Goals for 2025-2026

by Airbus320-214, May 11, 2025, 8:00 AM

Please write down your goal/goals for competitions here for 2025-2026.

[CASH PRIZES] IndyINTEGIRLS Spring Math Competition

by Indy_Integirls, May 11, 2025, 2:36 AM

https://cdn.artofproblemsolving.com/attachments/a/9/16c2f34cda3c77e900e650d177ce8439b98e9e.png

Greetings, AoPS! IndyINTEGIRLS will be hosting a virtual math competition on May 25,
2024 from 12 PM to 3 PM EST.
Join other woman-identifying and/or non-binary "STEMinists" in solving problems, socializing, playing games, winning prizes, and more! If you are interested in competing, please register here!

Important Information

Eligibility: This competition is open to all woman-identifying and non-binary students in middle and high school. Non-Indiana residents and international students are welcome as well!

Format: There will be a middle school and high school division. In each separate division, there will be an individual round and a team round, where students are grouped into teams of 3-4 and collaboratively solve a set of difficult problems. There will also be a buzzer/countdown/Kahoot-style round, where students from both divisions are grouped together to compete in a MATHCOUNTS-style countdown round! There will be prizes for the top competitors in each division.

Problem Difficulty: Our amazing team of problem writers is working hard to ensure that there will be problems for problem-solvers of all levels! The middle school problems will range from MATHCOUNTS school round to AMC 10 level, while the high school problems will be for more advanced problem-solvers. The team round problems will cover various difficulty levels and are meant to be more difficult, while the countdown/buzzer/Kahoot round questions will be similar to MATHCOUNTS state to MATHCOUNTS Nationals countdown round in difficulty.

Platform: This contest will be held virtually through Zoom. All competitors are required to have their cameras turned on at all times unless they have a reason for otherwise. Proctors and volunteers will be monitoring students at all times to prevent cheating and to create a fair environment for all students.

Prizes: At this moment, prizes are TBD, and more information will be provided and attached to this post as the competition date approaches. Rest assured, IndyINTEGIRLS has historically given out very generous cash prizes, and we intend on maintaining this generosity into our Spring Competition.

Contact & Connect With Us: Follow us on Instagram @indy.integirls, join our Discord, follow us on TikTok @indy.integirls, and email us at indy@integirls.org.

Help Us Out

Please help us in sharing the news of this competition! Our amazing team of officers has worked very hard to provide this educational opportunity to as many students as possible, and we would appreciate it if you could help us spread the word!
L

Jane street swag package? USA(J)MO

by arfekete, May 7, 2025, 4:34 PM

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.
L

Question about AMC 10

by MathNerdRabbit103, May 2, 2025, 2:53 AM

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.

usamOOK geometry

by KevinYang2.71, Mar 21, 2025, 12:00 PM

Let $H$ be the orthocenter of acute triangle $ABC$, let $F$ be the foot of the altitude from $C$ to $AB$, and let $P$ be the reflection of $H$ across $BC$. Suppose that the circumcircle of triangle $AFP$ intersects line $BC$ at two distinct points $X$ and $Y$. Prove that $C$ is the midpoint of $XY$.

what the yap

by KevinYang2.71, Mar 20, 2025, 12:00 PM

Alice the architect and Bob the builder play a game. First, Alice chooses two points $P$ and $Q$ in the plane and a subset $\mathcal{S}$ 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 $A,\,B$ of cities, they are connected with a road along the line segment $AB$ if and only if the following condition holds:
For every city $C$ distinct from $A$ and $B$, there exists $R\in\mathcal{S}$ such
that $\triangle PQR$ is directly similar to either $\triangle ABC$ or $\triangle BAC$.
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: $\triangle UVW$ is directly similar to $\triangle XYZ$ if there exists a sequence of rotations, translations, and dilations sending $U$ to $X$, $V$ to $Y$, and $W$ to $Z$.

Prove a polynomial has a nonreal root

by KevinYang2.71, Mar 20, 2025, 12:00 PM

Let $n$ and $k$ be positive integers with $k<n$. Let $P(x)$ be a polynomial of degree $n$ with real coefficients, nonzero constant term, and no repeated roots. Suppose that for any real numbers $a_0,\,a_1,\,\ldots,\,a_k$ such that the polynomial $a_kx^k+\cdots+a_1x+a_0$ divides $P(x)$, the product $a_0a_1\cdots a_k$ is zero. Prove that $P(x)$ has a nonreal root.

Stanford Math Tournament (SMT) 2025

by stanford-math-tournament, Feb 1, 2025, 3:16 AM

:trampoline: :first: Stanford Math Tournament :first: :trampoline:

https://i.ibb.co/j5XcBLM/smt-logo.png

We are excited to announce that registration is now open for Stanford Math Tournament (SMT) 2025!

This year, we will welcome 800 competitors from across the nation to participate in person on Stanford’s campus. The tournament will be held April 11-12, 2025, and registration is open to all high-school students from the United States. This year, we are extending registration to high school teams (strongly preferred), established local mathematical organizations, and individuals; please refer to our website for specific policies. Whether you’re an experienced math wizard, a puzzle hunt enthusiast, or someone looking to meet new friends, SMT has something to offer everyone!

Register here today! We’ll be accepting applications until March 2, 2025.

For those unable to travel, in middle school, or not from the United States, we encourage you to instead register for SMT 2025 Online, which will be held on April 13, 2025. Registration for SMT 2025 Online will open mid-February.

For more information visit our website! Please email us at stanford.math.tournament@gmail.com with any questions or reply to this thread below. We can’t wait to meet you all in April!

prime spam

by fruitmonster97, Nov 7, 2024, 4:54 PM

What is the sum of the digits of the smallest prime that can be written as a sum of $5$ distinct primes?

$\textbf{(A) }5\qquad\textbf{(B) }7\qquad\textbf{(C) }9\qquad\textbf{(D) }10\qquad\textbf{(E) }11$
This post has been edited 1 time. Last edited by fruitmonster97, Nov 7, 2024, 8:21 PM

1. Algebra and sigma algebra on a set

by adityaguharoy, Feb 28, 2018, 3:28 PM

Definitions of algebra on a set and sigma algebra on a set

Let $X$ be an infinite set. And let $\mathcal{A}$ be the collection of all subsets $A$ of $X$ such that either $A$ or $A^{c} ( = X \setminus A)$ is finite. Prove that $\mathcal{A}$ is an algebra on $X$, but not a sigma algebra on $X$.

Proof



A related exercise :
Let $X$ be an uncountable set. Let $\mathcal{A}$ be the collection of all subsets $A$ of $X$ such that either $A$ is countable or $A^{c} ( = X \setminus A )$ is countable.
Is $\mathcal{A}$ a $\sigma$ algebra on $X$ ?

Answer
Hint to sketch
This post has been edited 2 times. Last edited by adityaguharoy, Feb 28, 2018, 4:16 PM

2016 Sets

by NormanWho, Apr 20, 2016, 9:30 PM

Find, with proof, the least integer $N$ such that if any $2016$ elements are removed from the set ${1, 2,...,N}$, one can still find $2016$ distinct numbers among the remaining elements with sum $N$.
This post has been edited 1 time. Last edited by NormanWho, Apr 20, 2016, 9:31 PM

The oldest, shortest words — "yes" and "no" — are those which require the most thought.

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  • Oh really the blog has 100 posts! I never counted the number of posts here. If I get some free time I will create a new page on my wordpress website and there I will post all the contents of this blog. So, make sure that you check the wordpress site.

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