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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)!

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]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
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Introducing myself at AoPS, and what's your magic wand?
asuth_asuth   1165
N an hour ago by TrickyOtter60
Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.
1165 replies
asuth_asuth
Mar 30, 2025
TrickyOtter60
an hour ago
J
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Find function
trito11   3
N Yesterday at 8:37 PM by jasperE3
Find $f:\mathbb{R^+} \to \mathbb{R^+} $ such that
i) f(x)>f(y) $\forall$ x>y>0
ii) f(2x)$\ge$2f(x)$\forall$x>0
iii)$f(f(x)f(y)+x)=f(xf(y))+f(x)$$\forall$x,y>0
3 replies
trito11
Nov 11, 2019
jasperE3
Yesterday at 8:37 PM
J
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2024 Mock AIME 1 ** p15 (cheaters' trap) - 128 | n^{\sigma (n)} - \sigma(n^n)
parmenides51   1
N Yesterday at 8:09 PM by NamelyOrange
Let $N$ be the number of positive integers $n$ such that $n$ divides $2024^{2024}$ and $128$ divides
$$n^{\sigma (n)} - \sigma(n^n)$$where $\sigma (n)$ denotes the number of positive integers that divide $n$, including $1$ and $n$. Find the remainder when $N$ is divided by $1000$.
1 reply
parmenides51
Jan 29, 2025
NamelyOrange
Yesterday at 8:09 PM
J
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Inequalities
sqing   2
N Yesterday at 7:59 PM by maromex
Let $ a,b,c>0 $ . Prove that
$$\frac{a+5b}{b+c}+\frac{b+5c}{c+a}+\frac{c+5a}{a+b}\geq 9$$$$ \frac{2a+11b}{b+c}+\frac{2b+11c}{c+a}+\frac{2c+11a}{a+b}\geq \frac{39}{2}$$$$ \frac{25a+147b}{b+c}+\frac{25b+147c}{c+a}+\frac{25c+147a}{a+b} \geq258$$
2 replies
sqing
Yesterday at 3:46 AM
maromex
Yesterday at 7:59 PM
J
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Assam Mathematics Olympiad 2022 Category III Q14
SomeonecoolLovesMaths   2
N Yesterday at 7:21 PM by rachelcassano
The following sum of three four digits numbers is divisible by $75$, $7a71 + 73b7 + c232$, where $a, b, c$ are decimal digits. Find the necessary conditions in $a, b, c$.
2 replies
SomeonecoolLovesMaths
Sep 12, 2024
rachelcassano
Yesterday at 7:21 PM
J
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2019 SMT Team Round - Stanford Math Tournament
parmenides51   19
N Yesterday at 5:21 PM by SomeonecoolLovesMaths
p1. Given $x + y = 7$, find the value of x that minimizes $4x^2 + 12xy + 9y^2$.


p2. There are real numbers $b$ and $c$ such that the only $x$-intercept of $8y = x^2 + bx + c$ equals its $y$-intercept. Compute $b + c$.



p3. Consider the set of $5$ digit numbers $ABCDE$ (with $A \ne 0$) such that $A+B = C$, $B+C = D$, and $C + D = E$. What’s the size of this set?


p4. Let $D$ be the midpoint of $BC$ in $\vartriangle ABC$. A line perpendicular to D intersects $AB$ at $E$. If the area of $\vartriangle ABC$ is four times that of the area of $\vartriangle BDE$, what is $\angle ACB$ in degrees?


p5. Define the sequence $c_0, c_1, ...$ with $c_0 = 2$ and $c_k = 8c_{k-1} + 5$ for $k > 0$. Find $\lim_{k \to \infty} \frac{c_k}{8^k}$.


p6. Find the maximum possible value of $|\sqrt{n^2 + 4n + 5} - \sqrt{n^2 + 2n + 5}|$.


p7. Let $f(x) = \sin^8 (x) + \cos^8(x) + \frac38 \sin^4 (2x)$. Let $f^{(n)}$ (x) be the $n$th derivative of $f$. What is the largest integer $a$ such that $2^a$ divides $f^{(2020)}(15^o)$?


p8. Let $R^n$ be the set of vectors $(x_1, x_2, ..., x_n)$ where $x_1, x_2,..., x_n$ are all real numbers. Let $||(x_1, . . . , x_n)||$ denote $\sqrt{x^2_1 +... + x^2_n}$. Let $S$ be the set in $R^9$ given by $$S = \{(x, y, z) : x, y, z \in R^3 , 1 = ||x|| = ||y - x|| = ||z -y||\}.$$If a point $(x, y, z)$ is uniformly at random from $S$, what is $E[||z||^2]$?


p9. Let $f(x)$ be the unique integer between $0$ and $x - 1$, inclusive, that is equivalent modulo $x$ to $\left( \sum^2_{i=0} {{x-1} \choose i} ((x - 1 - i)! + i!) \right)$. Let $S$ be the set of primes between $3$ and $30$, inclusive. Find $\sum_{x\in S}^{f(x)}$.


p10. In the Cartesian plane, consider a box with vertices $(0, 0)$,$\left( \frac{22}{7}, 0\right)$,$(0, 24)$,$\left( \frac{22}{7}, 4\right)$. We pick an integer $a$ between $1$ and $24$, inclusive, uniformly at random. We shoot a puck from $(0, 0)$ in the direction of $\left( \frac{22}{7}, a\right)$ and the puck bounces perfectly around the box (angle in equals angle out, no friction) until it hits one of the four vertices of the box. What is the expected number of times it will hit an edge or vertex of the box, including both when it starts at $(0, 0)$ and when it ends at some vertex of the box?


p11. Sarah is buying school supplies and she has $\$2019$. She can only buy full packs of each of the following items. A pack of pens is $\$4$, a pack of pencils is $\$3$, and any type of notebook or stapler is $\$1$. Sarah buys at least $1$ pack of pencils. She will either buy $1$ stapler or no stapler. She will buy at most $3$ college-ruled notebooks and at most $2$ graph paper notebooks. How many ways can she buy school supplies?


p12. Let $O$ be the center of the circumcircle of right triangle $ABC$ with $\angle ACB = 90^o$. Let $M$ be the midpoint of minor arc $AC$ and let $N$ be a point on line $BC$ such that $MN \perp BC$. Let $P$ be the intersection of line $AN$ and the Circle $O$ and let $Q$ be the intersection of line $BP$ and $MN$. If $QN = 2$ and $BN = 8$, compute the radius of the Circle $O$.


p13. Reduce the following expression to a simplified rational $$\frac{1}{1 - \cos \frac{\pi}{9}}+\frac{1}{1 - \cos \frac{5 \pi}{9}}+\frac{1}{1 - \cos \frac{7 \pi}{9}}$$

p14. Compute the following integral $\int_0^{\infty} \log (1 + e^{-t})dt$.


p15. Define $f(n)$ to be the maximum possible least-common-multiple of any sequence of positive integers which sum to $n$. Find the sum of all possible odd $f(n)$


PS. You should use hide for answers. Collected here.
19 replies
parmenides51
Feb 6, 2022
SomeonecoolLovesMaths
Yesterday at 5:21 PM
J
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Complex Number Geometry
gauss202   1
N Yesterday at 3:08 PM by ANewName
Describe the locus of complex numbers, $z$, such that $\arg \left(\dfrac{z+i}{z-1} \right) = \dfrac{\pi}{4}$.
1 reply
gauss202
Yesterday at 12:21 PM
ANewName
Yesterday at 3:08 PM
J
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Inequalities
sqing   5
N Yesterday at 2:49 PM by sqing
Let $a,b,c >2 $ and $ ab+bc+ca \leq 75.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 1$$Let $a,b,c >2 $ and $ \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{6}{7}.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 2$$
5 replies
sqing
Tuesday at 11:31 AM
sqing
Yesterday at 2:49 PM
J
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Trig Identity
gauss202   1
N Yesterday at 12:33 PM by Lankou
Simplify $\dfrac{1-\cos \theta + \sin \theta}{\sqrt{1 - \cos \theta + \sin \theta - \sin \theta \cos \theta}}$
1 reply
gauss202
Yesterday at 12:12 PM
Lankou
Yesterday at 12:33 PM
J
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Trunk of cone
soruz   1
N Yesterday at 9:59 AM by Mathzeus1024
One hemisphere is putting a truncated cone, with the base circles hemisphere. How height should have truncated cone as its lateral area to be minimal side?
1 reply
soruz
May 6, 2015
Mathzeus1024
Yesterday at 9:59 AM
J
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Inequalities
sqing   7
N Yesterday at 8:29 AM by sqing
Let $a,b,c >1 $ and $ \frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}=1.$ Show that$$ab+bc+ca \geq 48$$$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\leq \frac{3}{4}$$Let $a,b,c >1 $ and $ \frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}=2.$ Show that$$ab+bc+ca \geq \frac{75}{4}$$$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\leq \frac{6}{5}$$Let $a,b,c >1 $ and $ \frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}=3.$ Show that$$ab+bc+ca \geq 12$$$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\leq \frac{3}{2}$$
7 replies
sqing
Tuesday at 9:04 AM
sqing
Yesterday at 8:29 AM
J
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k Glitch or Bug?
awesometriangles   5
N Yesterday at 4:18 AM by Craftybutterfly
I was asking for some $\LaTeX$ help in one of my classrooms, and one of the Halpers posted. Is this a glitch or a bug(see screenshot)?


It seems as though I can edit their post...
5 replies
awesometriangles
Yesterday at 1:08 AM
Craftybutterfly
Yesterday at 4:18 AM
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k Deleting collections
Sadigly   1
N May 12, 2025 by jlacosta
How to delete some collections? I accidently created 2 same collections, and one of them is useless
1 reply
Sadigly
May 11, 2025
jlacosta
May 12, 2025
J
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k Alcumus Reset
greenplanet2050   7
N May 12, 2025 by jlacosta
I want to reset my Alcumus but it says "You cannot reset your Alcumus data while you are in current AoPS classes."

But I don't have any ongoing AoPs classes and my last class Precalculus already ended.
7 replies
greenplanet2050
May 10, 2025
jlacosta
May 12, 2025
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k For The Win
Aaronjudgeisgoat   2
N Apr 15, 2025 by jlacosta
I don't know if this is the right place to post this, but when will For The Win stop undergoing maintenance?
hopefully theres some big update or smth...
2 replies
Aaronjudgeisgoat
Apr 14, 2025
jlacosta
Apr 15, 2025
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For The Win
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Reveal topic tags
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Aaronjudgeisgoat
900 posts
Aaronjudgeisgoat
#1 h  Apr 14, 2025, 6:28 PM • 1 Y
Y by Exponent11
I don't know if this is the right place to post this, but when will For The Win stop undergoing maintenance?
hopefully theres some big update or smth...
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jlacosta
648 posts
jlacosta
#3 h  Apr 14, 2025, 11:53 PM • 1 Y
Y by Exponent11
Thanks for letting us know. Our engineering team is looking into this.
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jlacosta
648 posts
jlacosta
#4 h  Apr 15, 2025, 12:04 AM • 1 Y
Y by Exponent11
For The Win should now be back up!
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