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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)!

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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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Combinatorics
Ro.Is.Te.   2
N 9 minutes ago by SpeedCuber7
$\binom{24}{24} + \binom{24}{23} + \binom{24}{22} + \binom{24}{21} + \binom{24}{20}+...+\binom{24}{2}$
2 replies
Ro.Is.Te.
2 hours ago
SpeedCuber7
9 minutes ago
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sillies are bad
Bummer12345   6
N 11 minutes ago by SpeedCuber7
I got 102nd and 89th place in 6th and 7th grade respectively; however, I feel like I definitely could've done much better (mainly due to sillies). For example, some of my worst sillies at nationals are
does anyone have tips to reduce silly mistakes (pls share, I really want to make top 56 this year)
6 replies
Bummer12345
3 hours ago
SpeedCuber7
11 minutes ago
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Great similarity
steven_zhang123   3
N 17 minutes ago by Lil_flip38
Source: a friend
As shown in the figure, there are two points $D$ and $E$ outside triangle $ABC$ such that $\angle DAB = \angle CAE$ and $\angle ABD + \angle ACE = 180^{\circ}$. Connect $BE$ and $DC$, which intersect at point $O$. Let $AO$ intersect $BC$ at point $F$. Prove that $\angle ACE = \angle AFC$.
3 replies
steven_zhang123
43 minutes ago
Lil_flip38
17 minutes ago
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Geometry Help
ILOVECATS127   1
N an hour ago by Inaaya
Hello, I needed some help understanding this concept from Chapter 12, Geometry:

Points P, Q and R are on circle O such that

Arc PQ = 78°, arc QR = 123°, and arc PQR = 201°.

1. Find ∠PQO
2. Find ∠POR

Please help me understand HOW to solve these 2 problems.
1 reply
ILOVECATS127
Yesterday at 1:07 PM
Inaaya
an hour ago
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AIME qualification
GallopingUnicorn45   8
N an hour ago by Inaaya
Hi, so I'm in 4th grade and I'm taking AMC 10 (both A and B) this year in November, and I really want to get AIME. Last time I did the 2023 AMC 10A was like four months ago (?) and I got 10 correct.

So I finished Intro to Counting and Number Theory and am almost done with Intro to Algebra B. Obviously there's some questions I don't know in those books, but I understand at least 90% of it.

I'm taking Intro to Geometry in the summer (it ends one week after AMC 10) and I'm just going to go over Intro to Algebra, Intro to Counting, and Intro to Number Theory (basically the questions I don't know and incorrect problems), plus Competition Math for Middle School and AoPS Volume 1: The Basics.

I will also do the past year AMC 10 papers, but is there anything else I can do to prepare and get into AIME? Thanks!
8 replies
GallopingUnicorn45
Monday at 8:40 PM
Inaaya
an hour ago
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AD=BE implies ABC right
v_Enhance   117
N 2 hours ago by cj13609517288
Source: European Girl's MO 2013, Problem 1
The side $BC$ of the triangle $ABC$ is extended beyond $C$ to $D$ so that $CD = BC$. The side $CA$ is extended beyond $A$ to $E$ so that $AE = 2CA$. Prove that, if $AD=BE$, then the triangle $ABC$ is right-angled.
117 replies
v_Enhance
Apr 10, 2013
cj13609517288
2 hours ago
J
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Geometry
gggzul   6
N 3 hours ago by Captainscrubz
In trapezoid $ABCD$ segments $AB$ and $CD$ are parallel. Angle bisectors of $\angle A$ and $\angle C$ meet at $P$. Angle bisectors of $\angle B$ and $\angle D$ meet at $Q$. Prove that $ABPQ$ is cyclic
6 replies
gggzul
Yesterday at 8:22 AM
Captainscrubz
3 hours ago
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Geometry
Lukariman   5
N 3 hours ago by Lukariman
Given circle (O) and point P outside (O). From P draw tangents PA and PB to (O) with contact points A, B. On the opposite ray of ray BP, take point M. The circle circumscribing triangle APM intersects (O) at the second point D. Let H be the projection of B on AM. Prove that $\angle HDM$ = 2∠AMP.
5 replies
Lukariman
Yesterday at 12:43 PM
Lukariman
3 hours ago
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Aime type Geo
ehuseyinyigit   4
N 5 hours ago by ehuseyinyigit
Source: Turkish First Round 2024
In a scalene triangle $ABC$, let $M$ be the midpoint of side $BC$. Let the line perpendicular to $AC$ at point $C$ intersect $AM$ at $N$. If $(BMN)$ is tangent to $AB$ at $B$, find $AB/MA$.
4 replies
ehuseyinyigit
Monday at 9:04 PM
ehuseyinyigit
5 hours ago
J
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n variables with n-gon sides
mihaig   1
N 5 hours ago by mihaig
Source: Own
Let $n\geq3$ and let $a_1,a_2,\ldots, a_n\geq0$ be reals such that $\sum_{i=1}^{n}{\frac{1}{2a_i+n-2}}=1.$
Prove
$$\frac{24}{(n-1)(n-2)}\cdot\sum_{1\leq i<j<k\leq n}{a_ia_ja_k}\geq3\sum_{i=1}^{n}{a_i}+n.$$
1 reply
mihaig
Apr 25, 2025
mihaig
5 hours ago
J
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Centroid, altitudes and medians, and concyclic points
BR1F1SZ   3
N Today at 5:48 AM by EeEeRUT
Source: Austria National MO Part 1 Problem 2
Let $\triangle{ABC}$ be an acute triangle with $BC > AC$. Let $S$ be the centroid of triangle $ABC$ and let $F$ be the foot of the perpendicular from $C$ to side $AB$. The median $CS$ intersects the circumcircle $\gamma$ of triangle $\triangle{ABC}$ at a second point $P$. Let $M$ be the point where $CS$ intersects $AB$. The line $SF$ intersects the circle $\gamma$ at a point $Q$, such that $F$ lies between $S$ and $Q$. Prove that the points $M,P,Q$ and $F$ lie on a circle.

(Karl Czakler)
3 replies
BR1F1SZ
Monday at 9:45 PM
EeEeRUT
Today at 5:48 AM
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area of O_1O_2O_3O_4 <=1, incenters of right triangles outside a square
parmenides51   2
N Today at 4:35 AM by Solilin
Source: Thailand Mathematical Olympiad 2012 p4
Let $ABCD$ be a unit square. Points $E, F, G, H$ are chosen outside $ABCD$ so that $\angle AEB =\angle BF C = \angle CGD = \angle DHA = 90^o$ . Let $O_1, O_2, O_3, O_4$, respectively, be the incenters of $\vartriangle ABE, \vartriangle BCF, \vartriangle CDG, \vartriangle DAH$. Show that the area of $O_1O_2O_3O_4$ is at most $1$.
2 replies
parmenides51
Aug 17, 2020
Solilin
Today at 4:35 AM
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Geo metry
TUAN2k8   3
N Today at 4:34 AM by TUAN2k8
Help me plss!
Given an acute triangle $ABC$. Points $D$ and $E$ lie on segments $AB$ and $AC$, respectively. Lines $BD$ and $CE$ intersect at point $F$. The circumcircles of triangles $BDF$ and $CEF$ intersect at a second point $P$. The circumcircles of triangles $ABC$ and $ADE$ intersect at a second point $Q$. Point $K$ lies on segment $AP$ such that $KQ \perp AQ$. Prove that triangles $\triangle BKD$ and $\triangle CKE$ are similar.
3 replies
TUAN2k8
Yesterday at 10:33 AM
TUAN2k8
Today at 4:34 AM
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China South East Mathematical Olympiad 2013 problem 2
s372102   3
N Today at 2:11 AM by AGCN
$\triangle ABC$, $AB>AC$. the incircle $I$ of $\triangle ABC$ meet $BC$ at point $D$, $AD$ meet $I$ again at $E$. $EP$ is a tangent of $I$, and $EP$ meet the extension line of $BC$ at $P$. $CF\parallel PE$, $CF\cap AD=F$. the line $BF$ meet $I$ at $M,N$, point $M$ is on the line segment $BF$, the line segment $PM$ meet $I$ again at $Q$. Show that $\angle ENP=\angle ENQ$
3 replies
s372102
Aug 10, 2013
AGCN
Today at 2:11 AM
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State target p8 sol
EaZ_Shadow   116
N Apr 18, 2025 by derekwang2048
This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!
116 replies
EaZ_Shadow
Apr 6, 2025
derekwang2048
Apr 18, 2025
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State target p8 sol
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Reveal topic tags
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andrewmao1221
16 posts
andrewmao1221
#106 h  Apr 16, 2025, 12:18 PM
Y by
What you mean 2 diagrams? I think here the second situation applies. Then this becomes the easiest 8th question. The probability of HTT happen is: 2/3*1/3*1/3=2/27. Thus the expected number of trials is 27/2.

However, I think the question is kinda of wrong. Here the expected number of trials is not the expected number of flipping. The trial includes 3 flipping. At least, the question should make it more clearly what it is asking about.
This post has been edited 1 time. Last edited by andrewmao1221, Apr 16, 2025, 12:29 PM
Reason: Additional thoughts
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Craftybutterfly
454 posts
Craftybutterfly
#108 h  Apr 16, 2025, 3:05 PM
Y by
Why do you have to reciprocate the fraction?
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andrewmao1221
16 posts
andrewmao1221
#109 h  Apr 16, 2025, 3:26 PM
Y by
A previous post derived the equation why $E(X)=\frac{1}{p}$. A simple intuition is:
Let $m$ be the number of trials for you to get one success. $m\times p=1$. Thus: $m=\frac{1}{p}$. An even simpler intuition: If you do something with a success rate of 0.2, how many times on average will you have to do so you get one success? Oh, it is 5. How do you get it? 1/0.2


Craftybutterfly wrote:
Why do you have to reciprocate the fraction?
This post has been edited 2 times. Last edited by andrewmao1221, Apr 16, 2025, 3:33 PM
Reason: typo
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pingpongmerrily
3611 posts
pingpongmerrily
#110 h  Apr 16, 2025, 6:14 PM
Y by
MC_ADe wrote:
States is a really good way to go about but realizing that after using CRT for p7 you won't have time to use states on p8 was kind of sadge

bro you don't need CRT for p7
its just like basic lcm work
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derekwang2048
1225 posts
derekwang2048
#111 h  Apr 16, 2025, 6:52 PM
Y by
wait i just grinded units digit
and then added 40 i think, even if you use crt it is the most basic form (0, 1, 2)
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Andyluo
960 posts
Andyluo
#112 h  Apr 16, 2025, 10:26 PM
Y by
dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716
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Aaronjudgeisgoat
897 posts
Aaronjudgeisgoat
#113 h  Apr 17, 2025, 12:38 AM • 2 Y
Y by RollingPanda4616, c_double_sharp
i thought the world was experiencing inflation, so why are the quality of problems in contests going down
This post has been edited 1 time. Last edited by Aaronjudgeisgoat, Apr 17, 2025, 12:38 AM
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Soupboy0
379 posts
Soupboy0
#114 h  Apr 17, 2025, 1:37 PM
Y by
bc why not
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K1mchi_
85 posts
K1mchi_
#115 h  Apr 17, 2025, 1:39 PM
Y by
Aaronjudgeisgoat wrote:
i thought the world was experiencing inflation, so why are the quality of problems in contests going down

quality is going down bc test writers cant keep up w inflation
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mulberrykid
141 posts
mulberrykid
#116 h  Apr 17, 2025, 3:08 PM
Y by
nothing is wrong with the solution, no whining about it. Not true for HHH but good for HHT.
Andyluo wrote:
dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716
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Craftybutterfly
454 posts
Craftybutterfly
#117 h  Apr 17, 2025, 3:09 PM
Y by
Aaronjudgeisgoat wrote:
i thought the world was experiencing inflation, so why are the quality of problems in contests going down

2025 AMC 8 is significantly easier so as 2024 AMC 10
This post has been edited 1 time. Last edited by Craftybutterfly, Apr 17, 2025, 3:09 PM
Reason: :D
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RollingPanda4616
256 posts
RollingPanda4616
#118 h  Apr 17, 2025, 3:32 PM
Y by
Aaronjudgeisgoat wrote:
i thought the world was experiencing inflation, so why are the quality of problems in contests going down

skimpflation!
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UberPiggy
43 posts
UberPiggy
#119 h  Apr 17, 2025, 5:15 PM
Y by
mulberrykid wrote:
nothing is wrong with the solution, no whining about it. Not true for HHH but good for HHT.
Andyluo wrote:
dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716

But that's the thing: if it using reciprocals works for HHT but not HHH, that means it does not work universally. It is most likely that MathCounts tried to use an incorrect shortcut that coincidentally ended up giving the same answer.
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Craftybutterfly
454 posts
Craftybutterfly
#120 h  Apr 18, 2025, 4:58 AM
Y by
Andyluo wrote:
dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716

have i been scammed
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derekwang2048
1225 posts
derekwang2048
#121 h  Apr 18, 2025, 5:26 PM
Y by
yes.
but it is also dottedcaculator not dottedcalculator
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