
Jun 10, 2020
Sit Back and Enjoy the Problems
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math129
700 posts
#428 • 2 Y
Y by Imayormaynotknowcalculus, samrocksnature
Imayormaynotknowcalculus wrote:

What I meant was $97\equiv 1\pmod{3}$.

LOL oops I got a 97.5 not 97
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zonee4
1258 posts
#429 • 1 Y
Y by samrocksnature
I got a wayyyyy worse score on the AMC 10
I got like a 66 or something
I'm bad at competition math but I do it just because I enjoy difficult things, always have. Its just a think about me. Probably started when I started playing suuuuuper hard video games. It feels almost euphoric. I go into the "zone" and it always feels great!
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superagh
1865 posts
#430 • 2 Y
Y by Imayormaynotknowcalculus, samrocksnature
Way to not give up!
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newphysicist101
206 posts
#431 • 2 Y
Y by OlympusHero, samrocksnature
Can the mods please lock this thread? I don't think it's going anywhere useful.
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hliu1
939 posts
#432 • 1 Y
Y by samrocksnature
I think it's going somewhere useful, particularly as a means of encouraging each other.
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zonee4
1258 posts
#433 • 2 Y
Y by samrocksnature, Mango247
hliu1 wrote:
I think it's going somewhere useful, particularly as a means of encouraging each other.

Same. That's pretty much the sole reason why I come here
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middletonkids
2460 posts
#434 • 1 Y
Y by samrocksnature
Just a question, but what is SSI?
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franzliszt
23531 posts
#435 • 2 Y
Y by Imayormaynotknowcalculus, samrocksnature
middletonkids wrote:
Just a question, but what is SSI?

I would avoid starting a discussion about that thank
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middletonkids
2460 posts
#436 • 1 Y
Y by samrocksnature
franzliszt wrote:
middletonkids wrote:
Just a question, but what is SSI?

I would avoid starting a discussion about that thank

But if I don't know what it is, I might start it on accident
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un57gcder1
312 posts
#437 • 1 Y
Y by samrocksnature
middletonkids wrote:
Just a question, but what is SSI?

Please read the announcement about SSI. Thanks!
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middletonkids
2460 posts
#438 • 1 Y
Y by samrocksnature
un57gcder1 wrote:
middletonkids wrote:
Just a question, but what is SSI?

Please read the announcement about SSI. Thanks!

I read it, but what does it stand for?
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aop2014
2416 posts
#439 • 1 Y
Y by samrocksnature
Just search SSI in the search function, now can we stop to avoid locking this
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OliverA
2588 posts
#440 • 1 Y
Y by samrocksnature
Please ask questions in a related thread. However, given that you already asked here: SSI stands from Summer STEM Institute
This post has been edited 2 times. Last edited by OliverA, Jun 10, 2020, 6:32 PM
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un57gcder1
312 posts
#441 • 1 Y
Y by samrocksnature
aop2014 wrote:
Just search SSI in the search function, now can we stop to avoid locking this
OliverA wrote:
Please ask that in a better suited thread. However, given that you already asked here: SSI stands from Summer STEM Institue

I already PMed him/her.

To get this back on topic:

This is kind of related. It actually helps you remember the similar problems from each contest that you saw.
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Piano_Man123
1774 posts
#442 • 2 Y
Y by samrocksnature, Mango247
The key is to not focus on the score, just focus on how well you enjoy the excellent problems!
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