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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
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.

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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 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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Alcumus specs
YeohZY   5
N 8 minutes ago by PikaPika999
Hi, can I ask about how Alcumus gives you points? (I mean the number on the red/orange/green/blue line on top that gains once you get correct answers. I'll just call it the score). I want to get my score up to 100, but I always can't and get stuck at like 98 or sth. Why is this so, and also how does alcumus make that "score" higher?
5 replies
YeohZY
Apr 27, 2025
PikaPika999
8 minutes ago
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Perpendicularity
April   31
N an hour ago by zuat.e
Source: CGMO 2007 P5
Point $D$ lies inside triangle $ABC$ such that $\angle DAC = \angle DCA = 30^{\circ}$ and $\angle DBA = 60^{\circ}$. Point $E$ is the midpoint of segment $BC$. Point $F$ lies on segment $AC$ with $AF = 2FC$. Prove that $DE \perp EF$.
31 replies
April
Dec 28, 2008
zuat.e
an hour ago
J
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Functional equation on the set of reals
abeker   26
N an hour ago by Bardia7003
Source: MEMO 2017 I1
Determine all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying
$$f(x^2 + f(x)f(y)) = xf(x + y)$$for all real numbers $x$ and $y$.
26 replies
abeker
Aug 25, 2017
Bardia7003
an hour ago
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prefix sum QRs
optimusprime154   2
N 2 hours ago by GreekIdiot
Source: BMO 2025 P1
oops.....
2 replies
optimusprime154
2 hours ago
GreekIdiot
2 hours ago
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Geometry with orthocenter config
thdnder   1
N 2 hours ago by thdnder
Source: Own
Let $ABC$ be a triangle, and let $AD, BE, CF$ be its altitudes. Let $H$ be its orthocenter, and let $O_B$ and $O_C$ be the circumcenters of triangles $AHC$ and $AHB$. Let $G$ be the second intersection of the circumcircles of triangles $FDO_B$ and $EDO_C$. Prove that the lines $DG$, $EF$, and $A$-median of $\triangle ABC$ are concurrent.
1 reply
thdnder
2 hours ago
thdnder
2 hours ago
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Can someone explain this one
hawa   6
N 2 hours ago by Andrew2019
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
6 replies
hawa
Today at 1:36 AM
Andrew2019
2 hours ago
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n = a*b , numbers of the form a^b
falantrng   3
N 2 hours ago by MuradSafarli
Source: Azerbaijan NMO 2023. Senior P1
The teacher calculates and writes on the board all the numbers $a^b$ that satisfy the condition $n = a\times b$ for the natural number $n.$ Here $a$ and $b$ are natural numbers. Is there a natural number $n$ such that each of the numbers $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ is the last digit of one of the numbers written by the teacher on the board? Justify your opinion.
3 replies
falantrng
Aug 24, 2023
MuradSafarli
2 hours ago
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Inequality with 3 variables and a special condition
Nuran2010   1
N 2 hours ago by arqady
Source: Azerbaijan Al-Khwarizmi IJMO TST 2024
For positive real numbers $a,b,c$ we have $3abc \geq ab+bc+ca$.
Prove that:

$\frac{1}{a^3+b^3+c}+\frac{1}{b^3+c^3+a}+\frac{1}{c^3+a^3+b} \leq \frac{3}{a+b+c}$.

Determine the equality case.
1 reply
Nuran2010
2 hours ago
arqady
2 hours ago
J
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find all functions
DNCT1   4
N 2 hours ago by jasperE3
Find all functions $f:\mathbb{R^+}\rightarrow \mathbb{R^+}$ such that
$$f(2f(x)+2y)=f(2x+y)+y\quad\forall x,y,\in\mathbb{R^+} $$
4 replies
DNCT1
Oct 10, 2020
jasperE3
2 hours ago
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Reflection of D moves on a line
Ankoganit   4
N 2 hours ago by bin_sherlo
Source: KöMaL A. 705
Triangle $ABC$ has orthocenter $H$. Let $D$ be a point distinct from the vertices on the circumcircle of $ABC$. Suppose that circle $BHD$ meets $AB$ at $P\ne B$, and circle $CHD$ meets $AC$ at $Q\ne C$. Prove that as $D$ moves on the circumcircle, the reflection of $D$ across line $PQ$ also moves on a fixed circle.

Michael Ren
4 replies
Ankoganit
Nov 11, 2017
bin_sherlo
2 hours ago
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USAMO 2003 Problem 1
MithsApprentice   67
N 2 hours ago by L13832
Prove that for every positive integer $n$ there exists an $n$-digit number divisible by $5^n$ all of whose digits are odd.
67 replies
MithsApprentice
Sep 27, 2005
L13832
2 hours ago
J
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D1024 : Can you do that?
Dattier   0
2 hours ago
Source: les dattes à Dattier
Let $x_{n+1}=x_n^2+1$ and $x_0=1$.

Can you calculate $\sum\limits_{i=1}^{2^{2025}} x_i \mod 10^{30}$?
0 replies
Dattier
2 hours ago
0 replies
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Math Problem I cant figure out how to do without bashing
equalsmc2   3
N 4 hours ago by NovaFrost
Hi,
I cant figure out how to do these 2 problems without bashing. Do you guys have any ideas for an elegant solution? Thank you!
Prob 1.
An RSM sports field has a square shape. Poles with letters M, A, T, H are located at the corners of the square (see the diagram). During warm up, a student starts at any pole, runs to another pole along a side of the square or across the field along diagonal MT (only in the direction from M to T), then runs to another pole along a side of the square or along diagonal MT, and so on. The student cannot repeat a run along the same side/diagonal of the square in the same direction. For instance, she cannot run from M to A twice, but she can run from M to A and at some point from A to M. How many different ways are there to complete the warm up that includes all nine possible runs (see the diagram)? One possible way is M-A-T-H-M-H-T-A-M-T (picture attached)

Prob 2.
In the expression 5@5@5@5@5 you replace each of the four @ symbols with either +, or, or x, or . You can insert one or more pairs of parentheses to control the order of operations. Find the second least whole number that CANNOT be the value of the resulting expression. For example, each of the numbers 25=5+5+5+5+5 and 605+(5+5)×5+5 can be the value of the resulting expression.

Prob 3. (This isnt bashing I don't understand how to do it though)
Suppose BC = 3AB in rectangle ABCD. Points E and F are on side BC such that BE = EF = FC. Compute the sum of the degree measures of the four angles EAB, EAF, EAC, EAD.

P.S. These are from an RSM olympiad. The answers are
3 replies
equalsmc2
Apr 6, 2025
NovaFrost
4 hours ago
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9 AMC 8 Scores
ChromeRaptor777   116
N 4 hours ago by NovaFrost
As far as I'm certain, I think all AMC8 scores are already out. Vote above.
116 replies
ChromeRaptor777
Apr 1, 2022
NovaFrost
4 hours ago
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J
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After Mathcounts
Existing_Human1   15
N Apr 6, 2025 by jb2015007
Hello Community!

I am officially done with my mathcounts career, as I have officially failed state, and I am now left an aloof blob reminiscing about the good old days.

So ... I was wondering if any of you have fun competitions I can do to relive the glory days of mathcounts. Obviously, their are the AMCs but I'm looking for something more team/travel based and one that preferably has a CDR.

Please specify if the competition is team based and if it has a cdr, and also when it takes place

Thank you in advance!
15 replies
Existing_Human1
Apr 5, 2025
jb2015007
Apr 6, 2025
J
After Mathcounts
G H J
Reveal topic tags
MATHCOUNTS
L
G H BBookmark kLocked kLocked NReply
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Existing_Human1
209 posts
Existing_Human1
#1 h  Apr 5, 2025, 6:21 PM • 2 Y
Y by PikaPika999, RocketScientist
Hello Community!

I am officially done with my mathcounts career, as I have officially failed state, and I am now left an aloof blob reminiscing about the good old days.

So ... I was wondering if any of you have fun competitions I can do to relive the glory days of mathcounts. Obviously, their are the AMCs but I'm looking for something more team/travel based and one that preferably has a CDR.

Please specify if the competition is team based and if it has a cdr, and also when it takes place

Thank you in advance!
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Dream9
82 posts
Dream9
#2 h  Apr 5, 2025, 6:23 PM • 1 Y
Y by PikaPika999
BmMT. Berkely mini math tornement. it's team based and registration ends today. The competition is online and in-person on June 7th
Z K Y
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franklin2013
272 posts
franklin2013
#3 h  Apr 5, 2025, 7:12 PM • 1 Y
Y by PikaPika999
Yes! BmMT is definitely a great choice. in fact I'm competing in the online tournament!
Z K Y
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Andyluo
945 posts
Andyluo
#4 h  Apr 5, 2025, 7:23 PM • 1 Y
Y by PikaPika999
here's some math stuff I'm going to do in the future

USAMTS (if can oly qual)
SMT Online
Purple Comet
MC Nationals
ARML
(Bmmt is probably good)
AMC 10/12
AIME
USAJMO trust
Ohio Math League (state stuff)
HMMT November
HMMT Februrary
CAMP stuff?
MOP!?!?!?!??!?!??!?!?!? (not happening)
This post has been edited 2 times. Last edited by Andyluo, Apr 5, 2025, 7:28 PM
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huajun78
67 posts
huajun78
#5 h  Apr 5, 2025, 8:34 PM • 1 Y
Y by PikaPika999
there are a lot of mu alpha theta competitions
Z K Y
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jkim0656
1010 posts
jkim0656
#6 h  Apr 5, 2025, 8:36 PM • 1 Y
Y by PikaPika999
give me some info on BmMt pls
im intrested maybe for next year
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jkim0656
1010 posts
jkim0656
#7 h  Apr 5, 2025, 8:36 PM • 1 Y
Y by PikaPika999
also my newbie brain does not know what HMMT is
Z K Y
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huajun78
67 posts
huajun78
#8 h  Apr 5, 2025, 8:39 PM • 1 Y
Y by PikaPika999
Harvard MIT Math Tournament
Z K Y
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DDCN_2011
354 posts
DDCN_2011
#9 h  Apr 5, 2025, 9:19 PM • 1 Y
Y by PikaPika999
im js doing amc 10 i also failed mc D:
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RocketScientist
341 posts
RocketScientist
#10 h  Apr 6, 2025, 1:46 AM • 1 Y
Y by PikaPika999
relatable post :(
from what i've heard, college comps like hmmt, pumac or cmimc are really fun
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Existing_Human1
209 posts
Existing_Human1
#11 h  Apr 6, 2025, 2:08 AM • 1 Y
Y by PikaPika999
Anything with CDR? I need to cope with the fact that FTW isn't useful

Also, can you put the registration dates? (Sorry, I'm just lazy)
This post has been edited 1 time. Last edited by Existing_Human1, Apr 6, 2025, 2:08 AM
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mathprodigy2011
324 posts
mathprodigy2011
#12 h  Apr 6, 2025, 2:31 AM • 1 Y
Y by PikaPika999
Existing_Human1 wrote:
Hello Community!

I am officially done with my mathcounts career, as I have officially failed state, and I am now left an aloof blob reminiscing about the good old days.

So ... I was wondering if any of you have fun competitions I can do to relive the glory days of mathcounts. Obviously, their are the AMCs but I'm looking for something more team/travel based and one that preferably has a CDR.

Please specify if the competition is team based and if it has a cdr, and also when it takes place

Thank you in advance!

ARML is a cool alternative
Z K Y
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jb2015007
1922 posts
jb2015007
#13 h  Apr 6, 2025, 2:56 AM • 1 Y
Y by PikaPika999
franklin2013 wrote:
Yes! BmMT is definitely a great choice. in fact I'm competing in the online tournament!

same! do u already have a team?
if not PM me!
Z K Y
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Existing_Human1
209 posts
Existing_Human1
#14 h  Apr 6, 2025, 3:17 AM • 1 Y
Y by PikaPika999
For BMMT I'll be out of middle school in june, do I still count as an 8th grader?
Z K Y
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franklin2013
272 posts
franklin2013
#15 h  Apr 6, 2025, 3:59 PM • 1 Y
Y by PikaPika999
jb2015007 wrote:
franklin2013 wrote:
Yes! BmMT is definitely a great choice. in fact I'm competing in the online tournament!

same! do u already have a team?
if not PM me!

I already have a team with 4 people.
Z K Y
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jb2015007
1922 posts
jb2015007
#16 h  Apr 6, 2025, 4:02 PM • 1 Y
Y by PikaPika999
Oh ok nvm then.
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