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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
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Inspired by Mihaela Berindeanu
sqing   1
N 4 minutes ago by lbh_qys
Source: Own
Let $ a,b,c>0 . $ Prove that
$$(4a+b+c)(a+b)(b+c)(c+a)\geq (ab+bc+ca)(2a+b+c)^2$$
1 reply
sqing
Yesterday at 2:08 PM
lbh_qys
4 minutes ago
J
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Max amount of equal numbers among (a_i^2 + a_j^2)/(a_i + a_j)
mshtand1   1
N 6 minutes ago by Rushery_10
Source: Ukrainian Mathematical Olympiad 2025. Day 2, Problem 9.8
Given $2025$ pairwise distinct positive integer numbers \(a_1, a_2, \ldots, a_{2025}\), find the maximum possible number of equal numbers among the fractions of the form
\[ \frac{a_i^2 + a_j^2}{a_i + a_j} \]
Proposed by Mykhailo Shtandenko
1 reply
mshtand1
Mar 14, 2025
Rushery_10
6 minutes ago
J
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Combinatorics from Iranian TST 2017
bgn   20
N 16 minutes ago by ezpotd
Source: Iranian TST 2017, first exam, day1, problem 2
In the country of Sugarland, there are $13$ students in the IMO team selection camp.
$6$ team selection tests were taken and the results have came out. Assume that no students have the same score on the same test.To select the IMO team, the national committee of math Olympiad have decided to choose a permutation of these $6$ tests and starting from the first test, the person with the highest score between the remaining students will become a member of the team.The committee is having a session to choose the permutation.
Is it possible that all $13$ students have a chance of being a team member?

Proposed by Morteza Saghafian
20 replies
bgn
Apr 5, 2017
ezpotd
16 minutes ago
J
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C-B=60 <degrees>
Sasha   26
N 34 minutes ago by shendrew7
Source: Moldova TST 2005, IMO Shortlist 2004 geometry problem 3
Let $O$ be the circumcenter of an acute-angled triangle $ABC$ with ${\angle B<\angle C}$. The line $AO$ meets the side $BC$ at $D$. The circumcenters of the triangles $ABD$ and $ACD$ are $E$ and $F$, respectively. Extend the sides $BA$ and $CA$ beyond $A$, and choose on the respective extensions points $G$ and $H$ such that ${AG=AC}$ and ${AH=AB}$. Prove that the quadrilateral $EFGH$ is a rectangle if and only if ${\angle ACB-\angle ABC=60^{\circ }}$.

Proposed by Hojoo Lee, Korea
26 replies
Sasha
Apr 10, 2005
shendrew7
34 minutes ago
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No more topics!
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Inmaximumlity
giangtruong13   1
N Yesterday at 8:24 AM by giangtruong13
Let $a,b,c>0$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \leq 3$. Find the maximum: $$A=\sum_{cyc} \frac{1}{\sqrt{a^2-ab+3b^2+1}}$$
1 reply
giangtruong13
Yesterday at 5:35 AM
giangtruong13
Yesterday at 8:24 AM
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Inmaximumlity
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Reveal topic tags
inequalities
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giangtruong13
#1 h  Yesterday at 5:35 AM
Y by
Let $a,b,c>0$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \leq 3$. Find the maximum: $$A=\sum_{cyc} \frac{1}{\sqrt{a^2-ab+3b^2+1}}$$
This post has been edited 1 time. Last edited by giangtruong13, Yesterday at 4:23 PM
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giangtruong13
#2 h  Yesterday at 8:24 AM
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This post has been edited 1 time. Last edited by giangtruong13, Yesterday at 4:23 PM
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