Art of Problem Solving
AoPS Online AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy AoPS Academy
Small live classes for advanced math
and language arts learners in grades 1-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

We have your learning goals covered with Spring and Summer courses available. Enroll today!
No tags match your search
M
G
Topic
First Poster
Last Poster
H
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:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29

Prealgebra 2 Self-Paced

Prealgebra 2
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21


Introduction to Algebra A Self-Paced

Introduction to Algebra A
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19

Introduction to Number Theory
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Sunday, Mar 2 - Jun 22
Wednesday, Apr 16 - Jul 30
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Intermediate: Grades 8-12

Intermediate Algebra
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22

Intermediate Counting & Probability
Sunday, Mar 23 - Aug 3
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2

Intermediate Number Theory
Friday, Apr 11 - Jun 27
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8

Advanced: Grades 9-12

Olympiad Geometry
Wednesday, Mar 5 - May 21
Tuesday, Jun 10 - Aug 26

Calculus
Sunday, Mar 30 - Oct 5
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17

Group Theory
Thursday, Jun 12 - Sep 11

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

MATHCOUNTS/AMC 8 Advanced
Friday, Apr 11 - Jun 27
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Problem Series
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21

AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22

AMC 12 Final Fives
Sunday, May 18 - Jun 15

F=ma Problem Series
Wednesday, Jun 11 - Aug 27

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!

MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT

Programming

Introduction to Programming with Python
Monday, Mar 24 - Jun 16
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22

Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22

USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1

Physics

Introduction to Physics
Sunday, Mar 30 - Jun 22
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Tuesday, Mar 25 - Sep 2
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15

Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
jlacosta
Mar 2, 2025
0 replies
J
H
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
H
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
J
H
deduction from function
MetaphysicalWukong   3
N 29 minutes ago by pco
can we then deduce that h has exactly 1 zero?
3 replies
MetaphysicalWukong
an hour ago
pco
29 minutes ago
J
H
weird FE on R
frac   4
N 40 minutes ago by NicoN9
Source: probably own
Find all functions $f:\mathbb{R} \rightarrow \mathbb{R}$ such that
$$f(x+y)^2=xf(x+f(y))+yf(f(y))+f(xy)$$for all $x,y\in \mathbb{R}$.
4 replies
1 viewing
frac
Jan 4, 2025
NicoN9
40 minutes ago
J
H
number theory question?
jag11   3
N an hour ago by Anabcde
Find the smallest positive integer n such that n is a multiple of 11, n +1 is a multiple of 10, n + 2 is a
multiple of 9, n + 3 is a multiple of 8, n +4 is a multiple of 7, n +5 is a multiple of 6, n +6 is a multiple of
5, n + 7 is a multiple of 4, n + 8 is a multiple of 3, and n + 9 is a multiple of 2.

I tried doing the mods and simplifying it but I'm kinda confused.
3 replies
jag11
Yesterday at 10:41 PM
Anabcde
an hour ago
J
H
Circles and Chords
steven_zhang123   0
an hour ago
(1) Let \( A \) , \( B \) and \( C \) be points on circle \( O \) divided into three equal parts. Construct three equal circles \( O_1 \), \( O_2 \), and \( O_3 \) tangent to \( O \) internally at points \( A \), \( B \), and \( C \) respectively. Let \( P \) be any point on arc \( AC \), and draw tangents \( PD \), \( PE \), and \( PF \) to circles \( O_1 \), \( O_2 \), and \( O_3 \) respectively. Prove that \( PE = PD + PF \).

(2) Let \( A_1 \), \( A_2 \), \( \cdots \), \( A_n \) be points on circle \( O \) divided into \( n \) equal parts. Construct \( n \) equal circles \( O_1 \), \( O_2 \), \( \cdots \), \( O_n \) tangent to \( O \) internally at \( A_1 \), \( A_2 \), \( \cdots \), \( A_n \). Let \( P \) be any point on circle \( O \), and draw tangents \( PB_1 \), \( PB_2 \), \( \cdots \), \( PB_n \) to circles \( O_1 \), \( O_2 \), \( \cdots \), \( O_n \). If the sum of \( k \) of \( PB_1 \), \( PB_2 \), \( \cdots \), \( PB_n \) equals the sum of the remaining \( n-k \) (where \( n \geq k \geq 1 \)), find all such \( n \).
0 replies
steven_zhang123
an hour ago
0 replies
J
H
Integer FE
GreekIdiot   1
N an hour ago by pco
Let $\mathbb{N}$ denote the set of positive integers
Find all $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for all $a,b \in \mathbb{N}$ it holds that $f(ab+f(b-1))|bf(a+b)f(3b-2+a)$
1 reply
GreekIdiot
Yesterday at 8:53 PM
pco
an hour ago
J
H
Double factorial inequality
Snoop76   2
N 2 hours ago by Snoop76
Source: own
Show that: $$2n \cdot \sum_{k=0}^n (2k-1)!!{n\choose k}>\sum_{k=0}^n (2k+1)!!{n\choose k}$$Note: consider $(-1)!!=1$ and $n>1$
2 replies
Snoop76
Feb 7, 2025
Snoop76
2 hours ago
J
H
Algebra Problem
JetFire008   1
N 2 hours ago by aidan0626
Find the sum of the series
$$1^2-2^2+3^2-4^2+...+(-1)^n+1n^2$$
1 reply
JetFire008
2 hours ago
aidan0626
2 hours ago
J
H
Hyperbolic tangent
MetaphysicalWukong   6
N 2 hours ago by MetaphysicalWukong
Source: Kunwei Ding
Consider the function below. Can someone explain to me why that is the correct answer and find the value of a?
6 replies
MetaphysicalWukong
3 hours ago
MetaphysicalWukong
2 hours ago
J
H
Inequality with real numbers
JK1603JK   4
N 3 hours ago by SunnyEvan
Source: unknown
Let a,b,c are real numbers. Prove that (a^3+b^3+c^3+3abc)^4+(a+b+c)^3(a+b-c)^3(-a+b+c)^3(a-b+c)^3>=0
4 replies
JK1603JK
Yesterday at 6:48 AM
SunnyEvan
3 hours ago
J
H
Interesting inequality
sqing   1
N 3 hours ago by SunnyEvan
Source: Own
Let $ a,b,c\geq 0,(ab+c)(ac+b)\neq 0 $ and $ a+b+c=3 . $ Prove that
$$ \frac{1}{ab+c+k}+\frac{1}{ac+b+k} \geq\frac{2}{k+2} $$Where $ k\geq 0. $
1 reply
sqing
6 hours ago
SunnyEvan
3 hours ago
J
H
Amc10 prep question
Shadow6885   21
N 4 hours ago by Shadow6885
My question is how much of the geo and IA textbooks is relevant to AMC 10?
21 replies
Shadow6885
Mar 17, 2025
Shadow6885
4 hours ago
J
H
Water Watermelon
hwenterprise   9
N 4 hours ago by huajun78
A giant watermelon weighed 50 pounds and was 99 percent water. After sitting in the hot sun, some of the water evaporated so that the watermelon was only 98 percent water. What is the new weight of the watermelon?
9 replies
hwenterprise
Sep 18, 2005
huajun78
4 hours ago
J
H
Mathcounts STRATEGIES
Existing_Human1   28
N 4 hours ago by chesswillow
Hello commuinty!

I am wondering what your strategies are for mathcounts. Please note I do not mean tips. These can be for all rounds, but please specify. BTW, this is for state, but it can apply to any competition.

Ex:
Team - sit in a specific order
Target - do the easiest first
Sprint - go as fast as possible

I just made up the examples, and you will probably have better strategies, so if you want to help out, please do
28 replies
Existing_Human1
Mar 20, 2025
chesswillow
4 hours ago
J
H
MATHCOUNTS State Competition Thread
ilikemath247365   16
N 4 hours ago by jkim0656
I'll assume mathcounts state examination is over, but you can tell me to delete this post if I'm wrong:

$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline ilikemath247365 & 7 & 34 \\ \end{tabular}$
16 replies
ilikemath247365
6 hours ago
jkim0656
4 hours ago
J
H
J
H
Good Mocks for STate
Existing_Human1   4
N 5 hours ago by huajun78
Hello Community!

I am wondering what are the best mocks for state, with solutions
4 replies
Existing_Human1
Friday at 11:52 PM
huajun78
5 hours ago
J
Good Mocks for STate
G H J
Reveal topic tags
L
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Existing_Human1
187 posts
Existing_Human1
#1 h  Friday at 11:52 PM
Y by
Hello Community!

I am wondering what are the best mocks for state, with solutions
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
giratina3
445 posts
giratina3
#2 h  Yesterday at 4:26 AM
Y by
Existing_Human1 wrote:
Hello Community!

I am wondering what are the best mocks for state, with solutions

There's always Math with Ms. Lin for past problems, and you can always go to the AoPS search bar and search up "Mathcounts State Mock Contests". You can also go to the AoPS Mock Contests forum to check out some Mathcounts mocks. In my opinion, I would say grinding past problems is better than doing mocks. But that's just me :play_ball:
This post has been edited 2 times. Last edited by giratina3, Yesterday at 4:26 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Leeoz
146 posts
Leeoz
#3 h  Yesterday at 4:51 PM
Y by
Existing_Human1 wrote:
Hello Community!

I am wondering what are the best mocks for state, with solutions

there are no "best" mocks, but if you want to find some mock contests, this is the forum: mock contests
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ChaitraliKA
973 posts
ChaitraliKA
#4 h  Today at 1:01 AM
Y by
Try the Outside the Box mathcounts series trust
Sprint
Target

You can find many other mathcounts mocks on mathdash too
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
huajun78
30 posts
huajun78
#5 h  5 hours ago
Y by
Existing_Human1 wrote:
Hello Community!

I am wondering what are the best mocks for state, with solutions

If you google a year + mathcounts state sprint/target problems there will usually be a link to the pdf and you can download and print the questions.

Search up year + mathcounts state solutions to get the solutions pdf.
Z K Y
N Quick Reply
G
H
=
a