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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jun 2, 2025
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
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[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this 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 a transformative 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)!

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[list][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
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0 replies
jlacosta
Jun 2, 2025
0 replies
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Aloo and Batata play game on N-gon
guptaamitu1   0
a few seconds ago
Source: LMAO revenge 2025 P6
Aloo and Batata are playing a game. They are given a regular $n$-gon, where $n > 2$ is an even integer. At the start, a line joining two vertices is chosen arbitrarily and one of its endpoints is chosen as its pivot. Now, Aloo rotates the line around the pivot either clockwise or anti-clockwise until it passes through another vertex of the $n$-gon. Then, the new vertex becomes the pivot and Batata again chooses to rotate the line clockwise or anti-clockwise
about the pivot. The player who moves the line into a position it has already been in (i.e. it passes through the same two vertices of the $n$-gon it was in at a previous time) loses.
Find all $n$ such that Batata always has a winning strategy irrespective of the starting edge.

Proposed by Anik Sardar, Om Patil and Anudip Giri
0 replies
guptaamitu1
a few seconds ago
0 replies
J
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Trig Inequality back in Olympiads!
guptaamitu1   0
6 minutes ago
Source: LMAO revenge 2025 P5
Let $x,y,z \in \mathbb R$ be such that $x + y + z = \frac{\pi}{2}$ and $0 < x,y,z \le \frac{\pi}{4}$. Prove that:
$$ \left( \frac{\sin x - \sin y}{\cos z} \right)^2 \le 1 - 8 \sin x \sin y \sin z $$
Proposed by Shreyas Deshpande
0 replies
guptaamitu1
6 minutes ago
0 replies
J
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Reflection of (BHC) in AH
guptaamitu1   0
13 minutes ago
Source: LMAO revenge 2025 P4
Let $ABC$ be a triangle with orthocentre $H$. Let $D,E,F$ be the foot of altitudes of $A,B,C$ onto the opposite sides, respectively. Consider $\omega$, the reflection of $\odot(BHC)$ about line $AH$. Let line $EF$ cut $\omega$ at distinct points $X,Y$, and let $H'$ be the orthocenter of $\triangle AYD$. Prove that points $A,H',X,D$ are concyclic.

Proposed by Mandar Kasulkar
0 replies
guptaamitu1
13 minutes ago
0 replies
J
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King's Constrained Walk
Hellowings   2
N 17 minutes ago by Hellowings
Source: Own
Given an n x n chessboard, with a king starting at any square, the king's task is to visit each square in the board exactly once (essentially an open path); this king moves how a king in chess would.
However, we are allowed to place k numbers on the board of any value such that for each number A we placed on the board, the king must be in the position of that number A on its Ath square in its journey, with the starting square as its 1st square.
Suppose after we placed k numbers, there is one and only one way to complete the king's task (this includes placing the king in a starting square), find the minimum value of k set by n.

Should've put one of its tag as "Open problem"; I have no idea how to tackle this problem either.
2 replies
1 viewing
Hellowings
May 30, 2025
Hellowings
17 minutes ago
J
No more topics!
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Geometry
VicKmath7   3
N Mar 28, 2020 by sunken rock
Source: 12th Russian MO "Leonhard Euler", final round
Given is a triangle ABC with 2<B=180°+<A. Point K is in the interior of the triangle, so that <ACK=2<BCK and L is on AB, so that BK=KL. Prove that CK+AL=AC
3 replies
VicKmath7
Mar 25, 2020
sunken rock
Mar 28, 2020
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Geometry
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Reveal topic tags
geometry
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G H BBookmark kLocked kLocked NReply
Source: 12th Russian MO "Leonhard Euler", final round
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VicKmath7
1391 posts
VicKmath7
#1 h  Mar 25, 2020, 7:44 PM
Y by
Given is a triangle ABC with 2<B=180°+<A. Point K is in the interior of the triangle, so that <ACK=2<BCK and L is on AB, so that BK=KL. Prove that CK+AL=AC
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parmenides51
30653 posts
parmenides51
#2 h  Mar 25, 2020, 8:34 PM
Y by
please lock this contest, the contest happens these days, it hasn't ended yet
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parmenides51
30653 posts
parmenides51
#3 h  Mar 28, 2020, 3:34 PM
Y by
contest has ended
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sunken rock
4402 posts
sunken rock
#4 h  Mar 28, 2020, 8:45 PM
Y by
My solution is quite different, although fully synthetic as well.
Pls, see it attached.

Best regards,
sunken rock
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