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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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)!

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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random fe
ChildFlower   1
N 4 minutes ago by jasperE3
Find all functions $f:\mathbb R\to\mathbb R$ such that
$$f(x-f(y))=f(f(y))+xf(y)+f(x)-1 \; \forall x,y \in \mathbb R$$
1 reply
ChildFlower
11 minutes ago
jasperE3
4 minutes ago
J
H
all functions satisfying f(x+yf(x))+y = xy + f(x+y)
falantrng   20
N 4 minutes ago by GreekIdiot
Source: Balkan MO 2025 P3
Find all functions $f\colon \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x,y \in \mathbb{R}$,
\[f(x+yf(x))+y = xy + f(x+y).\]
Proposed by Giannis Galamatis, Greece
20 replies
+3 w
falantrng
4 hours ago
GreekIdiot
4 minutes ago
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BMO 2024 SL C1
GreekIdiot   6
N 9 minutes ago by lksb
Let $n$, $k$ be positive integers. Julia and Florian play a game on a $2n \times 2n$ board. Julia
has secretly tiled the entire board with invisible dominos. Florian now chooses $k$ cells.
All dominos covering at least one of these cells then turn visible. Determine the minimal
value of $k$ such that Florian has a strategy to always deduce the entire tiling.
6 replies
GreekIdiot
3 hours ago
lksb
9 minutes ago
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Arbitrary point on BC and its relation with orthocenter
falantrng   11
N 15 minutes ago by bin_sherlo
Source: Balkan MO 2025 P2
In an acute-angled triangle \(ABC\), \(H\) be the orthocenter of it and \(D\) be any point on the side \(BC\). The points \(E, F\) are on the segments \(AB, AC\), respectively, such that the points \(A, B, D, F\) and \(A, C, D, E\) are cyclic. The segments \(BF\) and \(CE\) intersect at \(P.\) \(L\) is a point on \(HA\) such that \(LC\) is tangent to the circumcircle of triangle \(PBC\) at \(C.\) \(BH\) and \(CP\) intersect at \(X\). Prove that the points \(D, X, \) and \(L\) lie on the same line.
11 replies
+1 w
falantrng
4 hours ago
bin_sherlo
15 minutes ago
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No more topics!
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diagonals equal to sides in a quadrangle, convex or not
parmenides51   0
Jul 2, 2020
Source: All-Siberian Open School Olympiad 2013-14 10.2
Is it possible to find such convex and non-convex quadrangles in the plane, the lengths of the sides of which in some order and the lengths of the diagonals of which in some order coincide?
0 replies
parmenides51
Jul 2, 2020
0 replies
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diagonals equal to sides in a quadrangle, convex or not
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Reveal topic tags
convex
geometry
convex quadrilateral
diagonals
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Source: All-Siberian Open School Olympiad 2013-14 10.2
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parmenides51
30649 posts
parmenides51
#1 h  Jul 2, 2020, 5:47 PM • 1 Y
Y by Mango247
Is it possible to find such convex and non-convex quadrangles in the plane, the lengths of the sides of which in some order and the lengths of the diagonals of which in some order coincide?
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