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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.

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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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9 AMC 8 Scores
ChromeRaptor777   141
N 10 minutes ago by CJB19
As far as I'm certain, I think all AMC8 scores are already out. Vote above.
141 replies
ChromeRaptor777
Apr 1, 2022
CJB19
10 minutes ago
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Challenge: Make every number to 100 using 4 fours
CJB19   76
N 14 minutes ago by CJB19
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
76 replies
CJB19
Yesterday at 4:02 PM
CJB19
14 minutes ago
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9 1000th POST!!!!!!!
thegreatbrain   38
N 38 minutes ago by PikaPika999
THIS IS MY 1000TH POST!!!!!!!!!!!
38 replies
thegreatbrain
Yesterday at 7:44 PM
PikaPika999
38 minutes ago
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INMO 2007 Problem 6
Sathej   32
N an hour ago by math_genie
Source: Inequality
If $ x$, $ y$, $ z$ are positive real numbers, prove that
\[ \left(x + y + z\right)^2 \left(yz + zx + xy\right)^2 \leq 3\left(y^2 + yz + z^2\right)\left(z^2 + zx + x^2\right)\left(x^2 + xy + y^2\right) .\]
32 replies
Sathej
Feb 4, 2007
math_genie
an hour ago
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Prove that the triangle is isosceles.
TUAN2k8   3
N an hour ago by TUAN2k8
Source: My book
Given acute triangle $ABC$ with two altitudes $CF$ and $BE$.Let $D$ be the point on the line $CF$ such that $DB \perp BC$.The lines $AD$ and $EF$ intersect at point $X$, and $Y$ is the point on segment $BX$ such that $CY \perp BY$.Suppose that $CF$ bisects $BE$.Prove that triangle $ACY$ is isosceles.
3 replies
TUAN2k8
3 hours ago
TUAN2k8
an hour ago
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Choice of indexes in a sequence
randomusername   2
N an hour ago by EthanWYX2009
Source: Kürschák 2005, problem 1
Let $N>1$ and let $a_1,a_2,\dots,a_N$ be nonnegative reals with sum at most $500$. Prove that there exist integers $k\ge 1$ and $1=n_0<n_1<\dots<n_k=N$ such that
\[\sum_{i=1}^k n_ia_{n_{i-1}}<2005.\]
2 replies
randomusername
Jul 13, 2014
EthanWYX2009
an hour ago
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Simple but hard
Lukariman   3
N an hour ago by Giant_PT
Given triangle ABC. Outside the triangle, construct rectangles ACDE and BCFG with equal areas. Let M be the midpoint of DF. Prove that CM passes through the center of the circle circumscribing triangle ABC.
3 replies
Lukariman
Today at 2:47 AM
Giant_PT
an hour ago
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drawn to scale
A7456321   9
N an hour ago by giratina3
would you guys say that the diagrams drawn on math comp papers are usually drawn to scale (or at least close)? i have found that they are usually pretty accurate even tho the test always says that they are not necessarily to scale
9 replies
A7456321
Yesterday at 2:06 AM
giratina3
an hour ago
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Ah, easy one
irregular22104   2
N an hour ago by irregular22104
Source: Own
In the number series $1,9,9,9,8,...,$ every next number (from the fifth number) is the unit number of the sum of the four numbers preceding it. Is there any cases that we get the numbers $1234$ and $5678$ in this series?
2 replies
irregular22104
Wednesday at 4:01 PM
irregular22104
an hour ago
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power of a point
BekzodMarupov   1
N an hour ago by nabodorbuco2
Source: lemmas in olympiad geometry
Epsilon 1.3. Let ABC be a triangle and let D, E, F be the feet of the altitudes, with D on BC, E on CA, and F on AB. Let the parallel through D to EF meet AB at X and AC at Y. Let T be the intersection of EF with BC and let M be the midpoint of side BC. Prove that the points T, M, X, Y are concyclic.
1 reply
BekzodMarupov
Today at 5:41 AM
nabodorbuco2
an hour ago
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Functional Equation!
EthanWYX2009   5
N 2 hours ago by Miquel-point
Source: 2025 TST 24
Find all functions $f:\mathbb Z\to\mathbb Z$ such that $f$ is unbounded and
\[2f(m)f(n)-f(n-m)-1\]is a perfect square for all integer $m,n.$
5 replies
EthanWYX2009
Mar 29, 2025
Miquel-point
2 hours ago
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IMO Shortlist 2014 G3
hajimbrak   46
N 2 hours ago by Rayvhs
Let $\Omega$ and $O$ be the circumcircle and the circumcentre of an acute-angled triangle $ABC$ with $AB > BC$. The angle bisector of $\angle ABC$ intersects $\Omega$ at $M \ne B$. Let $\Gamma$ be the circle with diameter $BM$. The angle bisectors of $\angle AOB$ and $\angle BOC$ intersect $\Gamma$ at points $P$ and $Q,$ respectively. The point $R$ is chosen on the line $P Q$ so that $BR = MR$. Prove that $BR\parallel AC$.
(Here we always assume that an angle bisector is a ray.)

Proposed by Sergey Berlov, Russia
46 replies
1 viewing
hajimbrak
Jul 11, 2015
Rayvhs
2 hours ago
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Eight-point cicle
sandu2508   15
N 2 hours ago by Mamadi
Source: Balkan MO 2010, Problem 2
Let $ABC$ be an acute triangle with orthocentre $H$, and let $M$ be the midpoint of $AC$. The point $C_1$ on $AB$ is such that $CC_1$ is an altitude of the triangle $ABC$. Let $H_1$ be the reflection of $H$ in $AB$. The orthogonal projections of $C_1$ onto the lines $AH_1$, $AC$ and $BC$ are $P$, $Q$ and $R$, respectively. Let $M_1$ be the point such that the circumcentre of triangle $PQR$ is the midpoint of the segment $MM_1$.
Prove that $M_1$ lies on the segment $BH_1$.
15 replies
sandu2508
May 4, 2010
Mamadi
2 hours ago
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IMO Solution mistake
CHESSR1DER   1
N 2 hours ago by whwlqkd
Source: Mistake in IMO 1982/1 4th solution
I found a mistake in 4th solution at IMO 1982/1. It gives answer $660$ and $661$. But right answer is only $660$. Should it be reported somewhere in Aops?
1 reply
CHESSR1DER
5 hours ago
whwlqkd
2 hours ago
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Area of Polygon
AIME15   48
N Apr 21, 2025 by anticodon
The area of polygon $ ABCDEF$, in square units, is

IMAGE

\[ \textbf{(A)}\ 24 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 46 \qquad \textbf{(D)}\ 66 \qquad \textbf{(E)}\ 74 \]
48 replies
AIME15
Jan 12, 2009
anticodon
Apr 21, 2025
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Area of Polygon
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Reveal topic tags
geometry
rectangle
Why the bump
ancient boomer ah
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goonmaster
17 posts
goonmaster
#38 h  Jan 15, 2025, 1:02 AM
Y by
why are y'all necroposting smh
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WiseHawkCuteFriendly
589 posts
WiseHawkCuteFriendly
#39 h  Jan 15, 2025, 2:23 AM
Y by
solution?
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WWW.OMEGALEARN.ORG
22 posts
WWW.OMEGALEARN.ORG
#40 h  Jan 26, 2025, 6:09 AM
Y by
i have no idea
This post has been edited 1 time. Last edited by WWW.OMEGALEARN.ORG, Jan 27, 2025, 5:42 AM
Reason: don't know why i said CCCCCCCCCCCCCC
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eric201291
208 posts
eric201291
#41 h  Jan 26, 2025, 2:08 PM
Y by
5*(6-4)+9*4=10+36=46.
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Mrs-Say
2 posts
Mrs-Say
#42 h  Apr 20, 2025, 8:29 PM
Y by
6*5+(9-5)*4=46
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K1mchi_
119 posts
K1mchi_
#43 h  Apr 20, 2025, 9:25 PM
Y by
none of the angle measures are specified
it is assumable that the diagram is not drawn to scale, but again, is unspecified

this was a very lazy problem because of these two points, which make this problem impossible to solve by the given information
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franklin2013
296 posts
franklin2013
#44 h  Apr 20, 2025, 9:26 PM
Y by
It clearly specifies that All angles in this diagram are right.
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MathWinner121
525 posts
MathWinner121
#45 h  Apr 20, 2025, 9:27 PM
Y by
Easy dubs its C
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sangriabeaver5
7 posts
sangriabeaver5
#46 h  Apr 21, 2025, 1:30 AM
Y by
This was so easy
Click to reveal hidden text
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EthanNg6
35 posts
EthanNg6
#47 h  Apr 21, 2025, 1:59 AM
Y by
Click to reveal hidden text
This post has been edited 2 times. Last edited by EthanNg6, Apr 23, 2025, 1:29 AM
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K1mchi_
119 posts
K1mchi_
#48 h  Apr 21, 2025, 3:45 PM
Y by
franklin2013 wrote:
It clearly specifies that All angles in this diagram are right.

and that statement is obviously false. most angles in “this diagram” are not right unless u count the t
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Andrew2019
2316 posts
Andrew2019
#49 h  Apr 21, 2025, 5:03 PM
Y by
franklin2013 wrote:
It clearly specifies that All angles in this diagram are right.

so angle FAB is 90 degrees?
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K1mchi_
119 posts
K1mchi_
#50 h  Apr 21, 2025, 6:19 PM
Y by
Andrew2019 wrote:
franklin2013 wrote:
It clearly specifies that All angles in this diagram are right.

so angle FAB is 90 degrees?

was prob not referring to the diagram itself; just the phrase”this diagram”
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ReticulatedPython
712 posts
ReticulatedPython
#51 h  Apr 21, 2025, 7:24 PM
Y by
Answer is given by $4^2+5\cdot6.$
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anticodon
164 posts
anticodon
#52 h  Apr 21, 2025, 9:05 PM
Y by
Clearly, you divide the polygon into 1x1 squares and count the number of squares
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