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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next 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 an enriching 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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[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 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
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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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Overly wordy problems
ZMB038   11
N 24 minutes ago by Yiyj
Hey everyone, here we can post questions with way to many extraneous words, that are actually easy.
Try to solve the one above yours.
I'll start:
Click to reveal hidden text
11 replies
ZMB038
May 28, 2025
Yiyj
24 minutes ago
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Worst Sillies of All Time
pingpongmerrily   40
N an hour ago by Yiyj
Share the worst sillies you have ever made!

Mine was probably on the 2024 MathCounts State Target Round Problem 8, where I wrote my answer as a fraction instead of a percent, which cost me a trip to Nationals that year.
40 replies
pingpongmerrily
Yesterday at 12:34 PM
Yiyj
an hour ago
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Number Theory
fasttrust_12-mn   14
N an hour ago by Namisgood
Source: Pan African Mathematics Olympiad P1
Find all positive intgers $a,b$ and $c$ such that $\frac{a+b}{a+c}=\frac{b+c}{b+a}$ and $ab+bc+ca$ is a prime number
14 replies
fasttrust_12-mn
Aug 15, 2024
Namisgood
an hour ago
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find question
mathematical-forest   5
N 2 hours ago by Jupiterballs
Are there any contest questions that seem simple but are actually difficult? :-D
5 replies
1 viewing
mathematical-forest
Thursday at 10:19 AM
Jupiterballs
2 hours ago
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Own made functional equation
Primeniyazidayi   10
N 2 hours ago by Phat_23000245
Source: own(probably)
Find all functions $f:R \rightarrow R$ such that $xf(x^2+2f(y)-yf(x))=f(x)^3-f(y)(f(x^2)-2f(x))$ for all $x,y \in \mathbb{R}$
10 replies
Primeniyazidayi
May 26, 2025
Phat_23000245
2 hours ago
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Tough inequality
TUAN2k8   4
N 2 hours ago by Phat_23000245
Source: Own
Let $n \ge 2$ be an even integer and let $x_1,x_2,...,x_n$ be real numbers satisfying $x_1^2+x_2^2+...+x_n^2=n$.
Prove that
$\sum_{1 \le i < j \le n} \frac{x_ix_j}{x_i^2+x_j^2+1} \ge \frac{-n}{6}$
4 replies
TUAN2k8
May 28, 2025
Phat_23000245
2 hours ago
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MathDash help
Spacepandamath13   6
N 2 hours ago by elizhang101412
AkshajK ORZ by the way invited me to do MathDash a few months ago and I did try it one day but haven't done it much after (Sorry). Now, I'm getting back into it and finding the format kind of weird. When selecting certain problem type sometimes it lets me pick immediately, other times not. Any fixes?
6 replies
Spacepandamath13
Thursday at 9:32 PM
elizhang101412
2 hours ago
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Combi counting
Caasi_Gnow   2
N 3 hours ago by Justbrick
Find the number of different ways to arrange seven people around a circular meeting table if A and B must sit together and C and D cannot sit next to each other. (Note: the order for A and B might be A,B or B,A)
2 replies
Caasi_Gnow
Mar 20, 2025
Justbrick
3 hours ago
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Guess period of function
a1267ab   9
N 3 hours ago by HamstPan38825
Source: USA TST 2025
Let $n$ be a positive integer. Ana and Banana play a game. Banana thinks of a function $f\colon\mathbb{Z}\to\mathbb{Z}$ and a prime number $p$. He tells Ana that $f$ is nonconstant, $p<100$, and $f(x+p)=f(x)$ for all integers $x$. Ana's goal is to determine the value of $p$. She writes down $n$ integers $x_1,\dots,x_n$. After seeing this list, Banana writes down $f(x_1),\dots,f(x_n)$ in order. Ana wins if she can determine the value of $p$ from this information. Find the smallest value of $n$ for which Ana has a winning strategy.

Anthony Wang
9 replies
a1267ab
Dec 14, 2024
HamstPan38825
3 hours ago
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Inequality with abc=1
tenplusten   11
N 3 hours ago by sqing
Source: JBMO 2011 Shortlist A7
$\boxed{\text{A7}}$ Let $a,b,c$ be positive reals such that $abc=1$.Prove the inequality $\sum\frac{2a^2+\frac{1}{a}}{b+\frac{1}{a}+1}\geq 3$
11 replies
tenplusten
May 15, 2016
sqing
3 hours ago
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Central sequences
EeEeRUT   13
N 3 hours ago by v_Enhance
Source: EGMO 2025 P2
An infinite increasing sequence $a_1 < a_2 < a_3 < \cdots$ of positive integers is called central if for every positive integer $n$ , the arithmetic mean of the first $a_n$ terms of the sequence is equal to $a_n$.

Show that there exists an infinite sequence $b_1, b_2, b_3, \dots$ of positive integers such that for every central sequence $a_1, a_2, a_3, \dots, $ there are infinitely many positive integers $n$ with $a_n = b_n$.
13 replies
EeEeRUT
Apr 16, 2025
v_Enhance
3 hours ago
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Interesting inequality
sqing   0
3 hours ago
Source: Own
Let $ a,b,c\geq 0 , a^2+b^2+c^2 =3.$ Prove that
$$ a^4+ b^4+c^4+6abc\leq9$$$$ a^3+ b^3+ c^3+3( \sqrt{3}-1)abc\leq 3\sqrt 3$$
0 replies
sqing
3 hours ago
0 replies
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IMO Shortlist 2014 C7
hajimbrak   19
N 4 hours ago by quantam13
Let $M$ be a set of $n \ge 4$ points in the plane, no three of which are collinear. Initially these points are connected with $n$ segments so that each point in $M$ is the endpoint of exactly two segments. Then, at each step, one may choose two segments $AB$ and $CD$ sharing a common interior point and replace them by the segments $AC$ and $BD$ if none of them is present at this moment. Prove that it is impossible to perform $n^3 /4$ or more such moves.

Proposed by Vladislav Volkov, Russia
19 replies
hajimbrak
Jul 11, 2015
quantam13
4 hours ago
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<BAC = 2 <ABC wanted, AC + AI = BC given , incenter I
parmenides51   3
N 4 hours ago by LeYohan
Source: 2020 Dutch IMO TST 1.1
In acute-angled triangle $ABC, I$ is the center of the inscribed circle and holds $| AC | + | AI | = | BC |$. Prove that $\angle BAC = 2 \angle ABC$.
3 replies
parmenides51
Nov 21, 2020
LeYohan
4 hours ago
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Rgb ratios
mnopstuv5000   1
N Feb 13, 2025 by user538
What are the ratios 2 : 7 and 1 : 2 for Cascading Style Sheet RGB " 256 exponent 3 " ?
1 reply
mnopstuv5000
Mar 19, 2021
user538
Feb 13, 2025
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Rgb ratios
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Reveal topic tags
math
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mnopstuv5000
288 posts
mnopstuv5000
#1 h  Mar 19, 2021, 10:48 PM • 4 Y
Y by Mango247, Mango247, Mango247, PikaPika999
What are the ratios 2 : 7 and 1 : 2 for Cascading Style Sheet RGB " 256 exponent 3 " ?
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user538
2 posts
user538
#3 h  Feb 13, 2025, 2:26 PM • 1 Y
Y by PikaPika999
Total Parts Calculation:
For 2:7: Total parts = 2 + 7 = 9
For 1:2: Total parts = 1 + 2 = 3
Finding the RGB Values:
For 2:7:
Total value = 16,777,216
Value for first part (R) = (2/9) * 16,777,216 ≈ 3,728,086
Value for second part (G) = (7/9) * 16,777,216 ≈ 13,049,130
The blue (B) can be set to 0 for simplicity, giving us RGB (3,728,086, 13,049,130, 0). However, this exceeds 255 for typical RGB values, so we should scale down.
For 1:2:
Total value = 16,777,216
Value for first part (R) = (1/3) * 16,777,216 ≈ 5,592,405
Value for second part (G) = (2/3) * 16,777,216 ≈ 11,184,811
Again, blue can be set to 0, giving us RGB (5,592,405, 11,184,811, 0), which also exceeds 255.
Scaling Down to Standard RGB:
To convert these values to standard RGB (0-255), divide each component by 256:
For 2:7:
R: 3,728,086 / 256 ≈ 14.57 ≈ 15
G: 13,049,130 / 256 ≈ 51.00 ≈ 51
B: 0
Resulting RGB: (15, 51, 0)
For 1:2:
R: 5,592,405 / 256 ≈ 21.88 ≈ 22
G: 11,184,811 / 256 ≈ 43.65 ≈ 44
B: 0
Resulting RGB: (22, 44, 0)

Therefore,
For the ratio 2:7, the RGB values are approximately (15, 51, 0).
For the ratio 1:2, the RGB values are approximately (22, 44, 0).
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