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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
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
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
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 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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.

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0 replies
jlacosta
Apr 2, 2025
0 replies
J
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Combinatoric
spiderman0   1
N 4 hours ago by MathBot101101
Let $ S = \{1, 2, 3, \ldots, 2024\}.$ Find the maximum positive integer $n \geq 2$ such that for every subset $T \subset S$ with n elements, there always exist two elements a, b in T such that:

$|\sqrt{a} - \sqrt{b}| < \frac{1}{2} \sqrt{a - b}$
1 reply
spiderman0
Yesterday at 7:46 AM
MathBot101101
4 hours ago
J
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Combinatorial proof
MathBot101101   10
N 5 hours ago by MathBot101101
Is there a way to prove
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}=1-\frac{1}{{n+1)!}
without induction and using only combinatorial arguments?

Induction proof wasn't quite as pleasing for me.
10 replies
MathBot101101
Apr 20, 2025
MathBot101101
5 hours ago
J
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Simiplifying a Complicated Expression
phiReKaLk6781   6
N 5 hours ago by lbh_qys
Simplify: $ \frac{a^3}{(a-b)(a-c)}+\frac{b^3}{(b-a)(b-c)}+\frac{c^3}{(c-a)(c-b)}$
6 replies
phiReKaLk6781
Mar 15, 2010
lbh_qys
5 hours ago
J
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Introducing myself at AoPS, and what's your magic wand?
asuth_asuth   936
N Today at 4:49 AM by valisaxieamc
Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.
936 replies
asuth_asuth
Mar 30, 2025
valisaxieamc
Today at 4:49 AM
J
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Geometry Angle Chasing
Sid-darth-vater   2
N Yesterday at 10:21 PM by Sid-darth-vater
Is there a way to do this without drawing obscure auxiliary lines? (the auxiliary lines might not be obscure I might just be calling them obscure)

For example I tried rotating triangle MBC 80 degrees around point C (so the BC line segment would now lie on segment AC) but I couldn't get any results. Any help would be appreciated!
2 replies
Sid-darth-vater
Monday at 11:50 PM
Sid-darth-vater
Yesterday at 10:21 PM
J
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k Alcumus Error
AtlantisHSK2   4
N Yesterday at 8:25 PM by jlacosta
Hi I've been doing pre 2 (I'm almost done), however I am having a problem with the alcumus that is integrated into the program. I have finished these alcumus sections well over 3 times, but after a few days they display that they're unfinished, I was wondering whether this was a bug and if there is some way to fix it.
4 replies
AtlantisHSK2
Yesterday at 7:36 PM
jlacosta
Yesterday at 8:25 PM
J
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Absolute value
Silverfalcon   8
N Yesterday at 7:46 PM by zhoujef000
This problem seemed to be too obvious.. And I think I"m wrong.. :D

Problem:

Consider the sequence $x_0, x_1, x_2,...x_{2000}$ of integers satisfying

\[x_0 = 0, |x_n| = |x_{n-1} + 1|\]

for $n = 1,2,...2000$.

Find the minimum value of the expression $|x_1 + x_2 + ... x_{2000}|$.

My idea

Pretty sure I'm wrong but where did I go wrong?
8 replies
Silverfalcon
Jun 27, 2005
zhoujef000
Yesterday at 7:46 PM
J
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Tetrahedrons and spheres
ReticulatedPython   3
N Yesterday at 7:26 PM by vanstraelen
Let $OABC$ be a tetrahedron such that $\angle{AOB}=\angle{AOC}=\angle{BOC}=90^\circ.$ A sphere of radius $r$ is circumscribed about tetrahedron $OABC.$ Given that $OA=a$, $OB=b$, and $OC=c$, prove that $$r^2+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \ge \frac{9\sqrt[3]{4}}{4}$$with equality at $a=b=c=\sqrt[3]{2}.$
3 replies
ReticulatedPython
Monday at 6:39 PM
vanstraelen
Yesterday at 7:26 PM
J
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k help me PLEASE
dwead   4
N Yesterday at 6:29 PM by jlacosta
Im wondering if there is any way to reset progress in a specific subject in alcumus like algebra or geometry the reason i want to do that is because im getting progress when im not even doing them and it's kinda annoying when i have to skip the ones that ive done but really haven't
4 replies
dwead
Yesterday at 12:12 PM
jlacosta
Yesterday at 6:29 PM
J
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Σ to ∞
phiReKaLk6781   3
N Yesterday at 6:12 PM by Maxklark
Evaluate: $ \sum\limits_{k=1}^\infty \frac{1}{k\sqrt{k+2}+(k+2)\sqrt{k}}$
3 replies
phiReKaLk6781
Mar 20, 2010
Maxklark
Yesterday at 6:12 PM
J
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Geometric inequality
ReticulatedPython   0
Yesterday at 5:12 PM
Let $A$ and $B$ be points on a plane such that $AB=n$, where $n$ is a positive integer. Let $S$ be the set of all points $P$ such that $\frac{AP^2+BP^2}{(AP)(BP)}=c$, where $c$ is a real number. The path that $S$ traces is continuous, and the value of $c$ is minimized. Prove that $c$ is rational for all positive integers $n.$
0 replies
ReticulatedPython
Yesterday at 5:12 PM
0 replies
J
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Inequalities
sqing   27
N Yesterday at 3:51 PM by Jackson0423
Let $ a,b $ be reals such that $ a^2+ab+b^2 =3$ . Prove that
$$ \frac{4}{ 3}\geq \frac{1}{ a^2+5 }+ \frac{1}{ b^2+5 }+ab \geq -\frac{11}{4 }$$$$ \frac{13}{ 4}\geq \frac{1}{ a^2+5 }+ \frac{1}{ b^2+5 }+ab \geq -\frac{2}{3 }$$$$ \frac{3}{ 2}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }+ab \geq -\frac{17}{6 }$$$$ \frac{19}{ 6}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }-ab \geq -\frac{1}{2}$$Let $ a,b $ be reals such that $ a^2-ab+b^2 =1 $ . Prove that
$$ \frac{3}{ 2}\geq \frac{1}{ a^2+3 }+ \frac{1}{ b^2+3 }+ab \geq \frac{4}{15 }$$$$ \frac{14}{ 15}\geq \frac{1}{ a^2+3 }+ \frac{1}{ b^2+3 }-ab \geq -\frac{1}{2 }$$$$ \frac{3}{ 2}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }+ab \geq \frac{13}{42 }$$$$ \frac{41}{ 42}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }-ab \geq -\frac{1}{2 }$$
27 replies
sqing
Apr 16, 2025
Jackson0423
Yesterday at 3:51 PM
J
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Problem of the Week--The Sleeping Beauty Problem
FiestyTiger82   1
N Yesterday at 3:24 PM by martianrunner
Put your answers here and discuss!
The Problem
1 reply
FiestyTiger82
Yesterday at 2:30 PM
martianrunner
Yesterday at 3:24 PM
J
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k Happy Easter!!!
A_Crabby_Crab   37
N Monday at 11:43 AM by MathDolphin95
Happy Easter to all on Aops!!!

I hope everyone on this awesome website will be filled with peace, joy and love this season (its 50 days long y'all so start partying and eat some jelly beans if you can).

37 replies
A_Crabby_Crab
Apr 20, 2025
MathDolphin95
Monday at 11:43 AM
J
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J
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k New reaper game
Squidget   10
N Mar 27, 2025 by Cerberusman
What does this mean?

Is this a glitch
10 replies
Squidget
Mar 26, 2025
Cerberusman
Mar 27, 2025
J
New reaper game
G H J
Reveal topic tags
Reaper
L
G H BBookmark kLocked kLocked NReply
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Squidget
433 posts
Squidget
#1 h  Mar 26, 2025, 10:31 PM
Y by
What does this mean?

Is this a glitch
Attachments:
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Gabrielle.Esther
649 posts
Gabrielle.Esther
#2 h  Mar 26, 2025, 10:33 PM
Y by
if you click on it:
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Aminecraftbear
1415 posts
Aminecraftbear
#3 h  Mar 26, 2025, 10:35 PM • 1 Y
Y by skronkmonster
it starts on april first lol
its some kind of prank
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AmethystC
84 posts
AmethystC
#4 h  Mar 26, 2025, 10:36 PM
Y by
It starts on April Fools day, at 3:00 am. The description is: Is this a reaper game idk. Could be a prank/joke
This post has been edited 1 time. Last edited by AmethystC, Mar 26, 2025, 10:37 PM
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Aminecraftbear
1415 posts
Aminecraftbear
#5 h  Mar 26, 2025, 10:43 PM
Y by
nah its 3am eastern so it might just be based on midnight pst
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FunnyKoala17
170 posts
FunnyKoala17
#6 h  Mar 26, 2025, 10:58 PM
Y by
What is reaper
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cookie130
474 posts
cookie130
#7 h  Mar 26, 2025, 11:10 PM • 1 Y
Y by MathPerson12321
bruh if i want to play i cant sleep and will have to play at the cursed time
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rhydon516
550 posts
rhydon516
#9 h  Mar 27, 2025, 3:29 AM • 1 Y
Y by c_double_sharp
look up. there's a plane waving a banner saying "gullible."
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Demetri
1304 posts
Demetri
#10 h  Mar 27, 2025, 2:22 PM • 1 Y
Y by Exponent11
rhydon516 wrote:
look up. there's a plane waving a banner saying "gullible."
No :)
Great time to start a reaper game lol
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skronkmonster
2182 posts
skronkmonster
#11 h  Mar 27, 2025, 2:26 PM • 1 Y
Y by MathPerson12321
The game will probably disappear precisely on April 1st
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Cerberusman
316 posts
Cerberusman
#12 h  Mar 27, 2025, 2:31 PM • 2 Y
Y by MathPerson12321, Exponent11
Demetri wrote:
rhydon516 wrote:
look up. there's a plane waving a banner saying "gullible."
No :)
Great time to start a reaper game lol

the "goodbye richard" reaper game :rotfl:
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