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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 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
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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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Challenge: Make every number to 100 using 4 fours
CJB19   46
N 3 minutes ago by Capybara7017
I've seen this attempted a lot but I want to see if the AoPS community can actually do it. Using ONLY 4 fours and math operations, make as many numbers as you can. Try to go in order. I'll start:
$$(4-4)*4*4=0$$$$4-4+4/4=1$$$$4/4+4/4=2$$$$(4+4+4)/4=3$$$$4+(4-4)*4=4$$$$4+4^(4-4)=5$$$$4!/4+4-4=6$$$$4+4-4/4=7$$$$4+4+4-4=8$$
I can't get the exponent in 5 to work if someone knows how to fix it please tell me
46 replies
CJB19
Today at 4:02 PM
Capybara7017
3 minutes ago
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9 1000th POST!!!!!!!
thegreatbrain   19
N 5 minutes ago by evt917
THIS IS MY 1000TH POST!!!!!!!!!!!
19 replies
thegreatbrain
3 hours ago
evt917
5 minutes ago
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1234567890987654321
Marius_Avion_De_Vanatoare   7
N 22 minutes ago by Capybara7017
Is the number $1234567890987654321$ prime?
7 replies
Marius_Avion_De_Vanatoare
Nov 15, 2024
Capybara7017
22 minutes ago
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best times to work?
Spacepandamath13   3
N 23 minutes ago by Capybara7017
What do you think are the best times to work on math or whatever?
3 replies
Spacepandamath13
Today at 12:55 AM
Capybara7017
23 minutes ago
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abc = 1 Inequality generalisation
CHESSR1DER   6
N 3 hours ago by CHESSR1DER
Source: Own
Let $a,b,c > 0$, $abc=1$.
Find min $ \frac{1}{a^m(bx+cy)^n} + \frac{1}{b^m(cx+ay)^n} + \frac{1}{c^m(cx+ay)^n}$.
$1)$ $m,n,x,y$ are fixed positive integers.
$2)$ $m,n,x,y$ are fixed positive real numbers.
6 replies
CHESSR1DER
4 hours ago
CHESSR1DER
3 hours ago
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Fond all functions in M with a) f(1)=5/2, b) f(1)=√3
Amir Hossein   5
N 3 hours ago by jasperE3
Source: IMO LongList 1982 - P34
Let $M$ be the set of all functions $f$ with the following properties:

(i) $f$ is defined for all real numbers and takes only real values.

(ii) For all $x, y \in \mathbb R$ the following equality holds: $f(x)f(y) = f(x + y) + f(x - y).$

(iii) $f(0) \neq 0.$

Determine all functions $f \in M$ such that

(a) $f(1)=\frac 52$,

(b) $f(1)= \sqrt 3$.
5 replies
Amir Hossein
Mar 18, 2011
jasperE3
3 hours ago
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help me please
thuanz123   6
N 4 hours ago by pavel kozlov
find all $a,b \in \mathbb{Z}$ such that:
a) $3a^2-2b^2=1$
b) $a^2-6b^2=1$
6 replies
thuanz123
Jan 17, 2016
pavel kozlov
4 hours ago
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Problem 5 (Second Day)
darij grinberg   78
N 4 hours ago by cj13609517288
Source: IMO 2004 Athens
In a convex quadrilateral $ABCD$, the diagonal $BD$ bisects neither the angle $ABC$ nor the angle $CDA$. The point $P$ lies inside $ABCD$ and satisfies \[\angle PBC=\angle DBA\quad\text{and}\quad \angle PDC=\angle BDA.\] Prove that $ABCD$ is a cyclic quadrilateral if and only if $AP=CP$.
78 replies
darij grinberg
Jul 13, 2004
cj13609517288
4 hours ago
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concyclic wanted, PQ = BP, cyclic quadrilateral and 2 parallelograms related
parmenides51   2
N 4 hours ago by SuperBarsh
Source: 2011 Italy TST 2.2
Let $ABCD$ be a cyclic quadrilateral in which the lines $BC$ and $AD$ meet at a point $P$. Let $Q$ be the point of the line $BP$, different from $B$, such that $PQ = BP$. We construct the parallelograms $CAQR$ and $DBCS$. Prove that the points $C, Q, R, S$ lie on the same circle.
2 replies
parmenides51
Sep 25, 2020
SuperBarsh
4 hours ago
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Integer FE Again
popcorn1   43
N 4 hours ago by DeathIsAwe
Source: ISL 2020 N5
Determine all functions $f$ defined on the set of all positive integers and taking non-negative integer values, satisfying the three conditions:
[list]
[*] $(i)$ $f(n) \neq 0$ for at least one $n$;
[*] $(ii)$ $f(x y)=f(x)+f(y)$ for every positive integers $x$ and $y$;
[*] $(iii)$ there are infinitely many positive integers $n$ such that $f(k)=f(n-k)$ for all $k<n$.
[/list]
43 replies
popcorn1
Jul 20, 2021
DeathIsAwe
4 hours ago
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Long and wacky inequality
Royal_mhyasd   2
N 5 hours ago by Royal_mhyasd
Source: Me
Let $x, y, z$ be positive real numbers such that $x^2 + y^2 + z^2 = 12$. Find the minimum value of the following sum :
$$\sum_{cyc}\frac{(x^3+2y)^3}{3x^2yz - 16z - 8yz + 6x^2z}$$knowing that the denominators are positive real numbers.
2 replies
Royal_mhyasd
May 12, 2025
Royal_mhyasd
5 hours ago
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Perpendicular passes from the intersection of diagonals, \angle AEB = \angle CED
NO_SQUARES   1
N 5 hours ago by mathuz
Source: 239 MO 2025 10-11 p3
Inside of convex quadrilateral $ABCD$ point $E$ was chosen such that $\angle DAE = \angle CAB$ and $\angle ADE = \angle CDB$. Prove that if perpendicular from $E$ to $AD$ passes from the intersection of diagonals of $ABCD$, then $\angle AEB = \angle CED$.
1 reply
NO_SQUARES
May 5, 2025
mathuz
5 hours ago
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A game with balls and boxes
egxa   6
N 5 hours ago by Sh309had
Source: Turkey JBMO TST 2023 Day 1 P4
Initially, Aslı distributes $1000$ balls to $30$ boxes as she wishes. After that, Aslı and Zehra make alternated moves which consists of taking a ball in any wanted box starting with Aslı. One who takes the last ball from any box takes that box to herself. What is the maximum number of boxes can Aslı guarantee to take herself regardless of Zehra's moves?
6 replies
egxa
Apr 30, 2023
Sh309had
5 hours ago
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Angle Relationships in Triangles
steven_zhang123   2
N 5 hours ago by Captainscrubz
In $\triangle ABC$, $AB > AC$. The internal angle bisector of $\angle BAC$ and the external angle bisector of $\angle BAC$ intersect the ray $BC$ at points $D$ and $E$, respectively. Given that $CE - CD = 2AC$, prove that $\angle ACB = 2\angle ABC$.
2 replies
steven_zhang123
Yesterday at 11:09 PM
Captainscrubz
5 hours ago
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Something Interesting
ilikemath247365   11
N Apr 25, 2025 by ilikemath247365
I just realized: The 2013 National MathCounts Sprint #24 is the EXACT SAME as the 2001 National MathCounts Sprint #28.
11 replies
ilikemath247365
Apr 25, 2025
ilikemath247365
Apr 25, 2025
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Something Interesting
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Reveal topic tags
MATHCOUNTS
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ilikemath247365
256 posts
ilikemath247365
#1 h  Apr 25, 2025, 5:03 AM
Y by
I just realized: The 2013 National MathCounts Sprint #24 is the EXACT SAME as the 2001 National MathCounts Sprint #28.
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ethan2011
324 posts
ethan2011
#2 h  Apr 25, 2025, 12:05 PM
Y by
Can you share the problem then?
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Charizard_637
117 posts
Charizard_637
#3 h  Apr 25, 2025, 2:44 PM
Y by
OH SHOOT YOU'RE RIGHT I MOCKED 2013 AND KNEW I'VE SEEN SPRINT 28 BEFORE

If $a+b = 1$ and $a^2+b^2 = 2$, what is the value of $a^3+b^3$? Express your answer as a common fraction.
Answer
If you want the solution I can post that too
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K1mchi_
118 posts
K1mchi_
#4 h  Apr 25, 2025, 2:47 PM
Y by
ilikemath247365 wrote:
I just realized: The 2013 National MathCounts Sprint #24 is the EXACT SAME as the 2001 National MathCounts Sprint #28.

what did u expect

u cant have new problems every year or smth
Z K Y
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Charizard_637
117 posts
Charizard_637
#5 h  Apr 25, 2025, 2:52 PM
Y by
you can with that many problem writers for the national competition
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K1mchi_
118 posts
K1mchi_
#6 h  Apr 25, 2025, 2:54 PM
Y by
Charizard_637 wrote:
you can with that many problem writers for the national competition

then with that many writers then they must come up with the same problem at some point

must have been coincidental

or smth


ngl tho this topic is pretty random
Z K Y
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MathPerson12321
3785 posts
MathPerson12321
#7 h  Apr 25, 2025, 2:58 PM
Y by
K1mchi_ wrote:
Charizard_637 wrote:
you can with that many problem writers for the national competition

then with that many writers then they must come up with the same problem at some point

must have been coincidental

or smth


ngl tho this topic is pretty random

The exact same?
The problems being about the same thing is different
This is most definitely intentional
Z K Y
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K1mchi_
118 posts
K1mchi_
#8 h  Apr 25, 2025, 3:33 PM
Y by
MathPerson12321 wrote:
K1mchi_ wrote:
Charizard_637 wrote:
you can with that many problem writers for the national competition

then with that many writers then they must come up with the same problem at some point

must have been coincidental

or smth


ngl tho this topic is pretty random

The exact same?
The problems being about the same thing is different
This is most definitely intentional

intentionally doing the same problem? thats a new low
Z K Y
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MathPerson12321
3785 posts
MathPerson12321
#9 h  Apr 25, 2025, 3:36 PM
Y by
I am sure this is not accidental
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K1mchi_
118 posts
K1mchi_
#10 h  Apr 25, 2025, 3:37 PM
Y by
MathPerson12321 wrote:
I am sure this is not accidental

that makes more sense

idk anyone could be lazy

except me lol
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iwastedmyusername
151 posts
iwastedmyusername
#11 h  Apr 25, 2025, 4:06 PM
Y by
yes mathcounts has a habit of reusing problbems
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ilikemath247365
256 posts
ilikemath247365
#12 h  Apr 25, 2025, 11:56 PM
Y by
Yeah it was something really random, I just happened to mock those two tests and saw the same problems.
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