Stay ahead of learning milestones! Enroll in a class over the summer!

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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
minimizing sum
gggzul   1
N 4 minutes ago by RedFireTruck
Let $x, y, z$ be real numbers such that $x^2+y^2+z^2=1$. Find
$$min\{12x-4y-3z\}.$$
1 reply
1 viewing
gggzul
an hour ago
RedFireTruck
4 minutes ago
Equilateral Triangle inside Equilateral Triangles.
abhisruta03   2
N 4 minutes ago by Reacheddreams
Source: ISI 2021 P6
If a given equilateral triangle $\Delta$ of side length $a$ lies in the union of five equilateral triangles of side length $b$, show that there exist four equilateral triangles of side length $b$ whose union contains $\Delta$.
2 replies
abhisruta03
Jul 18, 2021
Reacheddreams
4 minutes ago
Number Theory
fasttrust_12-mn   12
N 8 minutes ago by KTYC
Source: Pan African Mathematics Olympiad P1
Find all positive intgers $a,b$ and $c$ such that $\frac{a+b}{a+c}=\frac{b+c}{b+a}$ and $ab+bc+ca$ is a prime number
12 replies
fasttrust_12-mn
Aug 15, 2024
KTYC
8 minutes ago
USAMO 1984 Problem 5 - Polynomial of degree 3n
Binomial-theorem   8
N 20 minutes ago by Assassino9931
Source: USAMO 1984 Problem 5
$P(x)$ is a polynomial of degree $3n$ such that

\begin{eqnarray*}
P(0) = P(3) = \cdots &=& P(3n) = 2, \\
P(1) = P(4) = \cdots &=& P(3n-2) = 1, \\
P(2) = P(5) = \cdots &=& P(3n-1) = 0, \quad\text{ and }\\
&& P(3n+1) = 730.\end{eqnarray*}

Determine $n$.
8 replies
Binomial-theorem
Aug 16, 2011
Assassino9931
20 minutes ago
No more topics!
construct point P such <APB= <BPC= <CPD iff (a+b)(b+c) < 4ac
parmenides51   0
May 23, 2019
Source: Austrian-Polish 1994
On the plane are given four distinct points $A,B,C,D$ on a line $g$ in this order, at the mutual distances $AB = a, BC = b, CD = c$.
(a) Construct (if possible) a point $P$ outside line $g$ such that $\angle APB =\angle BPC =\angle CPD$.
(b) Prove that such a point $P$ exists if and only if $ (a+b)(b+c) < 4ac$
0 replies
parmenides51
May 23, 2019
0 replies
construct point P such <APB= <BPC= <CPD iff (a+b)(b+c) < 4ac
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Source: Austrian-Polish 1994
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parmenides51
30651 posts
#1 • 2 Y
Y by Adventure10, Mango247
On the plane are given four distinct points $A,B,C,D$ on a line $g$ in this order, at the mutual distances $AB = a, BC = b, CD = c$.
(a) Construct (if possible) a point $P$ outside line $g$ such that $\angle APB =\angle BPC =\angle CPD$.
(b) Prove that such a point $P$ exists if and only if $ (a+b)(b+c) < 4ac$
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