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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
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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 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies

jlacosta

Apr 2, 2025

0 replies

k i Adding contests to the Contest Collections

dcouchman 1

N Apr 5, 2023 by v_Enhance

Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add

1 reply

dcouchman

Sep 9, 2019

v_Enhance

Apr 5, 2023

k i Zero tolerance

ZetaX 49

N May 4, 2019 by NoDealsHere

Source: Use your common sense! (enough is enough)

Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:

To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.

More specifically:

For new threads:

a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"

b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".

c) Good problem statement:
Some recent really bad post was:
[quote] $lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$ [/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.

For answers to already existing threads:

d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$ , do not answer with " $x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like " $x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.

To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!

Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.

49 replies

ZetaX

Feb 27, 2007

NoDealsHere

May 4, 2019

When MOP Letters Come Out

imagien_bad 14

N a few seconds ago by Aaronjudgeisgoat

Hello everyone, I would like to ask about the validity of MAA's claim that they would release USA(J)MO results in 2-3 weeks. Is this true or is MAA just yapping.

14 replies

imagien_bad

Apr 7, 2025

Aaronjudgeisgoat

a few seconds ago

9 Will I make AMO?

imagien_bad 9

N 6 minutes ago by martianrunner

Hi everyone, I got a 100.5 on AMC 12A 2024 what is my chance to make USAMO 2025? (i did not do 12B btw)

9 replies

imagien_bad

Nov 23, 2024

martianrunner

6 minutes ago

9 Practice AIME Exam

Melissa. 20

N 10 minutes ago by martianrunner

(This practice test is designed to be slightly harder than the real test. I would recommend you take this like a real test, using a 3 hour time limit and no calculator.)

Let me know any suggestions for improvement on test quality, difficulty, problem selection, problem placement, test topics, etc. for the next tests that I make!

Practice AIME

1.
Positive integers a, b, and c satisfy a + b + c = 49 and ab + bc + ca = 471. Find the value of the product abc.

2.
Find the integer closest to the value of (69^(1/2) + 420^(1/2))^2.

3.
Let G and A be two points that are 243 units apart. Suppose A_1 is at G, and for n > 1, A_n is the point on line GA such that A_nA_(n-1) = 243, and A_n is farther from A than G. Let L be the locus of points T such that GT + A_6T = 2025. Find the maximum possible distance from T to line GA as T varies across L.

4.
Find the value of (69 + 12 * 33^(1/2))^(1/2) + (69 - 12 * 33^(1/2))^(1/2).

5.
Find the sum of the numerator and denominator of the probability that two (not necessarily distinct) randomly chosen positive integer divisors of 900 are relatively prime, when expressed as a fraction in lowest terms.

6.
Find the limit of (1x^2 + 345x^6)/(5x^6 + 78x + 90) as x approaches infinity.

7.
Find the slope of the line tangent to the graph of y = 6x^2 + 9x + 420 at the point where y = 615 and x is positive.

8.
Find the smallest positive integer n such that the sum of the positive integer divisors of n is 1344.

9.
Find the first 3 digits after the decimal point in the decimal expansion of the square root of 911.

10.
Let n be the smallest positive integer in base 10 such that the base 2 expression of 60n contains an odd number of 1’s. Find the sum of the squares of the digits of n.

11.
Find the sum of the 7 smallest positive integers n such that n is a multiple of 7, and the repeating decimal expansion of 1/n does not have a period of 6.

12.
Let n be an integer from 1 to 999, inclusive. How many different numerators are possible when n/1000 is written as a common fraction in lowest terms?

13.
How many ways are there to divide a pile of 15 indistinguishable bricks?

14.
Let n be the unique 3-digit positive integer such that the value of the product 100n can be expressed in bases b, b + 1, b + 2, and b + 3 using only 0’s and 1’s, for some integer b > 1. Find n.

15.
For positive integers n, let f(n) be the sum of the positive integer divisors of n. Suppose a positive integer k is untouchable if there does not exist a positive integer a such that f(a) = k + a. For example, the integers 2 and 5 are untouchable, by the above definition. Find the next smallest integer after 2 and 5 that is untouchable.

Answer key:
WARNING: SPOILERS!!!

20 replies

Melissa.

Apr 8, 2025

martianrunner

10 minutes ago

2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!

audio-on 39

N 40 minutes ago by mkwhe

Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary

Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!

39 replies

audio-on

Jan 26, 2025

mkwhe

40 minutes ago

thank you

Piwbo 1

N 42 minutes ago by CHESSR1DER

Let $p_n$ be the n-th prime number in increasing order for $n\geq 1$ . Prove that there exists a sequence of distinct prime numbers $q_n$ satisfying $q_1+q_2+...+q_n=p_n$ for all $n\geq 1$

1 reply

Piwbo

Yesterday at 11:22 AM

CHESSR1DER

42 minutes ago

Difficult lattice point coloring problem

CBMaster 0

43 minutes ago

Source: Own

Is it possible to color all lattice points in plane into 3 colors such that

1. every line passing through lattice points and parallel to x axis has these three colors infinitely many(that is, every color appears infinitely many times in those lines).

2. every line passing through lattice points and not parallel to x axis cannot have three different color lattice points on it.

0 replies

CBMaster

43 minutes ago

0 replies

Stop Projecting your insecurities

naman12 52

N an hour ago by ihategeo_1969

Source: 2022 USA TST #2

Let $ABC$ be an acute triangle. Let $M$ be the midpoint of side $BC$ , and let $E$ and $F$ be the feet of the altitudes from $B$ and $C$ , respectively. Suppose that the common external tangents to the circumcircles of triangles $BME$ and $CMF$ intersect at a point $K$ , and that $K$ lies on the circumcircle of $ABC$ . Prove that line $AK$ is perpendicular to line $BC$ .

Kevin Cong

52 replies

naman12

Dec 12, 2022

ihategeo_1969

an hour ago

Digit sum

Disjeje 3

N an hour ago by jasperE3

Let’s say S(n) is digit sum of n does n exists thatS(n)>S(n^2)?

3 replies

Disjeje

4 hours ago

jasperE3

an hour ago

R+ Functional Equation

Mathdreams 3

N an hour ago by jasperE3

Source: Nepal TST 2025, Problem 3

Find all functions $f : \mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that $f(f(x)) + xf(xy) = x + f(y)$ for all positive real numbers $x$ and $y$ .

(Andrew Brahms, USA)

3 replies

Mathdreams

5 hours ago

jasperE3

an hour ago

TST Junior Romania 2025

ant_ 0

an hour ago

Source: ssmr

Consider the isosceles triangle $ABC$ , with $\angle BAC > 90^\circ$ , and the circle $\omega$ with center $A$ and radius $AC$ . Denote by $M$ the midpoint of side $AC$ . The line $BM$ intersects the circle $\omega$ for the second time in $D$ . Let $E$ be a point on the circle $\omega$ such that $BE \perp AC$ and $DE \cap AC = {N}$ . Show that $AN = 2AB$ .

0 replies

ant_

an hour ago

0 replies

Functional equation

Pmshw 16

N an hour ago by jasperE3

Source: Iran 2nd round 2022 P2

Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for any real value of $x,y$ we have:
$f(xf(y)+f(x)+y)=xy+f(x)+f(y)$

16 replies

Pmshw

May 8, 2022

jasperE3

an hour ago

Line passes through the fix point

moony_ 1

N an hour ago by GioOrnikapa

Source: idk

Let $ABC$ be a triangle. $P$ and $Q$ are points, such that $PA = PB$ , $QA$ = $QC$ and $\angle{PBC} =\angle{QCB}$ ( $P$ - inside $\triangle{ABC}$ and $Q$ - oitside). Proove that line $PQ$ passes through the fix point.

1 reply

moony_

4 hours ago

GioOrnikapa

an hour ago

Subsets of points lying in disks

oVlad 4

N an hour ago by Andyexists

Source: Romania TST 2023 Day 2 P4

Fix a positive integer $n.{}$ Consider an $n{}$ -point set $S{}$ in the plane. An eligible set is a non-empty set of the form $S\cap D,{}$ where $D$ is a closed disk in the plane. In terms of $n,$ determine the smallest possible number of eligible subsets $S{}$ may contain.

Proposed by Cristi Săvescu

4 replies

oVlad

Apr 7, 2024

Andyexists

an hour ago

hard ...

REGNA 3

N an hour ago by KenWuMath

find function $f:\mathbb{R^+}\rightarrow \mathbb{R^+}$ such that :
$f()\frac{f(x)}{y}=yf(y)f(f(x)) \;\;\;\;\;(x,y> 0)$

3 replies

REGNA

Oct 21, 2022

KenWuMath

an hour ago

When MOP Letters Come Out

G H J

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40 posts

#1 h Apr 7, 2025, 4:06 PM

Y by

Hello everyone, I would like to ask about the validity of MAA's claim that they would release USA(J)MO results in 2-3 weeks. Is this true or is MAA just yapping.

Attachments:

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517 posts

maxamc

#2 h Apr 7, 2025, 4:07 PM

Y by

This is true because MAA is always correct

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1839 posts

PEKKA

#5 h Apr 7, 2025, 5:08 PM

Y by

MAA's claims are always correct and accurate and their release of results is always timely.

Click to reveal hidden text

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greenturtle3141

3543 posts

greenturtle3141

#13 h Apr 7, 2025, 7:36 PM

Y by

imagien_bad wrote:

Hello everyone, I would like to ask about the validity of MAA's claim that they would release USA(J)MO results in 2-3 weeks. Is this true or is MAA just yapping.

This should be mostly true. Based on trustworthy sources you can expect the release to be on the high end of the estimate (3.5 weeks maybe?).

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2963 posts

#14 h Apr 7, 2025, 8:38 PM

Y by

We're already in the center of the 2-3 weeks range. It's possible that MAA is substantially more efficient than in previous years, but a substantial change is slightly unlikely.

Letters were out on 4/19 (?) last year, and the 2024 and 2025 USA(J)MO dates are very similar. Consequently, I'd expect letters to be out in a week if MAA is substantially faster, but it could full well be 2ish or more weeks.

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1503 posts

#15 h Apr 8, 2025, 2:39 AM • 3 Y

Y by greenturtle3141, bjump, golue3120

Since MOP letters are always unexpected by the unexpected hanging theorem they will never come out.

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6872 posts

#16 h Apr 9, 2025, 5:56 PM • 5 Y

Y by imagien_bad, Pengu14, aidan0626, solasky, resources

The sentence "grading of the USAMO takes place approx 10 days after" looks stale to me. That was correct back when grading was done in-person over a weekend, on-site. It hasn't been that way for a long time now (like at least 5 years). So I think you can just ignore that entire paragraph as outdated.

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40 posts

#17 h Apr 9, 2025, 5:59 PM

Y by

v_Enhance wrote:

The sentence "grading of the USAMO takes place approx 10 days after" looks stale to me. That was correct back when grading was done in-person over a weekend, on-site. It hasn't been that way for a long time now (like at least 5 years). So I think you can just ignore that entire paragraph as outdated.

imagien_bad.

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40 posts

#18 h Apr 9, 2025, 6:01 PM

Y by

evan, do you have a better estimate or are you not sure

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40 posts

#19 h Wednesday at 6:45 PM

Y by

imagien_bad wrote:

evan, do you have a better estimate or are you not sure

imagien_bad.

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115 posts

#20 h Yesterday at 4:03 AM

Y by

Do graders know the student name of the paper they are grading? What if they hold grudge against the student or do favor for the student?

v_Enhance wrote:

The sentence "grading of the USAMO takes place approx 10 days after" looks stale to me. That was correct back when grading was done in-person over a weekend, on-site. It hasn't been that way for a long time now (like at least 5 years). So I think you can just ignore that entire paragraph as outdated.

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3 posts

#21 h Yesterday at 4:22 AM

Y by

mulberrykid wrote:

Do graders know the student name of the paper they are grading? What if they hold grudge against the student or do favor for the student?

v_Enhance wrote:

The sentence "grading of the USAMO takes place approx 10 days after" looks stale to me. That was correct back when grading was done in-person over a weekend, on-site. It hasn't been that way for a long time now (like at least 5 years). So I think you can just ignore that entire paragraph as outdated.

no they don’t; that’s why we weren’t supposed to put our name on our solution sheets, only our IDs.

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55 posts

#22 h 20 minutes ago

Y by

imagien_bad wrote:

imagien_bad wrote:

evan, do you have a better estimate or are you not sure

imagien_bad.

kenwumath!

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135 posts

#23 h 18 minutes ago

Y by

PEKKA wrote:

MAA's claims are always correct and accurate and their release of results is always timely.

Click to reveal hidden text

MAA totally didn't change the AMC cutoffs this year after they released a final version

Z K Y

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Aaronjudgeisgoat

859 posts

Aaronjudgeisgoat

#24 h a few seconds ago

Y by

anticodon wrote:

PEKKA wrote:

MAA's claims are always correct and accurate and their release of results is always timely.

Click to reveal hidden text

MAA totally didn't change the AMC cutoffs this year after they released a final version

i wonder, has there ever been a time where maa has raised the cutoff after releasing a final version :think:

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