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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
J
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Interesting functional equation with polynomial
Iveela   0
a minute ago
Find all functions $f : \mathbb{R}^{+} \to \mathbb{R}^{+}$ and polynomial $P(x) \in \mathbb{R}[x]$ with nonnegative coefficients such that
\[f(x + P(x)f(y)) = (y + 1)f(x)\]for all $x, y \in \mathbb{R^{+}}$.
0 replies
Iveela
a minute ago
0 replies
J
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Math high school
Chantria   0
9 minutes ago
for x,y,z positive such that x+y+z=3 prove that (4^x+4^y+4^z)xyz≤12
0 replies
Chantria
9 minutes ago
0 replies
J
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Centrally symmetric polyhedron
genius_007   1
N 13 minutes ago by genius_007
Source: unknown
Does there exist a convex polyhedron with an odd number of sides, where each side is centrally symmetric?
1 reply
genius_007
May 28, 2025
genius_007
13 minutes ago
J
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Reachable Strings
numbertheorist17   22
N 16 minutes ago by cj13609517288
Source: USA TSTST 2014, Problem 1
Let $\leftarrow$ denote the left arrow key on a standard keyboard. If one opens a text editor and types the keys "ab$\leftarrow$ cd $\leftarrow \leftarrow$ e $\leftarrow \leftarrow$ f", the result is "faecdb". We say that a string $B$ is reachable from a string $A$ if it is possible to insert some amount of $\leftarrow$'s in $A$, such that typing the resulting characters produces $B$. So, our example shows that "faecdb" is reachable from "abcdef".

Prove that for any two strings $A$ and $B$, $A$ is reachable from $B$ if and only if $B$ is reachable from $A$.
22 replies
numbertheorist17
Jul 16, 2014
cj13609517288
16 minutes ago
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IMO 2013 Problem 3
liberator   3
N Aug 19, 2014 by liberator
Problem: Let the excircle of triangle $ABC$ opposite the vertex $A$ be tangent to the side $BC$ at the point $A_1$. Define the points $B_1$ on $CA$ and $C_1$ on $AB$ analogously, using the excircles opposite $B$ and $C$, respectively. Suppose that the circumcentre of triangle $A_1B_1C_1$ lies on the circumcircle of triangle $ABC$. Prove that triangle $ABC$ is right-angled.

Proposed by Alexander A. Polyansky, Russia

[b]My solution[/b]
3 replies
liberator
Aug 14, 2014
liberator
Aug 19, 2014
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IMO 2013 Problem 4
liberator   2
N Aug 19, 2014 by liberator
Problem: Let $ABC$ be an acute triangle with orthocenter $H$, and let $W$ be a point on the side $BC$, lying strictly between $B$ and $C$. The points $M$ and $N$ are the feet of the altitudes from $B$ and $C$, respectively. Denote by $\omega_1$ is the circumcircle of $BWN$, and let $X$ be the point on $\omega_1$ such that $WX$ is a diameter of $\omega_1$. Analogously, denote by $\omega_2$ the circumcircle of triangle $CWM$, and let $Y$ be the point such that $WY$ is a diameter of $\omega_2$. Prove that $X,Y$ and $H$ are collinear.

Proposed by Warut Suksompong and Potcharapol Suteparuk, Thailand

[b]My solution[/b]
2 replies
liberator
Aug 13, 2014
liberator
Aug 19, 2014
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mqoi_KOLA   0
Mar 30, 2025
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mqoi_KOLA
Mar 30, 2025
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