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k a My Retirement & New Leadership at AoPS
rrusczyk   1571
N Mar 26, 2025 by SmartGroot
I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE
1571 replies
rrusczyk
Mar 24, 2025
SmartGroot
Mar 26, 2025
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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
Our full course list for upcoming classes is below:
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0 replies
jlacosta
Mar 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
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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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GOTEEM #5: Circumcircle passes through fixed point
tworigami   22
N 18 minutes ago by ohiorizzler1434
Source: GOTEEM: Mock Geometry Contest
Let $ABC$ be a triangle and let $B_1$ and $C_1$ be variable points on sides $\overline{BA}$ and $\overline{CA}$, respectively, such that $BB_1 = CC_1$. Let $B_2 \neq B_1$ denote the point on $\odot(ACB_1)$ such that $BC_1$ is parallel to $B_1B_2$, and let $C_2 \neq C_1$ denote the point on $\odot(ABC_1)$ such that $CB_1$ is parallel to $C_1C_2$. Prove that as $B_1, C_1$ vary, the circumcircle of $\triangle AB_2C_2$ passes through a fixed point, other than $A$.

Proposed by tworigami
22 replies
tworigami
Jan 2, 2020
ohiorizzler1434
18 minutes ago
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Great orz
Hip1zzzil   2
N 26 minutes ago by pokmui9909
Source: FKMO 2025 P5
$S={1,2,...,1000}$ and $T'=\left\{ 1001-t|t \in T\right\}$.
A set $P$ satisfies the following three conditions:
$1.$ All elements of $P$ are a subset of $S$.
$2. A,B \in P \Rightarrow A \cap B \neq \O$
$3. A \in P \Rightarrow A' \in P$
Find the maximum of $|P|$.
2 replies
Hip1zzzil
an hour ago
pokmui9909
26 minutes ago
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Math Problem(s)
greenhuman23   2
N 30 minutes ago by corgi61
Fill in the blanks to make the equation true.
( __−__ ) ⋅ __ ÷ __ + __ = 59/7

With the digit(s) below make the equation true-

$1$, $3$, $5$, $7$, $9$.
2 replies
greenhuman23
2 hours ago
corgi61
30 minutes ago
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Easy Geometry
pokmui9909   3
N 35 minutes ago by whwlqkd
Source: FKMO 2025 P4
Triangle $ABC$ satisfies $\overline{CA} > \overline{AB}$. Let the incenter of triangle $ABC$ be $\omega$, which touches $BC, CA, AB$ at $D, E, F$, respectively. Let $M$ be the midpoint of $BC$. Let the circle centered at $M$ passing through $D$ intersect $DE, DF$ at $P(\neq D), Q(\neq D)$, respecively. Let line $AP$ meet $BC$ at $N$, line $BP$ meet $CA$ at $L$. Prove that the three lines $EQ, FP, NL$ are concurrent.
3 replies
pokmui9909
41 minutes ago
whwlqkd
35 minutes ago
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Math Competitions
anishka14   5
N an hour ago by iwillregretthisnamelater
Hi everyone!

So I am currently in grade 6, and if anyone could give any tips for getting high scores in math competition, that would be great!

I haven't been doing so well in AMC 8, and other competitions like Math Kangaroo, etc....

I feel like i'm stuck, so if anyone could give any resources that helped you learn and score better, could you share that with me?

Thank you so much!

( also how much time should i spend on math every day? )
5 replies
anishka14
Yesterday at 7:55 PM
iwillregretthisnamelater
an hour ago
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Powers of 10
PatTheKing806   4
N 2 hours ago by PatTheKing806
What is (9 x 10^10) - (4 x 10^10)
4 replies
PatTheKing806
Jun 29, 2022
PatTheKing806
2 hours ago
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Brasil NMO (OBM) - 2007
oscar_sanz012   1
N 2 hours ago by ND_
Show that there exists an integer ? such that
[tex3]\frac{a^{29} - 1}{a - 1}[/tex3]
have at least 2007 distinct prime factors.
1 reply
oscar_sanz012
Yesterday at 11:08 PM
ND_
2 hours ago
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Inspired by old results
sqing   5
N 2 hours ago by MathsII-enjoy
Source: Own
Let $ a,b,c > 0 $ and $ a+b+c +abc =4. $ Prove that
$$ a^2 + b^2 + c^2 + 3 \geq 2( ab+bc + ca )$$Let $ a,b,c > 0 $ and $ ab+bc+ca+abc=4. $ Prove that
$$ a^2 + b^2 + c^2 + 2abc \geq 5$$
5 replies
sqing
Mar 27, 2025
MathsII-enjoy
2 hours ago
J
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Inspired by Crux 4975
sqing   1
N 2 hours ago by sqing
Source: Own
Let $ a,b\geq 0 $ and $a^2+b^2+ab+a+b=1. $ Prove that
$$ a^2+b^2+3ab(a+ b-1 ) \geq \frac{1}{9} $$$$\frac{4}{9}\geq a^2+b^2+3ab(a+ b ) \geq \frac{3-\sqrt 5}{2}$$$$\frac{7}{9}\geq a^2+b^2+3ab(a+ b +1) \geq \frac{3-\sqrt 5}{2}$$
1 reply
sqing
2 hours ago
sqing
2 hours ago
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the nearest distance in geometric sequence
David-Vieta   7
N 2 hours ago by Anthony2025
Source: 2024 China High School Olympics A P1
A positive integer \( r \) is given, find the largest real number \( C \) such that there exists a geometric sequence $\{ a_n \}_{n\ge 1}$ with common ratio \( r \) satisfying
$$ \| a_n \| \ge C $$for all positive integers \( n \). Here, $\| x \|$ denotes the distance from the real number \( x \) to the nearest integer.
7 replies
David-Vieta
Sep 8, 2024
Anthony2025
2 hours ago
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Geometric Sequence Squared
scls140511   5
N 3 hours ago by Anthony2025
Source: China Round 1 (Gao Lian)
2 Let there be an infinite geometric sequence $\{a_n\}$, where the common ratio $0<|q|<1$. Given that

$$\sum_{i=1}^\infty a_n = \sum_{i=1}^\infty a_n^2$$
find the largest possible range of $a_2$.
5 replies
scls140511
Sep 8, 2024
Anthony2025
3 hours ago
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An FE lemma about you!
gghx   11
N 3 hours ago by jasperE3
Source: Own, inspired by problem 556 in the FE marathon
Suppose $f:\mathbb{R}\rightarrow \mathbb{R}$ is your favourite function, $g:\mathbb{R}\rightarrow \mathbb{R}$ is your mother's favourite function, and $h:\mathbb{R}\rightarrow \mathbb{R}$ is your father's favourite function. It was discovered that for any reals $x,y$, $$f(xy+g(x))=xf(y)+h(x)$$Prove that you are boring.

(Hint: you might need to use the quotable result that if someone's favourite function is a linear polynomial, they are boring)
11 replies
gghx
Jun 14, 2022
jasperE3
3 hours ago
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Perfect Numbers
steven_zhang123   1
N 3 hours ago by lyllyl
Source: China TST 2001 Quiz 8 P2
If the sum of all positive divisors (including itself) of a positive integer $n$ is $2n$, then $n$ is called a perfect number. For example, the sum of the positive divisors of 6 is $1 + 2 + 3 + 6 = 2 \times 6$, hence 6 is a perfect number.
Prove: There does not exist a perfect number of the form $p^a q^b r^c$, where $a, b, c$ are positive integers, and $p, q, r$ are odd primes.
1 reply
steven_zhang123
6 hours ago
lyllyl
3 hours ago
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Something Horrible-a Challenge
Xueshuxue   19
N 3 hours ago by pieMax2713
Hello, I was wondering if it's possible to make 8 with the numbers 5, 3, 5, and 7 under the following rules:
-You can only use 5 twice, 3 once, and 7 once.
-You must use all the numbers.
You can stack numbers to form larger numbers (example: I could take 3 and 5 and turn it into 35 or 53, or use 7, 3, and 5 to make 375.)
-You are allowed to use parentheses.
(Also, I already found out that no 3 digital numbers will work for the solution.)
19 replies
Xueshuxue
Friday at 7:09 PM
pieMax2713
3 hours ago
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real math problems
Soupboy0   22
N 5 hours ago by elizhang101412
Ill be posting questions once in a while. Here's the first question:

What fraction of numbers from $1$ to $1000$ have the digit $7$ and are divisible by $3$?
22 replies
Soupboy0
Mar 25, 2025
elizhang101412
5 hours ago
J
real math problems
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Reveal topic tags
is 3 divisible by 7
is 7 divisible by 3
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Soupboy0
218 posts
Soupboy0
#1 h  Mar 25, 2025, 11:40 PM
Y by
Ill be posting questions once in a while. Here's the first question:

What fraction of numbers from $1$ to $1000$ have the digit $7$ and are divisible by $3$?
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AbhayAttarde01
1463 posts
AbhayAttarde01
#2 h  Mar 26, 2025, 1:12 AM
Y by
i was typing up a casework solution and then realized I could do it a different way lol
kind of casework?
this is my first attempt at this if I'm wrong I'll see where I got it wrong
This post has been edited 1 time. Last edited by AbhayAttarde01, Mar 26, 2025, 1:12 AM
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Soupboy0
218 posts
Soupboy0
#4 h  Mar 26, 2025, 11:06 PM
Y by
Next problem: Find the exact value of $\lfloor(\frac{8}{3})^{10}\rfloor$ without a calculator.
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maromex
130 posts
maromex
#5 h  Mar 26, 2025, 11:38 PM
Y by
Click to reveal hidden text
hide tag no work we do a little trolling
This post has been edited 1 time. Last edited by maromex, Mar 26, 2025, 11:38 PM
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iwastedmyusername
49 posts
iwastedmyusername
#6 h  Mar 27, 2025, 2:03 AM
Y by
maromex wrote:
Click to reveal hidden text
hide tag no work we do a little trolling

yea i was thinking the same thing
i wonder if therers a non bash way to do it
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Soupboy0
218 posts
Soupboy0
#7 h  Mar 27, 2025, 3:41 AM
Y by
official approved solution
This post has been edited 2 times. Last edited by Soupboy0, Mar 27, 2025, 7:18 PM
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Soupboy0
218 posts
Soupboy0
#8 h  Mar 27, 2025, 7:15 PM
Y by
3) A $m \times n$ grid is made. $mn$ unit squares are created by separating the side with length $m$ in $m$ portions and separating the side with length $n$ in $n$ portions. Find, with proof, a formula for how many rectangles with sides parallel to the grid can be created in terms of $m$ and $n$. For example, when $m = 2$ and $n = 2$, it can be found by casework that $9$ rectangles can be created.
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cheltstudent
538 posts
cheltstudent
#9 h  Mar 27, 2025, 7:25 PM
Y by
sol
This post has been edited 2 times. Last edited by cheltstudent, Mar 27, 2025, 7:29 PM
Reason: gg
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elizhang101412
1189 posts
elizhang101412
#10 h  Mar 27, 2025, 8:01 PM
Y by
cheltstudent wrote:
sol

bro you are not slick with that ai usage :skull:
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cheltstudent
538 posts
cheltstudent
#11 h  Mar 27, 2025, 8:02 PM
Y by
wut... I have a parental controlled computer
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Soupboy0
218 posts
Soupboy0
#12 h  Friday at 2:18 PM
Y by
4) If positive integers $(a, b, c, d)$ satisfy $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}=\frac{13}{40}+\frac{13}{42}$, find the ordered pair $(a, b, c, d)$
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Mathdreams
1443 posts
Mathdreams
#13 h  Friday at 2:19 PM
Y by
Answer
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fruitmonster97
2415 posts
fruitmonster97
#14 h  Friday at 2:53 PM
Y by
that's the trivial sol @above, but i'd be suprised if this didn't have multiple sols:
greedy algorithm:
a=2: then 1/b+1/c+1/d=133/840. b=8 yields 1/c+1/d=1/105. The sols here can be found using sfft, some trivial ones for (c,d) are (106,105*106) and (210,210). b=9 and c=9 yields d=45, for example.
a=3: (3,4,21,840)
a=4: (4,4,8,105), (4,5,6,56)
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elizhang101412
1189 posts
elizhang101412
#15 h  Friday at 10:49 PM
Y by
cheltstudent wrote:
wut... I have a parental controlled computer

can you stop trying this bruh literally all the text is formatted like an ai
This post has been edited 1 time. Last edited by elizhang101412, Friday at 10:50 PM
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Soupboy0
218 posts
Soupboy0
#16 h  Friday at 11:19 PM
Y by
5) If $p$ and $q$ are positive integers, what is the probability that $5^p+7^q$ is divisible by $6$?
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corgi61
156 posts
corgi61
#17 h  Friday at 11:50 PM
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Solution
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iwastedmyusername
49 posts
iwastedmyusername
#18 h  Yesterday at 12:42 AM
Y by
cheltstudent wrote:
sol

idk man seems kinda sus
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cheltstudent
538 posts
cheltstudent
#19 h  Yesterday at 12:43 AM
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ya, it's same method but completely different wording
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RandomMathGuy500
53 posts
RandomMathGuy500
#20 h  Yesterday at 1:15 AM
Y by
cheltstudent wrote:
sol
yeah it's def AI
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cheltstudent
538 posts
cheltstudent
#21 h  Yesterday at 10:57 AM
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broooooooooooooooooo, i literally didn't
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maxamc
479 posts
maxamc
#22 h  Yesterday at 12:39 PM
Y by
cheltstudent wrote:
broooooooooooooooooo, i literally didn't

lying is banned
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Soupboy0
218 posts
Soupboy0
#23 h  Yesterday at 10:04 PM
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6) Leeoz posts a daily problem every $19, 20$, or $21$ hours, with equal probability. Soupboy0 posts a daily problem every $18, 21$, or $22$ hours, with equal probability. If both Leeoz and Soupboy0 post at the same time, what is the expected time that will elapse in hours before Leeoz and Soupboy0 post again?
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elizhang101412
1189 posts
elizhang101412
#24 h  5 hours ago
Y by
is it Click to reveal hidden text
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