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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
an hour ago
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 16th (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
+1 w
jlacosta
an hour ago
0 replies
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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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Find pair of m and n numbers
abduqahhor_math   5
N a minute ago by abduqahhor_math
(m+6:n)=4*(m;n)
5 replies
abduqahhor_math
Mar 31, 2025
abduqahhor_math
a minute ago
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Prove that
abduqahhor_math   2
N 3 minutes ago by abduqahhor_math
n^2+3n+5 is not divided to 121
2 replies
abduqahhor_math
Monday at 5:37 PM
abduqahhor_math
3 minutes ago
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geometry incentre config
Tony_stark0094   2
N 12 minutes ago by LearnMath_105
In a triangle $\Delta ABC$ $I$ is the incentre and point $F$ is defined such that $F \in AC$ and $F \in \odot BIC$
prove that $AI$ is the perpendicular bisector of $BF$
2 replies
Tony_stark0094
Yesterday at 4:09 PM
LearnMath_105
12 minutes ago
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Geo Mock #5
Bluesoul   1
N an hour ago by Sedro
Consider triangle $ABC$ with $AB=13, BC=14, AC=15$. Denote the orthocenter of $\triangle{ABC}$ as $H$, the intersection of $(BHC)$ and $AC$ as $P\neq C$. Compute the length of $AP$.
1 reply
Bluesoul
Yesterday at 7:03 AM
Sedro
an hour ago
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Any nice way to do this?
NamelyOrange   1
N 3 hours ago by HockeyMaster85
Source: Taichung P.S.1 math program tryouts

How many ordered pairs $(a,b,c)\in\mathbb{N}^3$ are there such that $c=ab$ and $1\le a\le b\le c\le60$?
1 reply
NamelyOrange
3 hours ago
HockeyMaster85
3 hours ago
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Polynomial optimization problem
ReticulatedPython   2
N 4 hours ago by Mathzeus1024
Let $$p(x)=-ax^4+x^3$$, where $a$ is a real number. Prove that for all positive $a$, $$p(x) \le \frac{27}{256a^3}.$$
2 replies
ReticulatedPython
Mar 31, 2025
Mathzeus1024
4 hours ago
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a+b+c=3 inequality
JK1603JK   1
N 4 hours ago by KhuongTrang
Let $a,b,c\ge 0: a+b+c=3$ then prove
$$\color{black}{\sqrt{a+b+2c^{2}}+\sqrt{b+c+2a^{2}}+\sqrt{c+a+2b^{2}}\le 3\sqrt{\frac{a^2+b^2+c^2}{ab+bc+ca}+3}.}$$
1 reply
JK1603JK
5 hours ago
KhuongTrang
4 hours ago
J
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Complex + Radical Evaluation
Saucepan_man02   4
N 4 hours ago by Mathzeus1024
Evaluate: (without calculators)
$$ (\sqrt{6 - 2 \sqrt{5}} + i \sqrt{2 \sqrt{5} + 10})^5 + (\sqrt{6 - 2 \sqrt{5}} - i \sqrt{2 \sqrt{5} + 10})^5$$
4 replies
Saucepan_man02
Mar 17, 2025
Mathzeus1024
4 hours ago
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Inequality
JK1603JK   1
N Today at 9:52 AM by lbh_qys
Let $a,b,c\ge 0: a+b+c=3$ then prove \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{2}\cdot\frac{abc}{ab+bc+ca}\ge \frac{5}{3}.$$
1 reply
JK1603JK
Today at 9:12 AM
lbh_qys
Today at 9:52 AM
J
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Inequality
JK1603JK   1
N Today at 8:38 AM by lbh_qys
Prove that 9ab\left(a-b+c\right)+9bc\left(b-c+a\right)+9ca\left(c-a+b\right)\ge \left(a+b+c\right)^{3},\ \ a\ge 0\ge b\ge c: a+b+c\le 0.
1 reply
JK1603JK
Today at 8:27 AM
lbh_qys
Today at 8:38 AM
J
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Solve the equetion
yt12   4
N Today at 8:00 AM by lgx57
Solve the equetion:$\sin 2x+\tan x=2$
4 replies
yt12
Mar 31, 2025
lgx57
Today at 8:00 AM
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Inequalities
sqing   2
N Today at 7:41 AM by sqing
Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=11.$ Prove that
$$a+ab+abc\leq\frac{49}{6}$$Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=10.$ Prove that
$$a+ab+abc\leq\frac{169}{24}$$Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=14.$ Prove that
$$a+ab+abc\leq\frac{63+5\sqrt 5}{6}$$Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=32.$ Prove that
$$a+ab+abc\leq48+\frac{64\sqrt{2}}{3}$$
2 replies
sqing
Yesterday at 2:59 PM
sqing
Today at 7:41 AM
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geometry
Tony_stark0094   1
N Today at 7:36 AM by Tony_stark0094
Consider $\Delta ABC$ let $\omega_1$ and $\omega_2$ be the circles passing through $A,B$ and $A,C$ respectively such that $BC$ is tangent to $\omega_1$ and $\omega_2$ define $R$ to be a point such that it lies on both the circles $\omega_1$ and $\omega_2$ prove that $HR$ and $AR$ are perpendicular.
1 reply
Tony_stark0094
Today at 7:04 AM
Tony_stark0094
Today at 7:36 AM
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one very nice!
MihaiT   1
N Today at 5:28 AM by MihaiT
Given $m_1$ weights, each weighing $k_1$ and another $m_2$ weights with $k_2$ each. Write a algorithm that determines the ways in which a scale can be balanced with a weight $X$ on the left pan, and display the number of possible solutions. (The weights can be placed on both pans and the program starts with the numbers $m_1,k_1,m_2,k_2,X$. What will be displayed after three successive runs: 5,2,5,1,4 | 5,2,5,1,11 | 5,2,5,1,20?

One answer is possible:
a)10;5;0;
b)20;7;0;
c)20;7;1;
d)10;10;0;
e)10;7;0;
f)20;5;0,
1 reply
MihaiT
Mar 31, 2025
MihaiT
Today at 5:28 AM
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reg. hexagon on 4 concentric circles, arithm.(Oral Moscow Team MO 2006.1.11A8)
parmenides51   2
N Dec 5, 2020 by parmenides51
Is there a regular hexagon whose vertices lie on six concentric spheres whose radii form an arithmetic progression?
2 replies
parmenides51
Dec 5, 2020
parmenides51
Dec 5, 2020
J
reg. hexagon on 4 concentric circles, arithm.(Oral Moscow Team MO 2006.1.11A8)
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Reveal topic tags
geometry
Arithmetic Progression
hexagon
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parmenides51
30629 posts
parmenides51
#1 h  Dec 5, 2020, 12:28 AM • 1 Y
Y by Mango247
Is there a regular hexagon whose vertices lie on six concentric spheres whose radii form an arithmetic progression?
This post has been edited 1 time. Last edited by parmenides51, Dec 5, 2020, 3:17 PM
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HamstPan38825
8857 posts
HamstPan38825
#2 h  Dec 5, 2020, 12:31 AM
Y by
Isn't this very similar to a previous post?
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parmenides51
30629 posts
parmenides51
#3 h  Dec 5, 2020, 11:04 AM
Y by
yes indeed, it refers to a different grade
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