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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Wednesday at 3:18 PM
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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Be sure to mark your calendars for the following events:
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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
Wednesday at 3:18 PM
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
J
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amc10 chances?
aoh11   3
N 15 minutes ago by jb2015007
if i got a 55.5 on amc10, what are my chances of making aime???
3 replies
aoh11
43 minutes ago
jb2015007
15 minutes ago
J
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FTW tournament!
evt917   55
N 21 minutes ago by jkim0656
[center]Since all FTW tournaments have dramatically failed, I'm trying a different format. Here is how it works:

1. Type \signup{your rating (type 800 for unrated)}

2. You will pick who you want to play with. You can play if they accept your challenge. So basically the players run everything. Just don't intentionally play low-rated people. Also try to play different people so everyone gets a chance to play!

3. If you win, you get 2 points. However, if you win games in a row, you get more points per win. When you win $n$ games in a row, you score $n+1$ points instead of $2$ points, until you hit getting $ > 8$ points per win, where you just get 8 points per win consistently. A tie equals $1$ point, and a loss is zero. A tie or a loss will break your win streak.

4. I do not know everybody's time preferences. Because so, I will announce in advance which two players will be playing, so they themselves can organize a game themselves. Remember, THE PLAYERS ARE ORGANIZING THE GAMES THEMSELVES!!! The format is up to them, but please make the time control at least 20 seconds. Please announce the results of the game here so i can update the scoreboard. Games can be unrated.

recommended format if you cannot decide



5. The tournament goes on until april 22nd! Extremely long, right? Note that you can still signup after the first games has started, but you will have a disadvantage because some people who signed up as soon as the tournament started already has points.

6. Once you are done with your game, you can find a new opponent and play with them if they want. Have fun!


[rule]

Questions and Answers

All signups and ratings

[rule]

LIVE LEADERBOARD:

1st place: 8 points | streak 1 | 3W 1L 1T |Yrock
2rd place: 3 points | streak 1 | 1W 3L 1T | sadas123
3nd place: 2 points | streak 1 | 1W 0L 0T | jb2015007

4th place: 0 points | streak 0 | 0W 1L 0T | IcyFire500
5th place:
55 replies
evt917
Yesterday at 9:34 PM
jkim0656
21 minutes ago
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skibidi dop
DhruvJha   21
N 29 minutes ago by jkim0656
Kai is singing the skibidi dop dop dop yes yes yes song 28 times in the span of a fortnite(two weeks). How many times using this rate does kai sing skibidi skibidi dop dop yes yes yes song in a span of 4 days using the rate. Express your answer in terms of sigma.
21 replies
DhruvJha
4 hours ago
jkim0656
29 minutes ago
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2⁠0⁠⁠2⁠4
Technodoggo   79
N 30 minutes ago by jkim0656
Happy New Year!
To celebrate the start of 2024, I've decided to put up a few facts about the year. I don't have many, so y'all should also

1

2

(1 and 2 are the same :sob: just distribute)

Post more cool facts here! Keep a running chain with quote boxes for facts. (I don't know if this technically qualifies as a marathon, but I hope this is allowed lol)
79 replies
Technodoggo
Jan 1, 2024
jkim0656
30 minutes ago
J
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Geometry problem-second time posting
kjhgyuio   0
an hour ago
Source: smo roudn 2

A square is cut into several rectangles, none of which is a square ,so that the sides of each rectangles are parallel to the sides of a square .For each rectangle with sides a,b,a<b compute the ratio a/b Prove that the sum of these ratios is at least 1
0 replies
kjhgyuio
an hour ago
0 replies
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Proving ZA=ZB
nAalniaOMliO   5
N an hour ago by EmersonSoriano
Source: Belarusian National Olympiad 2025
Point $H$ is the foot of the altitude from $A$ of triangle $ABC$. On the lines $AB$ and $AC$ points $X$ and $Y$ are marked such that the circumcircles of triangles $BXH$ and $CYH$ are tangent, call this circles $w_B$ and $w_C$ respectively. Tangent lines to circles $w_B$ and $w_C$ at $X$ and $Y$ intersect at $Z$.
Prove that $ZA=ZH$.
Vadzim Kamianetski
5 replies
nAalniaOMliO
Mar 28, 2025
EmersonSoriano
an hour ago
J
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Inequality from China
sqing   3
N an hour ago by sqing
Source: lemondian(https://kuing.cjhb.site/thread-13667-1-1.html)
Let $x\in (0,\frac{\pi}{2}) . $ Prove that $$tanx\ge x^k$$Where $ k=1,2,3,4.$
3 replies
sqing
Yesterday at 1:11 PM
sqing
an hour ago
J
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NMO (Nepal) Problem 4
khan.academy   8
N 2 hours ago by godchunguus
Find all integer/s $n$ such that $\displaystyle{\frac{5^n-1}{3}}$ is a prime or a perfect square of an integer.

Proposed by Prajit Adhikari, Nepal
8 replies
khan.academy
Mar 17, 2024
godchunguus
2 hours ago
J
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2019 Nepal National Mathematics Olympiad
Piinfinity   3
N 2 hours ago by godchunguus
Problem 31
Let $f:\mathbb{R}\to\mathbb{R}$ be a function such that
$f(f(x))=x^2-x+1$
for all real numbers $x$. Determine $f(0)$.
3 replies
Piinfinity
Oct 13, 2020
godchunguus
2 hours ago
J
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pretty well known
dotscom26   2
N 3 hours ago by Giant_PT
Let $\triangle ABC$ be a scalene triangle such that $\Omega$ is its incircle. $AB$ is tangent to $\Omega$ at $D$. A point $E$ ($E \notin \Omega$) is located on $BC$.

Let $\omega_1$, $\omega_2$, and $\omega_3$ be the incircles of the triangles $BED$, $ADE$, and $AEC$, respectively.

Show that the common tangent to $\omega_1$ and $\omega_3$ is also tangent to $\omega_2$.

2 replies
dotscom26
Yesterday at 2:03 AM
Giant_PT
3 hours ago
J
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Unsolved NT, 3rd time posting
GreekIdiot   10
N 3 hours ago by mathprodigy2011
Source: own
Solve $5^x-2^y=z^3$ where $x,y,z \in \mathbb Z$
Hint
10 replies
GreekIdiot
Mar 26, 2025
mathprodigy2011
3 hours ago
J
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Wot n' Minimization
y-is-the-best-_   24
N 3 hours ago by maromex
Source: IMO SL 2019 A3
Let $n \geqslant 3$ be a positive integer and let $\left(a_{1}, a_{2}, \ldots, a_{n}\right)$ be a strictly increasing sequence of $n$ positive real numbers with sum equal to 2. Let $X$ be a subset of $\{1,2, \ldots, n\}$ such that the value of
\[ \left|1-\sum_{i \in X} a_{i}\right| \]is minimised. Prove that there exists a strictly increasing sequence of $n$ positive real numbers $\left(b_{1}, b_{2}, \ldots, b_{n}\right)$ with sum equal to 2 such that
\[ \sum_{i \in X} b_{i}=1. \]
24 replies
1 viewing
y-is-the-best-_
Sep 23, 2020
maromex
3 hours ago
J
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Functional equations
hanzo.ei   12
N 3 hours ago by truongphatt2668
Source: Greekldiot
Find all $f: \mathbb R_+ \rightarrow \mathbb R_+$ such that $f(xf(y)+f(x))=yf(x+yf(x)) \: \forall \: x,y \in \mathbb R_+$
12 replies
hanzo.ei
Mar 29, 2025
truongphatt2668
3 hours ago
J
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Kosovo Mathematical Olympiad 2016 TST , Problem 1
dangerousliri   2
N 3 hours ago by navier3072
Solve equation in real numbers

$\sqrt{x+\sqrt{4x+\sqrt{16x+\sqrt{…+\sqrt{4^nx+3}}}}}-\sqrt{x}=1$
2 replies
dangerousliri
Jan 9, 2017
navier3072
3 hours ago
J
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J
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k How to pronounce Rusczyk
Dream9   22
N Mar 31, 2025 by MathNinja9
I've always said like ruzz icks. I don't know why I say it as plural but does anyone know how to say the sigma's last name?
22 replies
Dream9
Mar 29, 2025
MathNinja9
Mar 31, 2025
J
How to pronounce Rusczyk
G H J
Reveal topic tags
Richard Rusczyk
L
G H BBookmark kLocked kLocked NReply
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Dream9
78 posts
Dream9
#1 h  Mar 29, 2025, 11:48 PM • 2 Y
Y by DhruvJha, RainbowJessa
I've always said like ruzz icks. I don't know why I say it as plural but does anyone know how to say the sigma's last name?
Z Y
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jkim0656
536 posts
jkim0656
#2 h  Mar 29, 2025, 11:49 PM • 1 Y
Y by RainbowJessa
i say ruzz ick without the plural
and have heard people say it like that too
Z Y
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KF329
297 posts
KF329
#3 h  Mar 30, 2025, 2:13 AM • 1 Y
Y by RainbowJessa
i just like don't say it but if i have to i also say it like ruzz ick
Z Y
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K1mchi_
6 posts
K1mchi_
#4 h  Mar 30, 2025, 11:30 PM • 1 Y
Y by RainbowJessa
Rush KUH zick
But tbh im not sure.
Is this post spam or smth?
Z Y
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DhruvJha
809 posts
DhruvJha
#5 h  Mar 30, 2025, 11:34 PM
Y by
roosk-zik
Z Y
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Yihangzh
605 posts
Yihangzh
#6 h  Mar 30, 2025, 11:42 PM • 2 Y
Y by peppermint_cat, Exponent11
rus-ick$ $
Z Y
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mdk2013
563 posts
mdk2013
#7 h  Mar 30, 2025, 11:54 PM • 1 Y
Y by Exponent11
I heard richard RUCH-ick somewhere, i also say rus-ick if people give me weird glances
Z Y
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SpeedCuber7
1767 posts
SpeedCuber7
#8 h  Mar 31, 2025, 12:00 AM • 3 Y
Y by mdk2013, sehgalsh, Exponent11
The official Wikipedia article gives the pronounciation as /ˈrʌsɪk/ or $\boxed{\text{ruh-ssik}}$ $\blacksquare$.
Z Y
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snake2020
4479 posts
snake2020
#9 h  Mar 31, 2025, 12:05 AM
Y by
QED.$ $
Z Y
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vincentwant
1282 posts
vincentwant
#10 h  Mar 31, 2025, 12:36 AM
Y by
in Polish it's similar to "ruschik" with rolled r and english long u and short i
This post has been edited 2 times. Last edited by vincentwant, Mar 31, 2025, 12:36 AM
Z Y
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DhruvJha
809 posts
DhruvJha
#11 h  Mar 31, 2025, 12:40 AM • 1 Y
Y by Exponent11
vincentwant wrote:
in Polish it's similar to "ruschik" with rolled r and english long u and short i

Yeah that seems right

However when referring to him, I just say Richard
This post has been edited 1 time. Last edited by DhruvJha, Mar 31, 2025, 12:43 AM
Reason: sw
Z Y
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mathenrichmentaops
534 posts
mathenrichmentaops
#12 h  Mar 31, 2025, 12:45 AM
Y by
roos-chik
Z Y
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avyaank
50 posts
avyaank
#13 h  Mar 31, 2025, 12:53 AM • 1 Y
Y by Exponent11
rus-zik


weee
Z Y
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km2
2 posts
km2
#14 h  Mar 31, 2025, 1:06 AM
Y by
czyk makes like a check or chick sound I think so maybe Rus-chick or Rus-check?
Z Y
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km2
2 posts
km2
#15 h  Mar 31, 2025, 1:07 AM
Y by
My friend's last name is Tomczyk and its Tom-chick
Z Y
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WiseHawkCuteFriendly
565 posts
WiseHawkCuteFriendly
#16 h  Mar 31, 2025, 1:39 AM
Y by
I say Russ Zyuck for some reason
Z Y
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KF329
297 posts
KF329
#17 h  Mar 31, 2025, 9:32 AM
Y by
eh...but anyway

farewell, Richard Rusczyk
Z Y
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K1mchi_
6 posts
K1mchi_
#18 h  Mar 31, 2025, 3:34 PM
Y by
I apologize, my previous post was a joke.

The cyk part is something like check or chick.
Z Y
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MathNinja9
2670 posts
MathNinja9
#19 h  Mar 31, 2025, 4:44 PM
Y by
I just say "RUSC-zick" :rotfl: :P
Z Y
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Yrock
1259 posts
Yrock
#20 h  Mar 31, 2025, 4:56 PM
Y by
rooh-zeek

with a long u
This post has been edited 1 time. Last edited by Yrock, Mar 31, 2025, 4:57 PM
Z Y
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MrMustache
2924 posts
MrMustache
#21 h  Mar 31, 2025, 5:07 PM
Y by
rooz check is the correct pronunciation I believe
Z Y
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Dream9
78 posts
Dream9
#22 h  Mar 31, 2025, 5:48 PM • 2 Y
Y by MathNinja9, Exponent11
At least there's Richard :)
Z Y
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MathNinja9
2670 posts
MathNinja9
#23 h  Mar 31, 2025, 5:49 PM
Y by
Dream9 wrote:
At least there's Richard :)

yessss so much easier :rotfl:
Z Y
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