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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.

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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
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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Brilliant guessing game on triples
Assassino9931   2
N 12 minutes ago by Mirjalol
Source: Al-Khwarizmi Junior International Olympiad 2025 P8
There are $100$ cards on a table, flipped face down. Madina knows that on each card a single number is written and that the numbers are different integers from $1$ to $100$. In a move, Madina is allowed to choose any $3$ cards, and she is told a number that is written on one of the chosen cards, but not which specific card it is on. After several moves, Madina must determine the written numbers on as many cards as possible. What is the maximum number of cards Madina can ensure to determine?

Shubin Yakov, Russia
2 replies
Assassino9931
Saturday at 9:46 AM
Mirjalol
12 minutes ago
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ISI UGB 2025 P5
SomeonecoolLovesMaths   4
N 37 minutes ago by Shiny_zubat
Source: ISI UGB 2025 P5
Let $a,b,c$ be nonzero real numbers such that $a+b+c \neq 0$. Assume that $$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{a+b+c}$$Show that for any odd integer $k$, $$\frac{1}{a^k} + \frac{1}{b^k} + \frac{1}{c^k} = \frac{1}{a^k+b^k+c^k}.$$
4 replies
SomeonecoolLovesMaths
Yesterday at 11:15 AM
Shiny_zubat
37 minutes ago
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ISI UGB 2025 P2
SomeonecoolLovesMaths   6
N 38 minutes ago by quasar_lord
Source: ISI UGB 2025 P2
If the interior angles of a triangle $ABC$ satisfy the equality, $$\sin ^2 A + \sin ^2 B + \sin^2 C = 2 \left( \cos ^2 A + \cos ^2 B + \cos ^2 C \right),$$prove that the triangle must have a right angle.
6 replies
SomeonecoolLovesMaths
Yesterday at 11:16 AM
quasar_lord
38 minutes ago
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ISI UGB 2025 P6
SomeonecoolLovesMaths   3
N 40 minutes ago by Shiny_zubat
Source: ISI UGB 2025 P6
Let $\mathbb{N}$ denote the set of natural numbers, and let $\left( a_i, b_i \right)$, $1 \leq i \leq 9$, be nine distinct tuples in $\mathbb{N} \times \mathbb{N}$. Show that there are three distinct elements in the set $\{ 2^{a_i} 3^{b_i} \colon 1 \leq i \leq 9 \}$ whose product is a perfect cube.
3 replies
SomeonecoolLovesMaths
Yesterday at 11:18 AM
Shiny_zubat
40 minutes ago
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Shortest number theory you might've seen in your life
AlperenINAN   5
N an hour ago by Royal_mhyasd
Source: Turkey JBMO TST 2025 P4
Let $p$ and $q$ be prime numbers. Prove that if $pq(p+1)(q+1)$ is a perfect square, then $pq + 1$ is also a perfect square.
5 replies
AlperenINAN
Yesterday at 7:51 PM
Royal_mhyasd
an hour ago
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9 Mathcounts Nats Winner Poll
DhruvJha   61
N an hour ago by isache
We've had these the past year, but not this one so lets create a poll.
61 replies
DhruvJha
Today at 12:19 AM
isache
an hour ago
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Favorite Memory at MATHCOUNTS
MathRook7817   19
N an hour ago by MathPerson12321
Hey guys, what is everyone's favorite memory at any Mathcounts competition?

Mine was arriving at the hotel for the 2024 nats comp.
19 replies
MathRook7817
Today at 12:31 AM
MathPerson12321
an hour ago
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d+2 pts in R^d can partition
EthanWYX2009   0
2 hours ago
Source: Radon's Theorem
Show that: any set of $d + 2$ points in $\mathbb R^d$ can be partitioned into two sets whose convex hulls intersect.
0 replies
EthanWYX2009
2 hours ago
0 replies
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hard inequality omg
tokitaohma   4
N 2 hours ago by arqady
1. Given $a, b, c > 0$ and $abc=1$
Prove that: $ \sqrt{a^2+1} + \sqrt{b^2+1} + \sqrt{c^2+1} \leq \sqrt{2}(a+b+c) $

2. Given $a, b, c > 0$ and $a+b+c=1 $
Prove that: $ \dfrac{\sqrt{a^2+2ab}}{\sqrt{b^2+2c^2}} + \dfrac{\sqrt{b^2+2bc}}{\sqrt{c^2+2a^2}} + \dfrac{\sqrt{c^2+2ca}}{\sqrt{a^2+2b^2}} \geq \dfrac{1}{a^2+b^2+c^2} $
4 replies
tokitaohma
Yesterday at 5:24 PM
arqady
2 hours ago
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ISI UGB 2025 P4
SomeonecoolLovesMaths   6
N 2 hours ago by Atmadeep
Source: ISI UGB 2025 P4
Let $S^1 = \{ z \in \mathbb{C} \mid |z| =1 \}$ be the unit circle in the complex plane. Let $f \colon S^1 \longrightarrow S^2$ be the map given by $f(z) = z^2$. We define $f^{(1)} \colon = f$ and $f^{(k+1)} \colon = f \circ f^{(k)}$ for $k \geq 1$. The smallest positive integer $n$ such that $f^{(n)}(z) = z$ is called the period of $z$. Determine the total number of points in $S^1$ of period $2025$.
(Hint : $2025 = 3^4 \times 5^2$)
6 replies
SomeonecoolLovesMaths
Yesterday at 11:24 AM
Atmadeep
2 hours ago
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An innocent-looking inequality
Bryan0224   0
2 hours ago
Source: Idk
If $\{a_i\}_{1\le i\le n }$ and $\{b_i\}_{1\le i\le n}$ are two sequences between $1$ and $2$ and they satisfy $\sum_{i=1}^n a_i^2=\sum_{i=1}^n b_i^2$, prove that $\sum_{i=1}^n\frac{a_i^3}{b_i}\leq 1.7\sum_{i=1}^{n} a_i^2$, and determine when does equality hold
Please answer this @sqing :trampoline:
0 replies
Bryan0224
2 hours ago
0 replies
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Interesting inequalities
sqing   0
3 hours ago
Source: Own
Let $ a,b>0 $ . Prove that
$$ \frac{a^2+b^2}{ab+1}+ \frac{4}{ (\sqrt{a}+\sqrt{b})^2} \geq 2$$$$ \frac{a^2+b^2}{ab+1}+ \frac{3}{a+\sqrt{ab}+b} \geq 2$$$$ \frac{a^3+b^3}{ab+1}+ \frac{4}{(a+b)^2} \geq 2$$$$ \frac{a^3+b^3}{ab+1}+ \frac{3}{a^2+ab+b^2} \geq 2$$$$\frac{a^2+b^2}{ab+2}+ \frac{1}{2\sqrt{ab}} \geq \frac{2+3\sqrt{2}-2\sqrt{2(\sqrt{2}-1)}}{4} $$
0 replies
sqing
3 hours ago
0 replies
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Mathcounts Countdown Round Hub
DhruvJha   29
N 3 hours ago by RocketScientist
We will post cdr updates for those who are blocked at school! Also put your current rankings and predictions.
29 replies
DhruvJha
Yesterday at 11:58 PM
RocketScientist
3 hours ago
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system linear equation with substitution
Miranda2829   2
N 4 hours ago by Miranda2829
5x-3y=-22
6x+4y=-34

whats the steps by using substitution in this question?

many thanks
2 replies
Miranda2829
5 hours ago
Miranda2829
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
middle school math
ratio
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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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