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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.

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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
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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 zeroes!.
ericheathclifffry   22
N 2 hours ago by Yihangzh
i personally have no idea
22 replies
ericheathclifffry
May 5, 2025
Yihangzh
2 hours ago
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Thailand geometry
EeEeRUT   4
N 2 hours ago by MathLuis
Source: Thailand MO 2025 P7
Let $ABC$ be a triangle with $AB < AC$. The tangent to the circumcircle of $\triangle ABC$ at $A$ intersects $BC$ at $D$. The angle bisector of $\angle BAC$ intersect $BC$ at $E$. Suppose that the perpendicular bisector of $AE$ intersect $AB, AC$ at $P,Q$, respectively. Show that $$\sqrt{\frac{BP}{CQ}} = \frac{AC \cdot BD}{AB \cdot CD}$$
4 replies
EeEeRUT
May 14, 2025
MathLuis
2 hours ago
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JBMO Shortlist 2021 G2
Lukaluce   10
N 2 hours ago by Adventure1000
Source: JBMO Shortlist 2021
Let $P$ be an interior point of the isosceles triangle $ABC$ with $\hat{A} = 90^{\circ}$. If
$$\widehat{PAB} + \widehat{PBC} + \widehat{PCA} = 90^{\circ},$$prove that $AP \perp BC$.

Proposed by Mehmet Akif Yıldız, Turkey
10 replies
Lukaluce
Jul 2, 2022
Adventure1000
2 hours ago
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Find digits
MihaiT   9
N 2 hours ago by MihaiT
Find digits $a,b,c$ s.t. $\frac{a}{a+b+c}=\overline{0,abc }$
9 replies
MihaiT
Yesterday at 4:56 PM
MihaiT
2 hours ago
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geometry
EeEeRUT   5
N 2 hours ago by MathLuis
Source: Thailand MO 2025 P4
Let $D,E$ and $F$ be touch points of the incenter of $\triangle ABC$ at $BC, CA$ and $AB$, respectively. Let $P,Q$ and $R$ be the circumcenter of triangles $AFE, BDF$ and $CED$, respectively. Show that $DP, EQ$ and $FR$ concurrent.
5 replies
EeEeRUT
May 13, 2025
MathLuis
2 hours ago
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Challenge: Make every number to 100 using 4 fours
CJB19   174
N 3 hours ago by awesomeming327.
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:
$$(4-4)*4*4=0$$$$4-4+4/4=1$$$$4/4+4/4=2$$$$(4+4+4)/4=3$$$$4+(4-4)*4=4$$$$4+4^{4-4}=5$$$$4!/4+4-4=6$$$$4+4-4/4=7$$$$4+4+4-4=8$$
174 replies
CJB19
May 15, 2025
awesomeming327.
3 hours ago
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cant understand so dumb
greenplanet2050   8
N 4 hours ago by tikachaudhuri
am i stupid or smth

2001 AMC 10

Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?

umm why isnt it 3^4
8 replies
greenplanet2050
Yesterday at 6:02 PM
tikachaudhuri
4 hours ago
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Foot from vertex to Euler line
cjquines0   31
N 5 hours ago by awesomeming327.
Source: 2016 IMO Shortlist G5
Let $D$ be the foot of perpendicular from $A$ to the Euler line (the line passing through the circumcentre and the orthocentre) of an acute scalene triangle $ABC$. A circle $\omega$ with centre $S$ passes through $A$ and $D$, and it intersects sides $AB$ and $AC$ at $X$ and $Y$ respectively. Let $P$ be the foot of altitude from $A$ to $BC$, and let $M$ be the midpoint of $BC$. Prove that the circumcentre of triangle $XSY$ is equidistant from $P$ and $M$.
31 replies
cjquines0
Jul 19, 2017
awesomeming327.
5 hours ago
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Grand finale of 2021 Iberoamerican MO
jbaca   5
N Yesterday at 10:50 PM by MathLuis
Source: 2021 Iberoamerican Mathematical Olympiad, P6
Consider a $n$-sided regular polygon, $n \geq 4$, and let $V$ be a subset of $r$ vertices of the polygon. Show that if $r(r-3) \geq n$, then there exist at least two congruent triangles whose vertices belong to $V$.
5 replies
jbaca
Oct 20, 2021
MathLuis
Yesterday at 10:50 PM
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Geometry
AlexCenteno2007   1
N Yesterday at 9:05 PM by Diamond-jumper76
Let ABC be an acute triangle and A′
the point diametrically opposite A on the circumcircle of the triangle. Through point A, draw the tangent to the circumcircle of triangle ABC that intersects line BC at point D, and take a point E on segment BC such that AD = ED. Let A′′ be the point on the circumcircle of triangle ABC
(other than A) that lies between the reflection of line AA′
and line AE. Show that lines A′A′′ and BC are parallel.
1 reply
AlexCenteno2007
Yesterday at 8:33 PM
Diamond-jumper76
Yesterday at 9:05 PM
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f(x^3 + y^3 + z^3) = f(x)^3 + f(y)^3 + f(z)^3
pigfly   15
N Yesterday at 8:26 PM by MathIQ.
Source: VietNam TST 2005, problem 3
Find all functions $f: \mathbb{Z} \mapsto \mathbb{Z}$ satisfying the condition: $f(x^3 +y^3 +z^3 )=f(x)^3+f(y)^3+f(z)^3.$
15 replies
pigfly
Aug 4, 2004
MathIQ.
Yesterday at 8:26 PM
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geometry problem
invt   1
N Yesterday at 8:22 PM by Diamond-jumper76
In a triangle $ABC$ with $\angle B<\angle C$, denote its incenter and midpoint of $BC$ by $I$, $M$, respectively. Let $C'$ be the reflected point of $C$ wrt $AI$. Let the lines $MC'$ and $CI$ meet at $X$. Suppose that $\angle XAI=\angle XBI=90^{\circ}$. Prove that $\angle C=2\angle B$.
1 reply
invt
Saturday at 11:59 AM
Diamond-jumper76
Yesterday at 8:22 PM
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Gergonne point Harmonic quadrilateral
niwobin   3
N Yesterday at 7:51 PM by niwobin
Triangle ABC has incircle touching the sides at D, E, F as shown.
AD, BE, CF concurrent at Gergonne point G.
BG and CG cuts the incircle at X and Y, respectively.
AG cuts the incircle at K.
Prove: K, X, D, Y form a harmonic quadrilateral. (KX/KY = DX/DY)
3 replies
niwobin
Saturday at 8:17 PM
niwobin
Yesterday at 7:51 PM
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A "side chase" for juniors
Lukaluce   3
N Yesterday at 7:34 PM by lksb
Source: 2025 Junior Macedonian Mathematical Olympiad P5
Let $M$ be the midpoint of side $BC$ in $\triangle ABC$, and $P \neq B$ is such that the quadrilateral $ABMP$ is cyclic and the circumcircle of $\triangle BPC$ is tangent to the line $AB$. If $E$ is the second common point of the line $BP$ and the circumcircle of $\triangle ABC$, determine the ratio $BE: BP$.
3 replies
Lukaluce
Yesterday at 3:37 PM
lksb
Yesterday at 7:34 PM
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Nice Combinatorics Problem
RabtejKalra   10
N Apr 12, 2025 by sadas123
A number is considered happy if it contains at least one digit exactly twice. For instance, the numbers 2020 and 2024 are happy, but the numbers 2019 and 2022 are not. How many happy counting numbers are there that are less than 10,000?
10 replies
RabtejKalra
Apr 11, 2025
sadas123
Apr 12, 2025
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Nice Combinatorics Problem
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Reveal topic tags
combinatorics
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RabtejKalra
69 posts
RabtejKalra
#1 h  Apr 11, 2025, 10:16 PM
Y by
A number is considered happy if it contains at least one digit exactly twice. For instance, the numbers 2020 and 2024 are happy, but the numbers 2019 and 2022 are not. How many happy counting numbers are there that are less than 10,000?
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HacheB2031
397 posts
HacheB2031
#2 h  Apr 11, 2025, 10:32 PM
Y by
ez sol
This post has been edited 1 time. Last edited by HacheB2031, Apr 11, 2025, 10:36 PM
Reason: imagine having a computational error wouldnt be me
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Bummer12345
150 posts
Bummer12345
#3 h  Apr 11, 2025, 10:38 PM
Y by
@above there can also be numbers with a digit that repeats more than twice
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HacheB2031
397 posts
HacheB2031
#4 h  Apr 11, 2025, 10:42 PM
Y by
Bummer12345 wrote:
@above there can also be numbers with a digit that repeats more than twice

oops yeah i didn't count $0043$ and stuff let me fix that
HacheB2031 wrote:
idoit sol
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RabtejKalra
69 posts
RabtejKalra
#5 h  Apr 11, 2025, 11:03 PM
Y by
No, 0043 and stuf like that would just be considered 43, so they're sad numbers
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maxamc
581 posts
maxamc
#6 h  Apr 11, 2025, 11:05 PM
Y by
sol
This post has been edited 1 time. Last edited by maxamc, Apr 12, 2025, 12:19 AM
Reason: mistake
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iwastedmyusername
166 posts
iwastedmyusername
#7 h  Apr 12, 2025, 12:00 AM
Y by
maxamc wrote:
sol

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383
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maxamc
581 posts
maxamc
#8 h  Apr 12, 2025, 12:18 AM
Y by
iwastedmyusername wrote:
maxamc wrote:
sol

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383

oops, edited my post
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sadas123
1315 posts
sadas123
#9 h  Apr 12, 2025, 2:08 AM
Y by
Bashy 3 minute solution

I took a bit of inspiration from you @maxamc
This post has been edited 2 times. Last edited by sadas123, Apr 12, 2025, 1:23 PM
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maxamc
581 posts
maxamc
#10 h  Apr 12, 2025, 3:21 AM
Y by
sadas123 wrote:
Bashy 3 minute solution

I took a bit of inspiration from you @maxamc

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383
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sadas123
1315 posts
sadas123
#11 h  Apr 12, 2025, 1:22 PM
Y by
maxamc wrote:
sadas123 wrote:
Bashy 3 minute solution

I took a bit of inspiration from you @maxamc

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383

oh woops wait I am dumb :( I should have saw that updating my thingie
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