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!
Old High School Olympiads Regional, National, and International Math Olympiads before 2001 mostly, recent years have been posted in order to make contest collections richer
Regional, National, and International Math Olympiads before 2001 mostly, recent years have been posted in order to make contest collections richer
3 M G
BBookmark  VNew Topic kLocked
Old High School Olympiads Regional, National, and International Math Olympiads before 2001 mostly, recent years have been posted in order to make contest collections richer
Regional, National, and International Math Olympiads before 2001 mostly, recent years have been posted in order to make contest collections richer
3 M G
BBookmark  VNew Topic kLocked
t 
5,097 topics
w
0 users
TOPICS
No tags match your search
M
geometry
algebra
number theory
combinatorics
inequalities
combinatorial geometry
polynomial
Sum
diophantine
divides
Diophantine equation
divisible
functional
3D geometry
Geometric Inequalities
angles
Digits
functional equation
Perfect Square
system of equations
Sequence
Coloring
trigonometry
function
equal segments
areas
Equilateral
equal angles
game
max
recurrence relation
square
System
circumcircle
tetrahedron
rectangle
ratio
isosceles
circles
concurrent
min
parallelogram
perpendicular
right triangle
construction
Locus
angle bisector
game strategy
limit
Subsets
factors
Divisors
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 testing latex post , please ignore
parmenides51   3
N Feb 23, 2025 by parmenides51
Source: used with https://artofproblemsolving.com/community/c3170239_latex_testing_for_post_collections
issue 1 ..,
Click to reveal hidden text
3 replies
parmenides51
Oct 10, 2022
parmenides51
Feb 23, 2025
J
H
i Geo Collections + Forums + Greek Aops Index
parmenides51   57
N Oct 12, 2024 by parmenides51
In order to keep an eye to any contest collection that I have created and is not in aops contest collections, I created a collection with all that in a link: Geo Collections + Forums + Greek Aops Index

It contains so far (in these categories):

$\bullet$ Forums
$\bullet \bullet$ Geometry Mathley
$\bullet \bullet$ Old High School Olympiads
$\bullet \bullet$ Old Russian Math Olympiads

All geometry mentioned below in one forum collection:
$\bullet \bullet$ Geometry Collections and Contests

$\bullet$ Aops Geo Mocks
$\bullet$ Aops Mock Contests - Geometry


$\bullet \bullet$ geo national (geometry from:)
$\bullet$ Argentina NMO (Round 2-4, Finals, Provincial, Regional Round 2)
$\bullet$ Armenia NMO (outside aops)
$\bullet$ Belarus NMO VIII (outside aops)
$\bullet$ Belarus NMO IX (>>)
$\bullet$ Belarus NMO X (>>)
$\bullet$ Belarus NMO XI (>>)
$\bullet$ Belgium Flanders Juniors JWO (outside aops)
$\bullet$ Belgium Flanders Seniors VWO (>>)
$\bullet$ Belgium OMB Juniors (outside aops)
$\bullet$ Belgium OMB Seniors (>>)
$\bullet$ Brazil NMO (Round 2 + Finals)
$\bullet$ Bulgaria NMO Plane Geometry (outside aops)
$\bullet$ Bulgaria NMO 3D Geometry (>>)
$\bullet$ Costa Rica NMO (OLCOMA)
$\bullet$ Croatia MO (outside aops)
$\bullet$ Chile NMO (outside aops)
$\bullet$ Denmark MO (Mohr Contest) (outside aops)
$\bullet$ Estonia Open Junior MO (outside aops)
$\bullet$ Estonia Open Senior MO (>>)
$\bullet$ Greece JMO (outside aops)
$\bullet$ Greece NMO (outside aops)
$\bullet$ Hungary OKTV I (outside aops)
$\bullet$ Hungary OKTV II (>>)
$\bullet$ Hungary OKTV III (>>)
$\bullet$ Iceland NMO (outside aops)
$\bullet$ Indonesia MO Province OSP SMA (outside aops)
$\bullet$ Kazakhstan NMO IX (outside aops)
$\bullet$ Kazakhstan NMO X (>>)
$\bullet$ Kazakhstan NMO XI (>>)
$\bullet$ Lithuania juniors (outside aops)
$\bullet$ Mexico NMO (States Semifinals + Finals, Finals)
$\bullet$ Moldova NMO VII-VIII (outside aops)
$\bullet$ Moldova NMO IX-XII Plane Geometry (>>)
$\bullet$ Moldova NMO 3D Geometry (>>)
$\bullet$ New Zealand MO (outside aops)
$\bullet$ Paraguay NMO (OMAPA) (outside aops)
$\bullet$ Peru NMO (ONEM) (Rounds 2-3, Finals)
$\bullet$ Poland Juniors , Round 1+2 (outside aops)
$\bullet$ Poland Juniors, Finals (>>)
$\bullet$ Portugal NMO (outside aops)
$\bullet$ Romania District 3D Geometry (outside aops)
$\bullet$ Romania District Plane Geometry (>>)
$\bullet$ Romania NMO 3D Geometry (outside aops)
$\bullet $ Romania NMO Plane Geometry (>>)
$\bullet$ Swiss NMO (outside aops)
$\bullet$ Ukraine NMO VIII (outside aops)
$\bullet$ Ukraine NMO IX (>>)
$\bullet $ Ukraine NMO X-XI Plane Geometry (>>)
$\bullet$ Ukraine NMO 3D Geometry (>>)


$\bullet \bullet$ geo TST (geometry from:)
$\bullet$ Argentina Cono Sur TST (outside aops)
$\bullet$ Argentina Ibero TST (>>)
$\bullet$ Argentina IMO TST (>>)
$\bullet$ Argentina Training Lists Cono Sur (outside aops)
$\bullet$ Argentina Training Lists IberoAmerican (>>)
$\bullet$ Argentina Training Lists Rioplatense (>>)
$\bullet$ Bangladesh TST and Camp
$\bullet$ Belarus TST (outside aops)
$\bullet$ Brazil Training List Cono Sur 1999 - 2010 (outside aops)
$\bullet$ Brazil Training List Cono Sur 2011-20 (>>)
$\bullet$ Brazil Cono Sur TST (outside aops)
$\bullet$ Brazil IMO IberoAmerican TST (>>)
$\bullet$ Chile TST (outside aops)
$\bullet$ Croatia TST (outside aops)
$\bullet$ Cyprus TST (outside aops)
$\bullet$ Ecuador TST (outside aops)
$\bullet$ France TST (outside aops)
$\bullet$ Hong Kong TST (outside aops)
$\bullet$ Indonesia TST (outside aops)
$\bullet$ Italy TST (outside aops)
$\bullet$ Lithuania TST (outside aops)
$\bullet$ Peru Cono Sur TST (outside aops)
$\bullet$ Peru IberoAmerican TST (>>)
$\bullet$ Peru IMO TST (>>)
$\bullet$ Puerto Rico TST (outside aops)
$\bullet$ Serbia IMO TST (outside aops)
$\bullet$ Singapore TST (outside aops)
$\bullet$ Switzerland TST (outside aops)
$\bullet$ Taiwan TST (outside aops)
$\bullet$ Thailand TST (outside aops)
$\bullet$ Ukraine TST (outside aops)


$\bullet \bullet$ geo regional (geometry from:)
$\bullet$ 239 MO (St.Petersburg's Lyceum) (outside aops)
$\bullet$ Alberta High School Mathematics Competition (Canada) (outside aops)
$\bullet$ AESC MSU Internet Olympiad (Russia) (outside aops)
$\bullet$ All-Siberian Olympiad Finals (Russia) (outside aops)
$\bullet$ All-Siberian Olympiad Correspondence (Russia) (>>)
$\bullet$ All-Siberian Olympiad Qualifying (Russia) (>>)
$\bullet$ Almaty City MO (Kazakhstan) (outside aops)
$\bullet$ Association Mathematical Quebec Competition (Canada) (outside aops)
$\bullet$ Auckland MO (New Zealand) (outside aops)
$\bullet$ Champions Tournament (Ukraine) (Турнір чемпіонів) (outside aops)
$\bullet$ Clock-Tower School Junior (Romania) (outside aops)
$\bullet$ COMATEQ (Puerto Rico) (outside aops)
$\bullet$ Cordoba pre TSTs (Argentina) (outside aops)
$\bullet$ Dürer Math Competition (Hungary) (outside aops)
$\bullet$ El Número de Oro Certamen (Argentina) (outside aops)
$\bullet$ Euler Olympiad Remote (Russia) (outside aops)
$\bullet$ Euler Olympiad Regional & Final (Russia) (>>)
$\bullet$ Euler Teachers' MO (Russia) (outside aops)
$\bullet$ European Math Tournament (Belarus) (outside aops)
$\bullet$ Formula of Unity / Third Millennium Olympiad (Russia) (outside aops)
$\bullet$ HSGS Class 9 Contest (Vietnam) (outside aops)
$\bullet$ High Standards Olympiad (Russia) (Высшая проба) (outside aops)
$\bullet$ Innopolis University Open MO (Russia) (outside aops)
$\bullet$ Izumrud Olympiad Emerald by UrFU (Russia) (outside aops)
$\bullet$ Kharkiv City MO (Ukraine) (outside aops)
$\bullet$ Kharkiv Lyceum No 27 Olympiad (Ukraine) (outside aops)
$\bullet$ Kharkiv Masters Tournament (Ukraine) (outside aops)
$\bullet$ Kolomogorov Cup / Tournament (Russia)
$\bullet$ Kukin MO by OmSU (Russia) (outside aops)
$\bullet$ Kurchatov Olympiad (Russia) (outside aops)
$\bullet$ Kyiv City MO 1984-93 (Ukraine) (outside aops)
$\bullet$ Kyiv City MO 2003+ Round 1 (Ukraine) (>>)
$\bullet$ Kyiv City MO 2010+ Round 2 (Ukraine) (>>)
$\bullet$ Kyiv TST 2005-16 (for Ukraine MO) (outside aops)
$\bullet$ Kyiv TST 2017+ (for Ukraine MO) (>>)
$\bullet$ League of Winners Tournament (Russia) (outside aops)
$\bullet$ Lomonosov Tournament (Russia) (outside aops)
$\bullet$ Mathematical Multiathlon Tournament Juniors (Russia) (outside aops)
$\bullet$ Mathematical Multiathlon Tournament Seniors (Russia) (>>)
$\bullet$ Maths Beyond Limits Camp (Poland) (outside aops)
$\bullet$ May Olympiad, level 1 (Latin America) (outside aops)
$\bullet $ May Olympiad, level 2 (Latin America) (>>)
$\bullet$ Minsk City Internet Olympiad (Junior) (Belarus) (outside aops)
$\bullet$ MIPT Metropolitan Olympiad (Russia) (outside aops)
$\bullet$ Moscow Corespondence Competition 6-8 MO (Russia) (outside aops)
$\bullet$ Moscow Teachers' MO (Russia) (outside aops)
$\bullet$ OMAFOROS - OFO,FOFO, COFFEE (Argentina) (outside aops)
$\bullet$ Oral Moscow City MO VI-VII (Russia) (outside aops)
$\bullet$ Oral Moscow City Team MO 1999 - 2004 (Russia) (outside aops)
$\bullet$ Oral Moscow City Team MO 2005-19 (Russia) (>>)
$\bullet$ Oral Moscow City Team MO 2020+ (Russia) (>>)
$\bullet$ Rio de Janeiro MO (OMERJ) (Brazil) (outside aops)
$\bullet$ Rioplatense Olympiad, level 1 (Latin America) (outside aops)
$\bullet$ Rioplatense Olympiad, level 2 (Latin America) (>>)
$\bullet$ Rioplatense Olympiad, level 3 (Latin America) (>>)
$\bullet$ Rusanovsky Lyceum, Kyiv Olympiad(Ukraine) (outside aops)
$\bullet$ Savin Competition 1990 - 2015 (Russia) (outside aops)
$\bullet$ Savin Competition 2016+ (Russia) (>>)
$\bullet$ Savin Tournament (Russia) (>>)$\bullet$ SPBU School Olympiad besides Finals X-XI (Russia) (outside aops)
$\bullet$ SPBU School Olympiad, Finals X-XI - plane geometry (Russia) (>>)
$\bullet$ SPBU School Olympiad, Finals X-XI - 3D geometry (Russia) (>>)
$\bullet$ Ukraine Correspodence MO (outside aops)
$\bullet$ Ukrainian From Tasks to Tasks (outside aops)
$\bullet$ Ukrainian Tournament of Young Mathematicians Qualifying (outside aops)
$\bullet$ Ukrainian Tournament of Young Mathematicians Finals (>>)
$\bullet$ UNSW School Mathematics Competition Juniors (Australia) (outside aops)
$\bullet$ UNSW School Mathematics Competition Seniors (Australia) (>>)
$\bullet$ UQ/QAMT Problem Solving Competition (Australia) (outside aops)
$\bullet$ VU MIF Olympiad - geometry (Lithuania) (outside aops)
$\bullet$ Youth Mathematical School Olympiad ordinary (Russia) (outside aops)
$\bullet$ Youth Mathematical School Olympiad research (Russia) (>>)
$\bullet$ Zhautykov City Olympiad - geometry (Kazakstan) (outside aops)


$\bullet \bullet$ geo USA (geometry from:)
$\bullet$ BMT / Geometry Rounds
$\bullet$ BMT / Geometry problems from non Geometry Rounds
$\bullet$ CMIMC / Geometry Rounds
$\bullet$ CMIMC / Geometry problems from non Geometry Rounds
$\bullet$ HMMT / Geometry Rounds 2014-21
$\bullet$ PUMaC / Geometry Rounds 2006-14
$\bullet$ PUMaC / Geometry Rounds 2005-20
$\bullet$ PUMaC / Geometry problems from non Geometry Round


$\bullet \bullet$ geo olympiads
$\bullet$ Adygea Teachers' Geometry Olympiad (outside aops)
$\bullet$ Cabri Clubs (outside aops)
$\bullet$ Iranian Geometry Olympiad (outside aops)
$\bullet$ Mexican Geometry Olympiad (outside aops)
$\bullet$ Novosibirsk Oral Olympiad in Geometry (outside aops)
$\bullet$ Oral Moscow Geometry Olympiad (outside aops)
$\bullet$ Sharygin Geometry Olympiad (outside aops)
$\bullet$ Yaskinsky Geometry Olympiad (outside aops)
$\bullet$ Ukrainian Geometry Olympiad (outside aops)
$\bullet \bullet$ geometry olympiads not yet in contest collections


$\bullet \bullet$ geo shortlists (not IMO, BMO, JBMO, ELMO)
$\bullet$ Baltic Way Shortlist 2009-16 (outside aops)
$\bullet$ Baltic Way Shortlist 2017+ (outside aops)
$\bullet$ CentroAmerican Shortlist (outside aops)
$\bullet$ Cono Sur Olympiad Shortlist (outside aops)
$\bullet$ IberoAmerican Shortlist 1992 - 2010 (outside aops)
$\bullet$ IberoAmerican Shortlist 2011+ (>>)
$\bullet$ Indonesia Shortlist (INAMO OSN) (outside aops)
$\bullet$ IMOC Shortlist (Taiwan) (outside aops)
$\bullet$ Real IMO Shortlist (International Monster's Olympiad) (outside aops)
$\bullet$ Romanian Master in Mathematics Shortlist (outside aops)
$\bullet$ Thailand MO Shortlist (outside aops)


$\bullet \bullet$ geo IMO Longlists (outside aops)
$\bullet$ IMO Longlist I 1966-70 Geometry
$\bullet$ IMO Longlist II 1971-76 Geometry
$\bullet$ IMO Longlist III 1977-82 Geometry
$\bullet$ IMO Longlist IV 1983-85 Geometry
$\bullet$ IMO Longlist V 1986-88 Geometry
$\bullet$ IMO Longlist VI 1989-82 Geometry


$\bullet \bullet$ geo magazines
$\bullet$ Mathematical Excalibur - geometry (outside aops)
$\bullet$ Mathematical Reflections Junior - geometry (outside aops)
$\bullet$ Mathematical Reflections Senior - geometry (>>)
$\bullet$ Mathematical Reflections Olympiad - geometry (>>)
$\bullet$ Mathematical Reflections Undergraduate - geometry (>>)
$\bullet$ Quantum English - geometry (outside aops)
$\bullet$ Romanian Mathematical Magazine (outside aops)
$\bullet$ U sviti matematyky , part 1- geometry (In the World of Mathematics) (outside aops)
$\bullet$ U sviti matematyky , part 2 - geometry (In the World of Mathematics) (>>)


Akopyan's Geometry in Figures (random problems posted in aops)

$\bullet \bullet$ Greek Aops Index
$\bullet$ Greek Aops Index - Άλγεβρα
$\bullet$ Greek Aops Index - Ανισότητες
$\bullet$ Greek Aops Index - Γεωμετρία
$\bullet$ Greek Aops Index - Θεωρία Αριθμών
$\bullet$ Greek Aops Index - Συνδυαστική

PS.1. The links outside aops link to my blogspot page, in each competition's tab, imogeometry.blogspot.com.

PS.2. The geometry problems I have solved inside aops are collected here.
57 replies
parmenides51
Mar 7, 2020
parmenides51
Oct 12, 2024
J
H
i Forum's Purpose - Index of posted Contest Collections
parmenides51   29
N Mar 30, 2023 by huashiliao2020
I created this forum in order to post High School Math Olympiads before 2001 (not present in aops at the moment) in order to add more Contests to the existing Aops Contest Collections (without spamming the existing forums by posting too many posts in so little time). I also post recent problems not available at the moment at contest collections, in oder to create those post collections.
Anyone is welcome to post problems from a national competition (final round or TST) of his / her country not already posted in Aops Contest Collections, to get those links (just not post random problem but all from each year's competition). There is no limit to how many problems anyone may post in this forum, as it serves as a new problem collection source for more (older usually) posts collection (e.g. anyone may post in a day 40 different problems from 10 years of his \ her 4 problem's olympiad in 40 different posts - one problem at each post).

Forum Contests Collected:
- Mathcenter Contest (Thai)
- Mathlinks Contests (old name of aops)
- OIFMAT (FMAT - Chilean)
- Oliforum Contest (Italian)
- VMEO (VMF - Vietnamese)


Below are the contest collections I have created using this forum :
- Arab Math Olympiad
- Argentina NMO Finals: 2008
- Argentina NMO Round 4 / Regional Geo, L1, L2, L3, years 1995-2022
- Argentina Provincional Geo: L1, L2, L3 , 1995-2022
- Argentina TST / geometry : Ibero , IMO, Cono Sur
- Austrian - Polish Competition : 1979-2000
- Austria Beginners' Competition: 2001-08
- Belarus National MO: 1995, 1997 missing problems , 1998 , 2001, 2002, 2003,2006 , 2014
- Belarus TST : 1998 , 2000 , 2009 , 2010, 2011, 2012, 2014, 2015, 2016
- Bosnia and Herzegovina JBMO TST: 2003-07
- Brazil TSTs: EGMO, Geometry : Cono Sur, Cono Sur Training List , ΙΜΟ + Ibero ,
- Brazil IMO TST: 2007-16
- Bulgaria National MO: 1993-96
- Chile Contests / Chile NMO 1989 -2015
- Czech and Slovak Olympiad III A: so far 1986, 1991- 2001
- Czech-Polish-Slovak Junior Match: all
- Croatia National MO: 1996-2004
- Croatia TST: so far 2001, 2002, 2003
- Estonia Open Junior: 2001-2005, 2006, 2007, 2008-2019
- Estonia Open Senior: 2001-2005, 2006, 2007, 2008-2019
- Estonia National MO: so far 1996-2007, (soon 2008-2021)
- Estonia TST: 1992-95, 1998-2000, 2001-19
- French National MO: 1986, 1988-2003
- Final Mathematical Cup
- Germany / Bundeswettbewerb Mathematik : 1974-1982 , 1990
- Germany / National MO: so far 1965, 1996- 2001, 2009
- Germany / QUEDMO (11 /15 editions so far)
- Greece Junior: 1996 - 2020
- Hungary / Kürschák: 1947-84
- Hungary / Dürer / Finals: 2019-21
- India / LIMIT : 2020
- India / Postal Coaching: 2007-09 , 2012
- Israel / National (Gillis) : 1995-98
- Israel / Grosman: so far 1995, 1997, 1999, 2001
- Italy TST: so far 1993-94, 1998
- Kyrgystan TST: 2010, 2018
- Lithuania / Grand Duchy of Lithuania 2009-20
- Macedonia North National MO: so far 1994, 1995, 1996, 1997, 1998, 1999, 2002, 2003, 2004, 2005
- May Olympiad all
- Moldova Contests /JBMO TST: 1999- 2020
- Moldova National MO
- Mongolia National MO: 1999-2002, 2007
- Netherlands / Dutch ΙΜΟ TST: 2021
- New Zealand / NZMOC Camp Selection Problems, New Zealand MO
- Norway / Abels Math Contest (Final Round): 1993- 2006
- Polish MO Finals: 1966-84
- Rioplatense L3 1990-99
- Romania MOP: ROMOP 2011 Juniors
- Romania JBMO TST : 2002-19
- Romania TST: so far 1989, 1990 , 1991 (missing), 1992, 1993, 1995
- Saudi Arabia / BMO TST: 2010-11, 2013, 2015-19
/ GMO TST: 2013-16, 2018
/ IMO TST: 2011.2013, 2015-19
/ Pre-TST + Training Tests: 2010-11, 2021
- Saudi Arabia JBMO TST: 2017, 2019
- Serbia National MO: 1974 - 2006 (also known as Yugoslavia before 1990)
- Serbia TST:
- Singapore Junior : 2006-2019 collected
- Singapore Open: 1995 - 2004, 2014, 2016-17
- Singapore Senior : 1996 - 2008, 2011-13, 2015-19,
- Singapore TST: 1995 -2003
- Slovenia National MO: 1997-2001, 2005
- Slovenia TST: so far 1997, 1998, 2005
- Soros Olympiad
- Spanish MO: 1966-83
- Sweden National MO: 1961 - 2020
- Switzerland TST : so far 1997 - 2004, 2015 .
- Thailand MO: 2004- 15
- Ukraine National MO: 1997, 1998, 1999, 2005
- Ukraine TST: 1999, 2009-18
- USA / iΤest: 2005

Basic Source: Imomath

PS. My posting ability in public forums is as everyone’s else limited. Therefore when I post in public forums, I post only the geometry problems. When my source is written not in English, only the geometry ones are posted as I spend time translating them by google translate. When my source is written in English, I post the whole problem set in aops, posting the non-geometry problems in this forum and adding all the problems in contest collections.
In this forum’s index, anyone may find which contests’ years have been posted inside this forum.
In the future, each year's post collections shall be available in the Contests Collections, till then anyone may find them above.

Related forums:
Old Russian Math Olympiads
China High School Contests
KöMaL (Hungarian Magazine)

For the friends of geometry:
Olympiad Geometry Collections + Forums
A Beautiful Journey Through Olympiad Geometry - solutions forum
Evan Chen's EGMO study group
Lemmas in Olympiad Geometry - active forum
Tran Quang Hung's geometry group

uc = Under Construction

PS. It is not permitted to create contest collections of each year inside aops from National Contests of UK and Australia.

PS.2 Test
29 replies
parmenides51
Feb 11, 2020
huashiliao2020
Mar 30, 2023
J
H
square-free partition of 2n positive integers into n pairs
parmenides51   2
N 15 minutes ago by ilovemath0402
Source: 2018 Saudi Arabia BMO TST I p3
The partition of $2n$ positive integers into $n$ pairs is called square-free if the product of numbers in each pair is not a perfect square.Prove that if for $2n$ distinct positive integers, there exists one square-free partition, then there exists at least $n!$ square-free partitions.
2 replies
parmenides51
Jul 25, 2020
ilovemath0402
15 minutes ago
J
H
OI and CD are perpendicular into convex ABCD withAB = AC = BD
parmenides51   4
N Yesterday at 10:45 AM by fearsum_fyz
Source: Belarus TST 2000 8.1
The diagonals of a convex quadrilateral $ABCD$ with $AB = AC = BD$ intersect at $P$, and $O$ and $I$ are the circumcenter and incenter of $\vartriangle ABP$, respectively. Prove that if $O \ne I$ then $OI$ and $CD$ are perpendicular
4 replies
parmenides51
Feb 15, 2020
fearsum_fyz
Yesterday at 10:45 AM
J
H
a_{k+1} <= (a_k + a_{k+2} )/2
parmenides51   2
N Saturday at 7:33 PM by MathProGenius
Source: 2012 Romania JBMO TST 2.1
Let $a_1, a_2, ..., a_n$ be real numbers such that $a_1 = a_n = a$ and $a_{k+1} \le \frac{a_k + a_{k+2}}{2} $, for all $k = 1, 2, ..., n - 2$. Prove that $a_k \le a,$ for all $k = 1, 2, ..., n.$
2 replies
parmenides51
Jun 2, 2020
MathProGenius
Saturday at 7:33 PM
J
H
7^p - p - 16 is a perfect square.
parmenides51   2
N Mar 15, 2025 by MuradSafarli
Source: 2018 Romania JBMO TST 4.1
Determine the prime numbers $p$ for which the number $a = 7^p - p - 16$ is a perfect square.

Lucian Petrescu
2 replies
parmenides51
Jun 19, 2020
MuradSafarli
Mar 15, 2025
J
H
5 (a^2 + b^2 + c^2) = 6 (ab + bc + ca) if centroid lies on incircle
parmenides51   3
N Mar 8, 2025 by Marcus_Zhang
Source: 2001 Argentina IberoAmerican TST p5
Given a triangle with sides $a, b, c$ such that the centroid of the triangle lies on the circle inscribed in the triangle. Prove that $$5 (a^2 + b^2 + c^2) = 6 (ab + bc + ca)$$
3 replies
parmenides51
Jul 20, 2021
Marcus_Zhang
Mar 8, 2025
J
H
1/x_1 + 1/x_2 +... + 1/x_n = 1997/1998
parmenides51   1
N Mar 8, 2025 by grupyorum
Source: 1998 Swedish Mathematical Competition p5
Show that for any $n > 5$ we can find positive integers $x_1, x_2, ... , x_n$ such that $\frac{1}{x_1} + \frac{1}{x_2} +... + \frac{1}{x_n} = \frac{1997}{1998}$. Show that in any such equation there must be two of the $n$ numbers with a common divisor ($> 1$).
1 reply
parmenides51
Apr 2, 2021
grupyorum
Mar 8, 2025
J
H
c >= (a+b) sin(C/2)
parmenides51   2
N Mar 8, 2025 by grupyorum
Source: 1998 Swedish Mathematical Competition p2
$ABC$ is a triangle. Show that $c \ge (a+b) \sin \frac{C}{2}$
2 replies
parmenides51
Apr 2, 2021
grupyorum
Mar 8, 2025
J
H
concyclic wanted, OD _|_ BC, intersecting circles related
parmenides51   2
N Mar 8, 2025 by parmenides51
Source: Singapore Open Math Olympiad 2004 2nd Round p3 SMO
Let $AD$ be the common chord of two circles $\Gamma_1$ and $\Gamma_2$. A line through $D$ intersects $\Gamma_1$ at $B$ and $\Gamma_2$ at $C$. Let $E$ be a point on the segment $AD$, different from $A$ and $D$. The line $CE$ intersect $\Gamma_1$ at $P$ and $Q$. The line $BE$ intersects $\Gamma_2$ at $M$ and $N$.
(i) Prove that $P,Q,M,N$ lie on the circumference of a circle $\Gamma_3$.
(ii) If the centre of $\Gamma_3$ is $O$, prove that $OD$ is perpendicular to $BC$.
2 replies
parmenides51
Apr 2, 2020
parmenides51
Mar 8, 2025
J
H
necklace of marbles of n inhabitants of an island, friends of enemies
parmenides51   1
N Mar 8, 2025 by Bata325
Source: Norwegian Mathematical Olympiad 2004 - Abel Competition p4
Among the $n$ inhabitants of an island, where $n$ is even, every two are either friends or enemies. Some day, the chief of the island orders that each inhabitant (including himself) makes and wears a necklace consisting of marbles, in such a way that two necklaces have a marble of the same type if and only if their owners are friends.
(a) Show that the chief’s order can be achieved by using $n^2/4$ different types of stones.
(b) Prove that this is not necessarily true with less than $n^2/4$ types.
1 reply
parmenides51
Feb 11, 2020
Bata325
Mar 8, 2025
J
H
diophantine (x^2 + y^2)^n = (xy)^{2016} with no solutions
parmenides51   2
N Mar 6, 2025 by John_Mgr
Source: New Zealand NZMOC Camp Selection Problems 2016 p7
Find all positive integers $n$ for which the equation $$(x^2 + y^2)^n = (xy)^{2016}$$has positive integer solutions.
2 replies
parmenides51
Sep 19, 2021
John_Mgr
Mar 6, 2025
J
H
J
H
n is the sum the squares of its 4 smallest factors
parmenides51   2
N Jan 18, 2025 by Chanome
Source: Singapore Junior Math Olympiad 2018 2nd Round p4 SMO
Determine all positive integers $n$ with at least $4$ factors such that $n$ is the sum the squares of its $4$ smallest factors.
2 replies
parmenides51
Mar 26, 2020
Chanome
Jan 18, 2025
J
n is the sum the squares of its 4 smallest factors
G H J
Reveal topic tags
Sum
factors
Divisors
number theory
L
G H BBookmark kLocked kLocked NReply
Source: Singapore Junior Math Olympiad 2018 2nd Round p4 SMO
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
parmenides51
30628 posts
parmenides51
#1 h  Mar 26, 2020, 2:45 PM
Y by
Determine all positive integers $n$ with at least $4$ factors such that $n$ is the sum the squares of its $4$ smallest factors.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
charme7269
7 posts
charme7269
#2 h  Sep 22, 2023, 5:01 PM
Y by
Let $d_1$, $d_2$, $d_3$, $d_4$ be the smallest four positive divisors of $n$. We have $d_1 = 1$ and $$n-1={d_2}^2+{d_3}^2+{d_4}^2$$If $n$ were odd, then $d_1$, $d_2$, $d_3$, $d_4$ are all odd and $n$ is even, contradiction. So $n$ is even, therefore $d_2=2$. The equation reduces to $$n-5={d_3}^2+{d_4}^2$$. From here, ${d_3}^2+{d_4}^2$ must be odd, since $n$ is even. Thus one of $d_3$ and $d_4$ is odd while the other is even.

Case 1: If $d_4$ is even, say $d_4=2m$. If $m=2$, $d_3$ must be $3$ and $n=1^2+2^2+3^2+4^2=30$, but $d_4=4$ does not divide $30$, so $n=30$ is not a solution. If $m>2$, since $m$ must be a divisor (as $2m$ is a divisor), $d_3=m$ and $n=5+5m^2$. Finally, as $m \mid n$, $$m \mid 5+5m^2 \implies m \mid 5 \implies m=5$$and $n=130$, which satisfies the problem's conditions.

Case 2: If $d_3$ is even, and there were some $m \geq 3$ such that $d_3=2m$, then $m$ would be a divisor between $d_2$ and $d_3$, contradiction. So $m \leq 2$, and since $m=1$ yields $d_3=2$ which is absurd, $m=2$ and $d_3=4$. Hence, if we say $d_4=k$, $n=1^2+2^2+4^2+k^2=21+k^2$, and from $k \mid n$ we get $k \mid 21$, so $k=7$. However, this yields $n=70$ which does not satisfy the conditions since $4$ does not divide $70$.

Thus, the only $n$ that satisfies the problem's conditions is $130$.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Chanome
10 posts
Chanome
#3 h  Jan 18, 2025, 6:08 PM
Y by
Let \( n_i \) be the \( i \)-th factor of \( n \).

\[ n = 1 + (n_2)^2 + (n_3)^2 + (n_4)^2 \]
Case 1: \( n \) is even
If \( n \) is even, \( n_2 = 2 \).

Case 2: \( n \) is odd
If \( n \) is odd, \( n_2, n_3, n_4 \) are all odd. This means \( 1 + (n_2)^2 + (n_3)^2 + (n_4)^2 \) will be even, causing a contradiction.

Thus, \( n \) is even, and \( n_2 = 2 \).

\[ n = 5 + (n_3)^2 + (n_4)^2 \]
We can see that either \( n_3 \) or \( n_4 \) is even.

Subcase 1: \( n_3 \) is even
If \( n_3 \) is even, then \( \frac{n_3}{2} \) has to be a smaller factor of \( n \). Thus, if \( n_3 \) is even, \( n_3 = 4 \).

\[ n = 21 + (n_4)^2 \]
Let \( n = a n_4 \) where \( a > 1 \).

\[ a n_4 - (n_4)^2 = 21 \]
\[ a - n_4 = \frac{21}{n_4} \]
\( n_4 \) is an odd factor of 21 greater than 4, so \( n_4 = 7 \).

\[ n = 21 + 49 = 70 \]
However, the 4 smallest factors of 70 are \( 1, 2, 5, 7 \). Thus, by contradiction, \( n_3 \) is odd, and \( n_4 \) is even.

Subcase 2: \( n_4 \) is even
Let \( n_4 = b n_3 \) where \( b > 1 \) and \( b \) is not a multiple of 4.

\[ n = 5 + (b+1)(n_3)^2 \]
Since \( n \) and \( (b+1)(n_3)^2\) are divisible by \( n_3 \), thus \(5 \) is divisible by \( n_3 \). This must mean \( n_3 = 5 \).

If \( n_4 = 15 \), then \( n_3 = 3 \), which is a contradiction. Thus, \( n_4 = 10 \).

\[ n = 1^2 + 2^2 + 5^2 + 10^2 = 130 \]
Final Answer:
\[ n = 130 \]
This post has been edited 2 times. Last edited by Chanome, Jan 19, 2025, 11:32 PM
Reason: optimised the solution
Z K Y
N Quick Reply
G
H
=
a