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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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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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[*]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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Easy Diff NT
xToiletG   0
a minute ago
Prove that for every $n \geq 2$ there exists positive integers $x, y, z$ such that
$$\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$$
0 replies
xToiletG
a minute ago
0 replies
J
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Might be slightly generalizable
Rijul saini   5
N 20 minutes ago by guptaamitu1
Source: India IMOTC Day 3 Problem 1
Let $ABC$ be an acute angled triangle with orthocenter $H$ and $AB<AC$. Let $T(\ne B,C, H)$ be any other point on the arc $\stackrel{\LARGE\frown}{BHC}$ of the circumcircle of $BHC$ and let line $BT$ intersect line $AC$ at $E(\ne A)$ and let line $CT$ intersect line $AB$ at $F(\ne A)$. Let the circumcircles of $AEF$ and $ABC$ intersect again at $X$ ($\ne A$). Let the lines $XE,XF,XT$ intersect the circumcircle of $(ABC)$ again at $P,Q,R$ ($\ne X$). Prove that the lines $AR,BC,PQ$ concur.
5 replies
+1 w
Rijul saini
Yesterday at 6:39 PM
guptaamitu1
20 minutes ago
J
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A function on a 2D grid
Rijul saini   1
N 36 minutes ago by guptaamitu1
Source: India IMOTC 2025 Day 4 Problem 2
Does there exist a function $f:\{1,2,...,2025\}^2 \rightarrow \{1,2,...,2025\}$ such that:

$\bullet$ for any positive integer $i \leqslant 2025$, the numbers $f(i,1),f(i,2),...,f(i,2025)$ are all distinct, and
$\bullet$ for any positive integers $i \leqslant 2025$ and $j \leqslant 2024$, $f(f(i,j),f(i,j+1))=i$?

Proposed by Shantanu Nene
1 reply
Rijul saini
Yesterday at 6:46 PM
guptaamitu1
36 minutes ago
J
H
Cute geometry
Rijul saini   5
N 38 minutes ago by everythingpi3141592
Source: India IMOTC Practice Test 1 Problem 3
Let scalene $\triangle ABC$ have altitudes $BE, CF,$ circumcenter $O$ and orthocenter $H$. Let $R$ be a point on line $AO$. The points $P,Q$ are on lines $AB,AC$ respectively such that $RE \perp EP$ and $RF \perp FQ$. Prove that $PQ$ is perpendicular to $RH$.

Proposed by Rijul Saini
5 replies
Rijul saini
Yesterday at 6:51 PM
everythingpi3141592
38 minutes ago
J
No more topics!
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Odd edged regular polygon can't be partitioned into 4 pieces
Goutham   0
Oct 4, 2010
Prove that a regular polygon with an odd number of edges cannot be partitioned into four pieces with equal areas by two lines that pass through the center of polygon.
0 replies
Goutham
Oct 4, 2010
0 replies
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Odd edged regular polygon can't be partitioned into 4 pieces
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Goutham
3130 posts
Goutham
#1 h  Oct 4, 2010, 2:54 PM • 1 Y
Y by Adventure10
Prove that a regular polygon with an odd number of edges cannot be partitioned into four pieces with equal areas by two lines that pass through the center of polygon.
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