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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]
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0 replies
jlacosta
Mar 2, 2025
0 replies
"Mistakes were made" -Luke Rbotaille
a1267ab   9
N 11 minutes ago by asbodke
Source: USA TST 2025
Let $a_1, a_2, \dots$ and $b_1, b_2, \dots$ be sequences of real numbers for which $a_1 > b_1$ and
\begin{align*}
    a_{n+1} &= a_n^2 - 2b_n\\
    b_{n+1} &= b_n^2 - 2a_n
\end{align*}for all positive integers $n$. Prove that $a_1, a_2, \dots$ is eventually increasing (that is, there exists a positive integer $N$ for which $a_k < a_{k+1}$ for all $k > N$).

Holden Mui
9 replies
a1267ab
Dec 14, 2024
asbodke
11 minutes ago
Yet another circle!
Rushil   7
N 25 minutes ago by FireMaths
Source: INMO 1999 Problem 4
Let $\Gamma$ and $\Gamma'$ be two concentric circles. Let $ABC$ and $A'B'C'$ be any two equilateral triangles inscribed in $\Gamma$ and $\Gamma'$ respectively. If $P$ and $P'$ are any two points on $\Gamma$ and $\Gamma'$ respectively, show that \[ P'A^2 + P'B^2 + P'C^2 = A'P^2 + B'P^2 + C'P^2. \]
7 replies
Rushil
Oct 7, 2005
FireMaths
25 minutes ago
Binary Operator from AMC 10
pinetree1   36
N 38 minutes ago by Ilikeminecraft
Source: USA TSTST 2019 Problem 1
Find all binary operations $\diamondsuit: \mathbb R_{>0}\times \mathbb R_{>0}\to \mathbb R_{>0}$ (meaning $\diamondsuit$ takes pairs of positive real numbers to positive real numbers) such that for any real numbers $a, b, c > 0$,
[list]
[*] the equation $a\,\diamondsuit\, (b\,\diamondsuit \,c) = (a\,\diamondsuit \,b)\cdot c$ holds; and
[*] if $a\ge 1$ then $a\,\diamondsuit\, a\ge 1$.
[/list]
Evan Chen
36 replies
pinetree1
Jun 25, 2019
Ilikeminecraft
38 minutes ago
Interesting inequality
sqing   4
N an hour ago by lbh_qys
Source: Own
Let $ a,b\geq 2  . $ Prove that
$$(a^2-1)(b^2-1) -6ab\geq-15$$$$(a^2-1)(b^2-1)  -7ab\geq  -\frac{58}{3}$$$$(a^3-1)(b^3-1)  -\frac{21}{4}a^2b^2\geq -35$$$$(a^3-1)(b^3-1)  -6a^2b^2\geq-\frac{2391}{49}$$
4 replies
1 viewing
sqing
2 hours ago
lbh_qys
an hour ago
No more topics!
100 Selected Problems Handout
Asjmaj   32
N Yesterday at 1:26 PM by John_Mgr
Happy New Year to all AoPSers!
 :clap2:

Here’s my modest gift to you all. Although I haven’t been very active in the forums, the AoPS community contributed to an immense part of my preparation and left a huge impact on me as a person. Consider this my way of giving back. I also want to take this opportunity to thank Evan Chen—his work has consistently inspired me throughout my olympiad journey, and this handout is no exception.



With 2025 drawing near, my High School Olympiad career will soon be over, so I want to share a compilation of the problems that I liked the most over the years and their respective detailed write-ups. Originally, I intended it just as a personal record, but I decided to give it some “textbook value” by not repeating the topics so that the selection would span many different approaches, adding hints, and including my motivations and thought process.

While IMHO it turned out to be quite instructive, I cannot call it a textbook by any means. I recommend solving it if you are confident enough and want to test your skills on miscellaneous, unordered, challenging, high-quality problems. Hints will allow you to not be stuck for too long, and the fully motivated solutions (often with multiple approaches) should help broaden your perspective. 



This is my first experience of writing anything in this format, and I’m not a writer by any means, so please forgive any mistakes or nonsense that may be written here. If you spot any typos, inconsistencies, or flawed arguments whatsoever (no one is immune :blush: ), feel free to DM me. In fact, I welcome any feedback or suggestions.

I left some authors/sources blank simply because I don’t know them, so if you happen to recognize where and by whom a problem originated, please let me know. And quoting the legend: “The ideas of the solution are a mix of my own work, the solutions provided by the competition organizers, and solutions found by the community. However, all the writing is maintained by me.” 



I’ll likely keep a separate file to track all the typos, and when there’s enough, I will update the main file. Some problems need polishing (at least aesthetically), and I also have more remarks to add.

This content is only for educational purposes and is not meant for commercial usage.



This is it! Good luck in 45^2, and I hope you enjoy working through these problems as much as I did!

Here's a link to Google Drive because of AoPS file size constraints: Selected Problems
32 replies
Asjmaj
Dec 31, 2024
John_Mgr
Yesterday at 1:26 PM
100 Selected Problems Handout
G H J
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Asjmaj
7 posts
#1 • 46 Y
Y by BaishuakRayimbek, Trenod, Ender_Claddy217, menpo, erke667, farbyy, Abidabi, megarnie, cursed_tangent1434, ehuseyinyigit, NicoN9, Ab_Rin, Dattier, Funcshun840, Pekiban, onyqz, Oksutok, GeorgeRP, Om245, happypi31415, Tem8, Jack_w, jason02, GeoKing, YaoAOPS, Aryan27, R8kt, anantmudgal09, Supercali, TestX01, Sedro, math_comb01, g0USinsane777, Vivouaf, TensorGuy666, CyclicISLscelesTrapezoid, devrandom42, ohhh, internationalnick123456, cubres, Iveela, yobu, hectorleo123, zhenghua, EpicBird08, Rounak_iitr
Happy New Year to all AoPSers!
 :clap2:

Here’s my modest gift to you all. Although I haven’t been very active in the forums, the AoPS community contributed to an immense part of my preparation and left a huge impact on me as a person. Consider this my way of giving back. I also want to take this opportunity to thank Evan Chen—his work has consistently inspired me throughout my olympiad journey, and this handout is no exception.



With 2025 drawing near, my High School Olympiad career will soon be over, so I want to share a compilation of the problems that I liked the most over the years and their respective detailed write-ups. Originally, I intended it just as a personal record, but I decided to give it some “textbook value” by not repeating the topics so that the selection would span many different approaches, adding hints, and including my motivations and thought process.

While IMHO it turned out to be quite instructive, I cannot call it a textbook by any means. I recommend solving it if you are confident enough and want to test your skills on miscellaneous, unordered, challenging, high-quality problems. Hints will allow you to not be stuck for too long, and the fully motivated solutions (often with multiple approaches) should help broaden your perspective. 



This is my first experience of writing anything in this format, and I’m not a writer by any means, so please forgive any mistakes or nonsense that may be written here. If you spot any typos, inconsistencies, or flawed arguments whatsoever (no one is immune :blush: ), feel free to DM me. In fact, I welcome any feedback or suggestions.

I left some authors/sources blank simply because I don’t know them, so if you happen to recognize where and by whom a problem originated, please let me know. And quoting the legend: “The ideas of the solution are a mix of my own work, the solutions provided by the competition organizers, and solutions found by the community. However, all the writing is maintained by me.” 



I’ll likely keep a separate file to track all the typos, and when there’s enough, I will update the main file. Some problems need polishing (at least aesthetically), and I also have more remarks to add.

This content is only for educational purposes and is not meant for commercial usage.



This is it! Good luck in 45^2, and I hope you enjoy working through these problems as much as I did!

Here's a link to Google Drive because of AoPS file size constraints: Selected Problems
Z K Y
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WheatNeat
224 posts
#2 • 7 Y
Y by alexanderhamilton124, NicoN9, ihatemath123, Sedro, DensSv, cubres, LawofCosine
"Good luck in 45^2", what a cold statement
Z K Y
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BaishuakRayimbek
8 posts
#3 • 1 Y
Y by cubres
Would recommend checking it out, very high-quality handout with a lot of effort put into it
Z K Y
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Ender_Claddy217
1 post
#4 • 1 Y
Y by cubres
Thank you for this book Miron!! This is a huge contribution to olympiad community
Z K Y
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fracta1l
1 post
#5 • 2 Y
Y by BaishuakRayimbek, cubres
I've never participated in math olympiads, but now I can finally "pochalit olmateshu".
Happy New Year
Z K Y
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youochange
157 posts
#6 • 1 Y
Y by cubres
Thanks.!!
Z K Y
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Forgood
1 post
#7 • 4 Y
Y by youochange, ehuseyinyigit, DensSv, cubres
maybe someday this book will be just a “beginning problem list” for future seventh graders
Z K Y
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bekshhh
2 posts
#8 • 1 Y
Y by cubres
for me personally, this is the best gift for the new year
Z K Y
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sunshine_2025
1 post
#9 • 3 Y
Y by NicoN9, ehuseyinyigit, cubres
High-quality book,book includes very good and selected problems,I recommend it for every problem solver,it will Increase your skills in problem solving. Thank you Miron for this book!
Z K Y
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pokpokben
17 posts
#10 • 1 Y
Y by cubres
excellent work!
Z K Y
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Nagibator007
10 posts
#11 • 1 Y
Y by cubres
Great work has been done, its very exciting book for math lovers, thank you very much, i am highly recommending this book
Z K Y
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quantam13
83 posts
#12 • 1 Y
Y by cubres
thanks so much for this high quality problem set!!
Z K Y
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AshAuktober
920 posts
#13 • 2 Y
Y by NicoN9, cubres
This is gonna be fun to try out!
I'm assuming problems aren't in difficulty order?
Z K Y
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ehuseyinyigit
773 posts
#14 • 1 Y
Y by cubres
Marvelous work!
Z K Y
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ehuseyinyigit
773 posts
#15 • 1 Y
Y by cubres
AshAuktober wrote:
This is gonna be fun to try out!
I'm assuming problems aren't in difficulty order?
It shouldn't because I GOT A JUMPSCARE AT FIRST SEEING MOSNTROUS IMO 2021 P2 RAAHAAAAAAA
This post has been edited 2 times. Last edited by ehuseyinyigit, Dec 31, 2024, 1:54 PM
Z K Y
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Oksutok
198 posts
#16 • 2 Y
Y by NicoN9, cubres
Nice, Happy New Year
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icepeach107
17 posts
#17 • 6 Y
Y by infinitymath2024, NicoN9, BGR2025, LegendsShine, cubres, COOLESTGUY
Wow, thanks for the book, it's excellent!
Happy New Year~!
Z K Y
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math_holmes15
8 posts
#18 • 2 Y
Y by NicoN9, cubres
Thank You for this amazing Happy New Year Gift! :-D
Happy New Year everyone!
Z K Y
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NicoN9
79 posts
#19 • 1 Y
Y by cubres
Happy New Year!!!
Z K Y
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jason02
24 posts
#20 • 1 Y
Y by cubres
Thanks for the book! Happy New Year!! :roll:
Z K Y
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Polymath45
1 post
#21 • 1 Y
Y by cubres
Thanks and Happy New Year!
Z K Y
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xytunghoanh
14 posts
#22 • 1 Y
Y by cubres
yeah thanks you so muchhh :D
Z K Y
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L13832
250 posts
#23 • 1 Y
Y by cubres
Amazing pset!! can anyone tell where I can find IOM problems, I think I might have a nice solution for IOM '19 P3
Z K Y
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Lufin
8 posts
#24 • 1 Y
Y by cubres
Wow! Thank you so much! Happy new year~
Z K Y
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TestX01
329 posts
#25 • 1 Y
Y by cubres
thank you so much <3333
Z K Y
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Yunzsi
9 posts
#26 • 1 Y
Y by cubres
Thank you! Your work will be shared and greatly appreciated.
Z K Y
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scienliet
1 post
#28 • 1 Y
Y by cubres
Nice handout!
Z K Y
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AVY2024
7 posts
#29 • 1 Y
Y by cubres
Thanks @Asjmaj
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ali123456
27 posts
#30 • 1 Y
Y by cubres
Thanks ;)
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GreekIdiot
108 posts
#31
Y by
Thank you very much man appreciate the effort. Excellent compilation :D :D
Z K Y
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BR1F1SZ
513 posts
#32
Y by
Thanks, great compilation!!! :D
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BGR2025
1 post
#33
Y by
Thanks for the book!
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John_Mgr
47 posts
#34
Y by
Thanks a lot!!
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