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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)!

Be sure to mark your calendars for the following upcoming events:
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[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]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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Inspired by qrxz17
sqing   1
N 8 minutes ago by Roots_Of_Moksha
Source: Own
Let $ a,b,c $ be reals such that $ (a^2+b^2)^2 + (b^2+c^2)^2 +(c^2+a^2)^2 = 28 $ and $ (a^2+b^2+c^2)^2 =16. $ Find the value of $ a^2(a^2-1) + b^2(b^2-1)+c^2(c^2-1).$
1 reply
1 viewing
sqing
23 minutes ago
Roots_Of_Moksha
8 minutes ago
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Shortest number theory you might've seen in your life
AlperenINAN   10
N 9 minutes ago by blug
Source: Turkey JBMO TST 2025 P4
Let $p$ and $q$ be prime numbers. Prove that if $pq(p+1)(q+1)+1$ is a perfect square, then $pq + 1$ is also a perfect square.
10 replies
AlperenINAN
May 11, 2025
blug
9 minutes ago
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an equation from the a contest
alpha31415   3
N 11 minutes ago by Mathzeus1024
Find all (complex) roots of the equation:
(z^2-z)(1-z+z^2)^2=-1/7
3 replies
alpha31415
May 21, 2025
Mathzeus1024
11 minutes ago
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Inspired by a9opsow_
sqing   3
N 33 minutes ago by sqing
Source: Own
Let $ a,b > 0 .$ Prove that
$$ \frac{(ka^2 - kab-b)^2 + (kb^2 - kab-a)^2 + (ab-ka-kb )^2}{ (ka+b)^2 + (kb+a)^2+(a - b)^2 }\geq \frac {1}{(k+1)^2}$$Where $ k\geq 0.37088 .$
$$\frac{(a^2 - ab-b)^2 + (b^2 - ab-a)^2 + ( ab-a-b)^2}{a^2 +b^2+(a - b)^2 } \geq 1$$$$ \frac{(2a^2 - 2ab-b)^2 + (2b^2 - 2ab-a)^2 + (ab-2a-2b )^2}{ (2a+b)^2 + (2b+a)^2+(a - b)^2 }\geq \frac 19$$
3 replies
sqing
Today at 1:49 AM
sqing
33 minutes ago
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Equation with primes
oVlad   8
N 35 minutes ago by Assassino9931
Source: Russian TST 2014, Day 11 P2 (Groups A & B)
Let $p,q$ and $s{}$ be prime numbers such that $2^sq =p^y-1$ where $y > 1.$ Find all possible values of $p.$
8 replies
oVlad
Jan 8, 2024
Assassino9931
35 minutes ago
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Cup of Combinatorics
M11100111001Y1R   2
N an hour ago by sansgankrsngupta
Source: Iran TST 2025 Test 4 Problem 2
There are \( n \) cups labeled \( 1, 2, \dots, n \), where the \( i \)-th cup has capacity \( i \) liters. In total, there are \( n \) liters of water distributed among these cups such that each cup contains an integer amount of water. In each step, we may transfer water from one cup to another. The process continues until either the source cup becomes empty or the destination cup becomes full.

$a)$ Prove that from any configuration where each cup contains an integer amount of water, it is possible to reach a configuration in which each cup contains exactly 1 liter of water in at most \( \frac{4n}{3} \) steps.

$b)$ Prove that in at most \( \frac{5n}{3} \) steps, one can go from any configuration with integer water amounts to any other configuration with the same property.
2 replies
M11100111001Y1R
May 27, 2025
sansgankrsngupta
an hour ago
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Inspired by Adhyayan Jana
sqing   3
N an hour ago by sqing
Source: Own
Let $a,b,c,d>0,a^2 + d^2-ad = (b + c)^2 $ aand $ a^2 +c^2 = b^2 + d^2.$ Prove that$$ \frac{ab+cd}{ad+bc} \geq \frac{ 4}{5}$$Let $a,b,c,d>0,a^2 + d^2-ad = b^2 + c^2 + bc $ aand $ a^2 +c^2 = b^2 + d^2.$ Prove that$$ \frac{ab+cd}{ad+bc} \geq \frac{\sqrt 3}{2}$$Let $a,b,c,d>0,a^2 + d^2 - ad = b^2 + c^2 + bc $ aand $ a^2 + b^2 = c^2 + d^2.$ Prove that $$ \frac{ab+cd}{ad+bc} =\frac{\sqrt 3}{2}$$
3 replies
sqing
Yesterday at 2:38 AM
sqing
an hour ago
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One old Long List No.1
prof.   0
an hour ago
Source: Netherland proposal
A circle is inscribed in a rhombus. In each corner of the rhombus, a circle is inscribed such that it touches two sides of the rhombus and inscribed circle. These corner circles have radii $r_1$ and $r_2$ and the radius of the inscribed circle is $r$. If $r_1$ and $r_2$ are natural numbers and $r=r_1\cdot r_2$, find the value of $r_1,r_2$ and $r$.
0 replies
prof.
an hour ago
0 replies
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IMO ShortList 1999, geometry problem 2
orl   13
N an hour ago by ezpotd
Source: IMO ShortList 1999, geometry problem 2
A circle is called a separator for a set of five points in a plane if it passes through three of these points, it contains a fourth point inside and the fifth point is outside the circle. Prove that every set of five points such that no three are collinear and no four are concyclic has exactly four separators.
13 replies
orl
Nov 13, 2004
ezpotd
an hour ago
J
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4 var inequality
SunnyEvan   0
2 hours ago
Source: Own
Let $ x,y,z,t \in R^+ ,$ such that : $ (x+y+z+t)^2 = x+y+z+t + (x+z)(y+t) $ and $ x \geq y \geq z \geq t .$
Try to prove or disprove : $$ \frac{2 \sqrt{x+y+z+t +(x+t)(y+z)}}{x^2+y^2+z^2+t^2 +3xz+3yt+xt+yz} \geq \frac{11(x+z)(z+t)-(x+y+z+t)}{x+y+z+t +(x+z)(y+t)} $$
0 replies
SunnyEvan
2 hours ago
0 replies
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9 Mock AMC 8
Leeoz   2
N 4 hours ago by Yihangzh
This is just your average mock AMC 8 on AoPS... nothing sus at all...
Just PM me your answers if you actually want to try it and be on the leaderboard...

Leaderboard

This test is for entertainment purposes only...

Also if you all want, I can post the solutions in June.
2 replies
Leeoz
4 hours ago
Yihangzh
4 hours ago
J
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Trivial Factoring MathCounts Question? 2025 MathCounts National Sprint Round #29
ilikemath247365   28
N 5 hours ago by Schintalpati
What is the value of the expression below?

$\frac{(1! + 2! + 3!)(2! + 3! + 4!)(3! + 4! + 5!)...(98! + 99! + 100!)}{(1! - 3(2!) + 3!)(2! - 3(3!) + 4!)(3! - 3(4!) + 5!)...(98! - 3(99!) + 100!)}$.
28 replies
ilikemath247365
Yesterday at 1:16 AM
Schintalpati
5 hours ago
J
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Overly wordy problems
ZMB038   4
N 5 hours ago by CJB19
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
4 replies
ZMB038
Yesterday at 11:14 PM
CJB19
5 hours ago
J
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Math with Connect4 Boards
Math-lover1   7
N Today at 2:34 AM by CJB19
Hi! So I was playing Connect4 with my friends the other day and I wondered: how many "legal" arrangements of Connect4 can be reached at the ending position?

We assume that we do not stop the game when there is a four in a row, and we have 21 red pieces and 21 yellow pieces. We also drop the pieces one by one into a standard 7 by 6 board. We can start the game with any color piece.

https://en.wikipedia.org/wiki/Connect_Four

Initial Thoughts
Attempt to use one-to-one correspondences
7 replies
Math-lover1
May 1, 2025
CJB19
Today at 2:34 AM
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simplify
ngelyy   9
N Apr 25, 2025 by EthanNg6
$\frac{24x}{21}+\frac{35x}{49}-\frac{x}{2}$
9 replies
ngelyy
Apr 18, 2025
EthanNg6
Apr 25, 2025
J
simplify
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Reveal topic tags
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ngelyy
140 posts
ngelyy
#1 h  Apr 18, 2025, 2:59 AM
Y by
$\frac{24x}{21}+\frac{35x}{49}-\frac{x}{2}$
This post has been edited 1 time. Last edited by Eternica, Apr 27, 2025, 12:03 PM
Z K Y
The post below has been deleted. Click to close.
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maxamc
585 posts
maxamc
#4 h  Apr 18, 2025, 3:04 AM
Y by
This question is impossible.
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ngelyy
140 posts
ngelyy
#6 h  Apr 18, 2025, 3:06 AM
Y by
maxamc wrote:
This question is impossible.

thank youu!!
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ngelyy
140 posts
ngelyy
#7 h  Apr 18, 2025, 3:13 AM
Y by
ive answered these 2 questions but i think i made a mistake

$3y+\frac{y-8}{2}+\frac{6y}{4}$

$\frac{20z-1}{3}-\frac{8z+4}{12}$

can anyone help me?
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UberPiggy
55 posts
UberPiggy
#8 h  Apr 18, 2025, 3:31 AM • 1 Y
Y by ngelyy
first one

second one
This post has been edited 1 time. Last edited by UberPiggy, Apr 18, 2025, 3:34 AM
Reason: added second problem
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maxamc
585 posts
maxamc
#9 h  Apr 18, 2025, 3:34 AM • 1 Y
Y by ngelyy
ngelyy wrote:
ive answered these 2 questions but i think i made a mistake

$3y+\frac{y-8}{2}+\frac{6y}{4}$

$\frac{20z-1}{3}-\frac{8z+4}{12}$

can anyone help me?

second one
Z K Y
The post below has been deleted. Click to close.
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ngelyy
140 posts
ngelyy
#10 h  Apr 18, 2025, 3:35 AM • 1 Y
Y by UberPiggy
oh i miscalculated the first one
thank you so much guys!! :thumbup:
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EthanNg6
35 posts
EthanNg6
#11 h  Apr 19, 2025, 2:25 AM
Y by
If you're solving for x, this question is impossible.
Z K Y
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K1mchi_
155 posts
K1mchi_
#13 h  Apr 19, 2025, 2:19 PM
Y by
EthanNg6 wrote:
If you're solving for x, this question is impossible.

“Simplify inequality”
Z K Y
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EthanNg6
35 posts
EthanNg6
#14 h  Apr 25, 2025, 11:41 PM
Y by
K1mchi_ wrote:
EthanNg6 wrote:
If you're solving for x, this question is impossible.

“Simplify inequality”

Click to reveal hidden text
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