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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.

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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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[*]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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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
J
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
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In a school of $800$ students, $224$ students play cricket, $240$ students play
Vulch   1
N 20 minutes ago by RollingPanda4616
Hello everyone,
In a school of $800$ students, $224$ students play cricket, $240$ students play hockey and $336$ students play basketball. $64$ students play both basketball and hockey, $80$ students play both cricket and basketball, $40$ students play both cricket and hockey, and $24$ students play all three: basketball, hockey, and cricket. Find the number of students who do not play any game.

Edit:
In the above problem,I just want to know that why the number of students who don't play any game shouldn't be 0, because,if we add 224,240 and 336 it comes out to be 800.I have solution,but I just want to know how to explain it without theoretically.Thank you!
1 reply
Vulch
an hour ago
RollingPanda4616
20 minutes ago
J
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100th post
MathJedi108   1
N an hour ago by mdk2013
Well I guess this is my 100th post, it would be really funny if it isn't can yall share your favorite experience on AoPS here?
1 reply
MathJedi108
2 hours ago
mdk2013
an hour ago
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VOLUNTEERING OPPORTUNITIES OPEN TO HIGH/MIDDLE SCHOOLERS
im_space_cadet   12
N 2 hours ago by SmartGroot
Hi everyone!
Do you specialize in contest math? Do you have a passion for teaching? Do you want to help leverage those college apps? Well, I have something for all of you.

I am im_space_cadet, and during the fall of last year, I opened my non-profit DeltaMathPrep which teaches students preparing for contest math the problem-solving skills they need in order to succeed at these competitions. Currently, we are very much understaffed and would greatly appreciate the help of more tutors on our platform.

Each week on Saturday and Wednesday, we meet once for each competition: Wednesday for AMC 8 and Saturday for AMC 10 and we go over a past year paper for the entire class. On both of these days, we meet at 9PM EST in the night.

This is a great opportunity for anyone who is looking to have a solid activity to add to their college resumes that requires low effort from tutors and is very flexible with regards to time.

This is the link to our non-profit for anyone who would like to view our initiative:
https://www.deltamathprep.org/

If you are interested in this opportunity, please send me a DM on AoPS or respond to this post expressing your interest. I look forward to having you all on the team!

Thanks,
im_space_cadet
12 replies
im_space_cadet
Yesterday at 2:27 PM
SmartGroot
2 hours ago
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Find all triples
pedronis   2
N 2 hours ago by Kempu33334
Find all triples of positive integers $(n, r, s)$ such that $n^2 + n + 1$ divides $n^r + n^s + 1$.
2 replies
pedronis
Apr 19, 2025
Kempu33334
2 hours ago
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D860 : Flower domino and unconnected
Dattier   4
N 2 hours ago by Haris1
Source: les dattes à Dattier
Let G be a grid of size m*n.

We have 2 dominoes in flowers and not connected like here
IMAGE
Determine a necessary and sufficient condition on m and n, so that G can be covered with these 2 kinds of dominoes.

4 replies
Dattier
May 26, 2024
Haris1
2 hours ago
J
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Equal Distances in an Isosceles Setting
mojyla222   3
N 3 hours ago by sami1618
Source: IDMC 2025 P4
Let $ABC$ be an isosceles triangle with $AB=AC$. The circle $\omega_1$, passing through $B$ and $C$, intersects segment $AB$ at $K\neq B$. The circle $\omega_2$ is tangent to $BC$ at $B$ and passes through $K$. Let $M$ and $N$ be the midpoints of segments $AB$ and $AC$, respectively. The line $MN$ intersects $\omega_1$ and $\omega_2$ at points $P$ and $Q$, respectively, where $P$ and $Q$ are the intersections closer to $M$. Prove that $MP=MQ$.

Proposed by Hooman Fattahi
3 replies
mojyla222
Yesterday at 5:05 AM
sami1618
3 hours ago
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standard Q FE
jasperE3   1
N 3 hours ago by ErTeeEs06
Source: gghx, p19004309
Find all functions $f:\mathbb Q\to\mathbb Q$ such that for any $x,y\in\mathbb Q$:
$$f(xf(x)+f(x+2y))=f(x)^2+f(y)+y.$$
1 reply
jasperE3
Yesterday at 6:27 PM
ErTeeEs06
3 hours ago
J
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Dear Sqing: So Many Inequalities...
hashtagmath   33
N 3 hours ago by GeoMorocco
I have noticed thousands upon thousands of inequalities that you have posted to HSO and was wondering where you get the inspiration, imagination, and even the validation that such inequalities are true? Also, what do you find particularly appealing and important about specifically inequalities rather than other branches of mathematics? Thank you :)
33 replies
hashtagmath
Oct 30, 2024
GeoMorocco
3 hours ago
J
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3 knightlike moves is enough
sarjinius   1
N 3 hours ago by markam
Source: Philippine Mathematical Olympiad 2025 P6
An ant is on the Cartesian plane. In a single move, the ant selects a positive integer $k$, then either travels [list]
[*] $k$ units vertically (up or down) and $2k$ units horizontally (left or right); or
[*] $k$ units horizontally (left or right) and $2k$ units vertically (up or down).
[/list]
Thus, for any $k$, the ant can choose to go to one of eight possible points.
Prove that, for any integers $a$ and $b$, the ant can travel from $(0, 0)$ to $(a, b)$ using at most $3$ moves.
1 reply
sarjinius
Mar 9, 2025
markam
3 hours ago
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Weird Geo
Anto0110   0
3 hours ago
In a trapezium $ABCD$, the sides $AB$ and $CD$ are parallel and the angles $\angle ABC$ and $\angle BAD$ are acute. Show that it is possible to divide the triangle $ABC$ into 4 disjoint triangle $X_1. . . , X_4$ and the triangle $ABD$ into 4 disjoint triangles $Y_1,. . . , Y_4$ such that the triangles $X_i$ and $Y_i$ are congruent for all $i$.
0 replies
Anto0110
3 hours ago
0 replies
J
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Is the geometric function injective?
Project_Donkey_into_M4   1
N 3 hours ago by Funcshun840
Source: Mock RMO TDP and Kayak 2018, P3
A non-degenerate triangle $\Delta ABC$ is given in the plane, let $S$ be the set of points which lie strictly inside it. Also let $\mathfrak{C}$ be the set of circles in the plane. For a point $P \in S$, let $A_P, B_P, C_P$ be the reflection of $P$ in sides $\overline{BC}, \overline{CA}, \overline{AB}$ respectively. Define a function $\omega: S \rightarrow \mathfrak{C}$ such that $\omega(P)$ is the circumcircle of $A_PB_PC_P$. Is $\omega$ injective?

Note: The function $\omega$ is called injective if for any $P, Q \in S$, $\omega(P) = \omega(Q) \Leftrightarrow P = Q$
1 reply
Project_Donkey_into_M4
Yesterday at 6:23 PM
Funcshun840
3 hours ago
J
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numbers at vertices of triangle / tetrahedron, consecutive and gcd related
parmenides51   1
N 4 hours ago by TheBaiano
Source: 2022 May Olympiad L2 p4
a) A positive integer is written at each vertex of a triangle. Then on each side of the triangle the greatest common divisor of its ends is written. It is possible that the numbers written on the sides be three consecutive integers, in some order?
b) A positive integer is written at each vertex of a tetrahedron. Then, on each edge of the tetrahedron is written the greatest common divisor of its ends . It is possible that the numbers written in the edges are six consecutive integers, in some order?
1 reply
parmenides51
Sep 4, 2022
TheBaiano
4 hours ago
J
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red squares in a 7x7 board
parmenides51   2
N 4 hours ago by TheBaiano
Source: 2022 May Olympiad L2 p1
In a $7\times7$ board, some squares are painted red. Let $a$ be the number of rows that have an odd number of red squares and let $b$ be the number of columns that have an odd number of red squares. Find all possible values of $a+b$. For each value found, give a example of how the board can be painted.
2 replies
parmenides51
Sep 4, 2022
TheBaiano
4 hours ago
J
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winning strategy, vertices of regular n-gon
parmenides51   1
N 4 hours ago by TheBaiano
Source: 2022 May Olympiad L2 p5
The vertices of a regular polygon with $N$ sides are marked on the blackboard. Ana and Beto play alternately, Ana begins. Each player, in turn, must do the following:
$\bullet$ join two vertices with a segment, without cutting another already marked segment; or
$\bullet$ delete a vertex that does not belong to any marked segment.
The player who cannot take any action on his turn loses the game. Determine which of the two players can guarantee victory:
a) if $N=28$
b) if $N=29$
1 reply
parmenides51
Sep 4, 2022
TheBaiano
4 hours ago
J
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J
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What is an isogonal conjugate and why is it useful?
EaZ_Shadow   6
N Apr 5, 2025 by maxamc
What is an isogonal conjugate and why is it useful? People use them in Olympiad geometry proofs but I don’t understand why and what is the purpose, as it complicates me because of me not understanding it.
6 replies
EaZ_Shadow
Dec 28, 2024
maxamc
Apr 5, 2025
J
What is an isogonal conjugate and why is it useful?
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Reveal topic tags
geometry
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EaZ_Shadow
1228 posts
EaZ_Shadow
#1 h  Dec 28, 2024, 6:08 PM • 4 Y
Y by 1217662, 1218865, 1220118, Ad112358
What is an isogonal conjugate and why is it useful? People use them in Olympiad geometry proofs but I don’t understand why and what is the purpose, as it complicates me because of me not understanding it.
Z K Y
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EaZ_Shadow
1228 posts
EaZ_Shadow
#2 h  Dec 29, 2024, 7:21 PM • 4 Y
Y by 1217662, 1218865, 1220118, Ad112358
/bump help please
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vanstraelen
8976 posts
vanstraelen
#3 h  Dec 29, 2024, 7:31 PM
Y by
https://en.wikipedia.org/wiki/Isogonal_conjugate
Z K Y
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EaZ_Shadow
1228 posts
EaZ_Shadow
#4 h  Dec 29, 2024, 7:41 PM • 4 Y
Y by 1217662, 1218865, 1220118, Ad112358
vanstraelen wrote:
https://en.wikipedia.org/wiki/Isogonal_conjugate

I don’t understand it though, can you explain it more simply
Z K Y
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greenturtle3141
3546 posts
greenturtle3141
#5 h  Dec 29, 2024, 9:00 PM
Y by
Can you provide an example of the appearance of the isogonal conjugate in Olympiad geometry? This can help explain why it was needed for that particular problem.
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EaZ_Shadow
1228 posts
EaZ_Shadow
#6 h  Dec 29, 2024, 9:47 PM • 4 Y
Y by 1217662, 1218865, 1220118, Ad112358
greenturtle3141 wrote:
Can you provide an example of the appearance of the isogonal conjugate in Olympiad geometry? This can help explain why it was needed for that particular problem.

Like in general
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maxamc
549 posts
maxamc
#7 h  Apr 5, 2025, 2:40 PM
Y by
it mean you have a point p. draw line from ap bp and cp. reflec the line about angle bisector for 3 new liine that intersec at p'. p abd p' are isogonal conjucates. for example orthoscenter and circumsceter are isogbal conjuacates.
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