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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]
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0 replies
jlacosta
May 1, 2025
0 replies
helpppppppp me
stupid_boiii   1
N 2 hours ago by vanstraelen
Given triangle ABC. The tangent at ? to the circumcircle(ABC) intersects line BC at point T. Points D,E satisfy AD=BD, AE=CE, and ∠CBD=∠BCE<90 ∘ . Prove that D,E,T are collinear.
1 reply
stupid_boiii
Yesterday at 4:22 AM
vanstraelen
2 hours ago
MATHCOUNTS
ILOVECATS127   45
N 3 hours ago by Glowworm
Hi,

I am looking to get on my school MATHCOUNTS team next year in 7th grade, and I had a question: Where do the school round questions come from? (Sprint, Chapter, Team, Countdown)
45 replies
ILOVECATS127
May 7, 2025
Glowworm
3 hours ago
Algebra Polynomials
Foxellar   2
N 3 hours ago by Foxellar
The real root of the polynomial \( p(x) = 8x^3 - 3x^2 - 3x - 1 \) can be written in the form
\[
\frac{\sqrt[3]{a} + \sqrt[3]{b} + 1}{c},
\]where \( a, b, \) and \( c \) are positive integers. Find the value of \( a + b + c \).
2 replies
Foxellar
4 hours ago
Foxellar
3 hours ago
relay race!
A7456321   8
N 4 hours ago by Craftybutterfly
Welcome to the math relay race! To participate, answer the problem in the latest post, then post one yourself! Please also mark the question number. E.x. if the one before you is question #35, then mark yours as question #36. Easy as pi!

Note: If you choose to help someone with a problem you don't have to make one yourself unless you want to. You are also welcome to ask a question without having to post a new problem. Please do not post a new problem until the previous one is solved. All topics are welcome except for anything >12th grade. Trig is fine. Calculus is not. :D

Question 1: If it takes 5 monkeys 5 days to eat 5 bananas, then how many days will it take for 4 monkeys to eat 4 bananas? (Hint: It's not 4)

Please upvote! :thumbup:

Goal: 100 questions!

Timeline
8 replies
A7456321
Today at 2:20 AM
Craftybutterfly
4 hours ago
9 How many squares do you have memorized
LXC007   91
N 5 hours ago by valisaxieamc
How many squares have you memorized. I have 1-20

Edit: to clarify i mean positive squares from 1 so if you say ten you mean you memorized the squares 1,2,3,4,5,6,7,8,9 and 10
91 replies
LXC007
May 17, 2025
valisaxieamc
5 hours ago
9 Pythagorean Triples
ZMB038   50
N 5 hours ago by valisaxieamc
Please put some of the ones you know, and try not to troll/start flame wars! Thank you :D
50 replies
ZMB038
May 19, 2025
valisaxieamc
5 hours ago
geometry
luckvoltia.112   0
Today at 2:29 AM
Let \( \triangle ABC \) be an acute triangle with \( AB < AC \), and its vertices lie on the circle \( (O) \). Let \( AD \) be the altitude from vertex \( A \). Let \( E \) and \( F \) be the feet of the perpendiculars from \( D \) to the lines \( AB \) and \( AC \), respectively. Let \( EF \) intersect the circle \( (O) \) again at points \( P \) and \( Q \) such that \( E \) lies between \( Q \) and \( F \). Let the lines \( AD \) and \( EF \) intersect at point \( G \). Let \( I \) be the midpoint of segment \( AD \). Let \( AO \) intersect line \( BC \) at point \( K \).
a) Prove that \( AP = AQ = AD \).
b) Prove that line \( OI \) is parallel to line \( KG \).
c)Let \( H \) be the orthocenter of triangle \( ABC \), and let \( M \) be the midpoint of segment \( BC \). $S$ is the center (HBC). Let point \( T \) lie on line \( DS \) such that ray \( KD \) is the angle bisector of \( \angle GKT \). Prove that lines \( AD \) and \( MT \) intersect at a point lying on circle \( (O) \).
0 replies
luckvoltia.112
Today at 2:29 AM
0 replies
Great Geometry with Squares on sides of triangles
SomeonecoolLovesMaths   2
N Today at 1:50 AM by happypi31415
Three squares are drawn on the sides of triangle \(ABC\) (i.e., the square on \(AB\) has \(AB\) as one of its sides and lies outside \(ABC\)). Show that the lines drawn from the vertices \(A\), \(B\), and \(C\) to the centers of the opposite squares are concurrent.

IMAGE
2 replies
SomeonecoolLovesMaths
Yesterday at 9:44 PM
happypi31415
Today at 1:50 AM
A suspcious assumption
NamelyOrange   2
N Today at 1:30 AM by maromex
Let $a,b,c,d$ be positive integers. Maximize $\max(a,b,c,d)$ if $a+b+c+d=a^2-b^2+c^2-d^2=2012$.
2 replies
NamelyOrange
Yesterday at 1:53 PM
maromex
Today at 1:30 AM
n is divisible by 5
spiralman   1
N Yesterday at 8:42 PM by KSH31415
n is an integer. There are n integers such that they are larger or equal to 1, and less or equal to 6. Sum of them is larger or equal to 4n, while sum of their square is less or equal to 22n. Prove n is divisible by 5.
1 reply
spiralman
Wednesday at 7:38 PM
KSH31415
Yesterday at 8:42 PM
Monochromatic Triangle
FireBreathers   1
N Yesterday at 8:08 PM by KSH31415
We are given in points in a plane and we connect some of them so that 10n^2 + 1 segments are drawn. We color these segments in 2 colors. Prove that we can find a monochromatic triangle.
1 reply
FireBreathers
Yesterday at 2:28 PM
KSH31415
Yesterday at 8:08 PM
how difficult are these problems
rajukaju   1
N Yesterday at 7:28 PM by Shan3t
I can solve only the first 4 problems of the last general round of the HMMT competition: https://hmmt-archive.s3.amazonaws.com/tournaments/2024/nov/gen/problems.pdf

As a prediction, would this mean I am good enough to qualify for AIME? How does the difficulty compare?

1 reply
rajukaju
Yesterday at 6:43 PM
Shan3t
Yesterday at 7:28 PM
Maximum value of function (with two variables)
Saucepan_man02   1
N Yesterday at 1:39 PM by Saucepan_man02
If $f(\theta) = \min(|2x-7|+|x-4|+|x-2 -\sin \theta|)$, where $x, \theta \in \mathbb R$, then maximum value of $f(\theta)$.
1 reply
Saucepan_man02
Yesterday at 1:25 PM
Saucepan_man02
Yesterday at 1:39 PM
It is given that $M=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{23}=\frac{n}{23!},
Vulch   3
N Yesterday at 11:58 AM by mohabstudent1
It is given that $M=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{23}=\frac{n}{23!},$ where $n$ is a natural number.What is the remainder when $n$ is divided by $13?$
3 replies
Vulch
Apr 9, 2025
mohabstudent1
Yesterday at 11:58 AM
Geometry Transformation Problems
ReticulatedPython   7
N Apr 22, 2025 by ReticulatedPython
Problem 1:
A regular hexagon of side length $1$ is rotated $360$ degrees about one side. The space through which the hexagon travels during the rotation forms a solid. Find the volume of this solid.

Problem 2:

A regular octagon of side length $1$ is rotated $360$ degrees about one side. The space through which the octagon travels through during the rotation forms a solid. Find the volume of this solid.

Source:Own

Hint

Useful Formulas
7 replies
ReticulatedPython
Apr 17, 2025
ReticulatedPython
Apr 22, 2025
Geometry Transformation Problems
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ReticulatedPython
713 posts
#1
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Problem 1:
A regular hexagon of side length $1$ is rotated $360$ degrees about one side. The space through which the hexagon travels during the rotation forms a solid. Find the volume of this solid.

Problem 2:

A regular octagon of side length $1$ is rotated $360$ degrees about one side. The space through which the octagon travels through during the rotation forms a solid. Find the volume of this solid.

Source:Own

Hint

Useful Formulas
This post has been edited 11 times. Last edited by ReticulatedPython, Apr 21, 2025, 3:33 PM
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jb2015007
1968 posts
#2
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ack i hate transformation problems and i suck at them so ill do this lol ill do it when i get home from school
@reticulated python check out the problem i posted in the intro to geo message board its real interesting
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ReticulatedPython
713 posts
#3
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Ok I will.
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ReticulatedPython
713 posts
#4
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Anyone want to give it a try?
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cheltstudent
629 posts
#5
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wait which intro to geo class is this
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ReticulatedPython
713 posts
#6
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\bump :)
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ReticulatedPython
713 posts
#7
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I will present the solution to problem 1 and see if anyone can use that to solve problem 2. Solution
This post has been edited 2 times. Last edited by ReticulatedPython, Apr 21, 2025, 7:26 PM
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ReticulatedPython
713 posts
#8
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Alright I will give the answer to problem 2; the method is similar to that of problem 1. Answer
This post has been edited 1 time. Last edited by ReticulatedPython, Apr 22, 2025, 3:31 PM
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