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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:
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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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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

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

Why is the old one deleted?

EeEeRUT 3

N an hour ago by NicoN9

Source: EGMO 2025 P1

For a positive integer $N$ , let $c_1 < c_2 < \cdots < c_m$ be all positive integers smaller than $N$ that are coprime to $N$ . Find all $N \geqslant 3$ such that $\gcd( N, c_i + c_{i+1}) \neq 1$ for all $1 \leqslant i \leqslant m-1$

Here $\gcd(a, b)$ is the largest positive integer that divides both $a$ and $b$ . Integers $a$ and $b$ are coprime if $\gcd(a, b) = 1$ .

3 replies

EeEeRUT

Today at 1:33 AM

NicoN9

an hour ago

A set with seven elements

steven_zhang123 0

an hour ago

Let $A = \{a_1, a_2, \ldots, a_7\}$ be a set with seven elements, where each element is a positive integer not exceeding $26$ . Prove that there exist positive integers $t, m$ ( $1 \leq t < m \leq 7$ ) such that the equation
$x_1 + x_2 + \cdots + x_t = x_{t+1} + x_{t+2} + \cdots + x_m$ has a solution in the set $A$ , and $x_1, x_2, \ldots, x_m$ are all distinct.

0 replies

steven_zhang123

an hour ago

0 replies

Inequality while on a trip

giangtruong13 6

N an hour ago by GeoMorocco

Source: Trip

I find this inequality while i was on a trip, it was pretty fun and i have some new experience:
Let $a,b,c \geq -2$ such that: $a^2+b^2+c^2 \leq 8$ . Find the maximum: $A= \sum_{cyc} \frac{1}{16+a^3}$

6 replies

giangtruong13

Apr 12, 2025

GeoMorocco

an hour ago

A Characterization of Rectangles

buratinogigle 1

N 2 hours ago by lbh_qys

Source: VN Math Olympiad For High School Students P8 - 2025

Prove that if a convex quadrilateral $ABCD$ satisfies the equation
$(AB + CD)^2 + (AD + BC)^2 = (AC + BD)^2,$ then $ABCD$ must be a rectangle.

1 reply

1 viewing

buratinogigle

Today at 1:35 AM

lbh_qys

2 hours ago

A Segment Bisection Problem

buratinogigle 1

N 2 hours ago by Giabach298

Source: VN Math Olympiad For High School Students P9 - 2025

In triangle $ABC$ , let the incircle $\omega$ touch sides $BC, CA, AB$ at $D, E, F$ , respectively. Let $P$ lie on the line through $D$ perpendicular to $BC$ . Let $Q, R$ be the intersections of $PC, PB$ with $EF$ , respectively. Let $K, L$ be the projections of $R, Q$ onto line $BC$ . Let $M, N$ be the second intersections of $DQ, DR$ with the incircle $\omega$ . Let $S$ be the intersection of $KM$ and $LN$ . Prove that the line $DS$ bisects segment $QR$ .

1 reply

buratinogigle

Today at 1:36 AM

Giabach298

2 hours ago

2017 PAMO Shortlsit: Power of a prime is a sum of cubes

DylanN 3

N 2 hours ago by AshAuktober

Source: 2017 Pan-African Shortlist - N2

For which prime numbers $p$ can we find three positive integers $n$ , $x$ and $y$ such that $p^n = x^3 + y^3$ ?

3 replies

DylanN

May 5, 2019

AshAuktober

2 hours ago

Hard number theory

Hip1zzzil 14

N 2 hours ago by bonmath

Source: FKMO 2025 P6

Positive integers $a, b$ satisfy both of the following conditions.
For a positive integer $m$ , if $m^2 \mid ab$ , then $m = 1$ .
There exist integers $x, y, z, w$ that satisfies the equation $ax^2 + by^2 = z^2 + w^2$ and $z^2 + w^2 > 0$ .
Prove that there exist integers $x, y, z, w$ that satisfies the equation $ax^2 + by^2 + n = z^2 + w^2$ , for each integer $n$ .

14 replies

Hip1zzzil

Mar 30, 2025

bonmath

2 hours ago

Constant Angle Sum

i3435 6

N 3 hours ago by bin_sherlo

Source: AMASCIWLOFRIAA1PD (mock oly geo contest) P3

Let $ABC$ be a triangle with circumcircle $\Omega$ , $A$ -angle bisector $l_A$ , and $A$ -median $m_A$ . Suppose that $l_A$ meets $\overline{BC}$ at $D$ and meets $\Omega$ again at $M$ . A line $l$ parallel to $\overline{BC}$ meets $l_A$ , $m_A$ at $G$ , $N$ respectively, so that $G$ is between $A$ and $D$ . The circle with diameter $\overline{AG}$ meets $\Omega$ again at $J$ .

As $l$ varies, show that $\angle AMN + \angle DJG$ is constant.

MP8148

6 replies

i3435

May 11, 2021

bin_sherlo

3 hours ago

NEPAL TST 2025 DAY 2

Tony_stark0094 8

N 3 hours ago by cursed_tangent1434

Consider an acute triangle $\Delta ABC$ . Let $D$ and $E$ be the feet of the altitudes from $A$ to $BC$ and from $B$ to $AC$ respectively.

Define $D_1$ and $D_2$ as the reflections of $D$ across lines $AB$ and $AC$ , respectively. Let $\Gamma$ be the circumcircle of $\Delta AD_1D_2$ . Denote by $P$ the second intersection of line $D_1B$ with $\Gamma$ , and by $Q$ the intersection of ray $EB$ with $\Gamma$ .

If $O$ is the circumcenter of $\Delta ABC$ , prove that $O$ , $D$ , and $Q$ are collinear if and only if quadrilateral $BCQP$ can be inscribed within a circle.

$\textbf{Proposed by Kritesh Dhakal, Nepal.}$

8 replies

Tony_stark0094

Apr 12, 2025

cursed_tangent1434

3 hours ago

Interesting inequalities

sqing 4

N 3 hours ago by sqing

Source: Own

Let $a,b,c\geq 0$ and $ab+bc+ca+abc=4$ . Prove that
$k(a+b+c) -ab-bc\geq 4\sqrt{k(k+1)}-(k+4)$ Where $k\geq \frac{16}{9}.$
$\frac{16}{9}(a+b+c) -ab-bc\geq \frac{28}{9}$

4 replies

1 viewing

sqing

6 hours ago

sqing

3 hours ago

State target p8 sol

EaZ_Shadow 101

N 3 hours ago by Craftybutterfly

This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!

101 replies

EaZ_Shadow

Apr 6, 2025

Craftybutterfly

3 hours ago

Math and AI 4 Girls

mkwhe 18

N 3 hours ago by EvaLin

Hey everyone!

The 2025 MA4G competition is now open!

Apply Here: https://xmathandai4girls.submittable.com/submit

Visit https://www.mathandai4girls.org/ to get started!

Feel free to PM or email mathandai4girls@yahoo.com if you have any questions!

18 replies

mkwhe

Apr 5, 2025

EvaLin

3 hours ago

The daily problem!

Leeoz 106

N 4 hours ago by Leeoz

Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)

Please hide solutions and answers, hints are fine though! :)

Problems usually get harder throughout the week, so Sunday is the easiest and Saturday is the hardest!

Past Problems!

106 replies

Leeoz

Mar 21, 2025

Leeoz

4 hours ago

2025 MATHCOUNTS State Hub

SirAppel 551

N 6 hours ago by DhruvJha

Previous Years' "Hubs": (2022) (2023) (2024)Please Read

Now that it's April and we're allowed to discuss ...
[list=disc]
[*] CA: 43 (45 44 43 43 43 42 42 41 41 41)
[*] NJ: 43 (45 44 44 43 39 42 40 40 39 38) *
[*] NY: 42 (43 42 42 42 41 40)
[*] TX: 42 (43 43 43 42 42 40 40 38 38 38)
[*] MA: 41 (45 43 42 41)
[*] WA: 41 (41 45 42 41 41 41 41 41 41 40) *
[*]VA: 40 (41 40 40 40)
[*] FL: 39 (42 41 40 39 38 37 37)
[*] IN: 39 (41 40 40 39 36 35 35 35 34 34)
[*] NC: 39 (42 42 41 39)
[*] IL: 38 (41 40 39 38 38 38)
[*] OR: 38 (44 40? 38 38)
[*] PA: 38 (41 40 40 38 38 37 36 36 34 34) *
[*] MD: 37 (43 39 39 37 37 37)
[*] AZ: 36 (40? 39? 39 36)
[*] CT: 36 (44 38 38 36 35 35 34 34 34 33 33)
[*] MI: 36 (39 41 41 36 37 37 36 36 36 36) *
[*] MN: 36 (40 36 36 36 35 35 35 34)
[*] CO: 35 (41 37 37 35 35 35 ?? 31 31 30) *
[*] GA: 35 (38 37 36 35 34 34 34 34 34 33)
[*] OH: 35 (41 37 36 35)
[*] AR: 34 (46 45 35 34 33 31 31 31 29 29)
[*] NV: 34 (41 38 ?? 34)
[*] TN: 34 (38 ?? ?? 34)
[*] WI: 34 (40 37 37 34 35 30 28 29 29 29) *
[*] HI: 32 (35 34 32 32)
[*] NH: 31 (42 35 33 31 30)
[*] DE: 30 (34 33 32 30 30 29 28 27 26? 24)
[*] SC: 30 (33 33 31 30)
[*] IA: 29 (33 30 31 29 29 29 29 29 29 29 29 29) *
[*] NE: 28 (34 30 28 28 27 27 26 26 25 25)
[*] SD: 22 (30 29 24 22 22 22 21 21 20 20)
[/list]
Cutoffs Unknown

* means that CDR is official in that state.

Notes

For those asking about the removal of the tiers, I'd like to quote Jason himself:
[quote=peace09]
learn from my mistakes
[/quote]

Help contribute by sharing your state's cutoffs!

551 replies

SirAppel

Apr 1, 2025

DhruvJha

6 hours ago

State target p8 sol

G H J

Reveal topic tags

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G H BBookmark kLocked kLocked NReply

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1220 posts

#1 h Apr 6, 2025, 3:53 PM • 3 Y

Y by PikaPika999, Soupboy0, jkim0656

This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!

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greenplanet2050

1315 posts

greenplanet2050

#2 h Apr 6, 2025, 3:55 PM • 1 Y

Y by PikaPika999

ikr i literally kinda guessed this one correct

This post has been edited 1 time. Last edited by greenplanet2050, Apr 6, 2025, 3:55 PM

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1220 posts

#3 h Apr 6, 2025, 3:56 PM • 1 Y

Y by PikaPika999

greenplanet2050 wrote:

ikr i literally kinda guessed this one correct

Lowk mathcounts was def cooking with that sol!

This post has been edited 1 time. Last edited by EaZ_Shadow, Apr 6, 2025, 3:56 PM

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2308 posts

evt917

#4 h Apr 6, 2025, 3:56 PM • 1 Y

Y by PikaPika999

i didn't take mathcounts cuz i'm only in 5th grade

but i also checked the problems

the solution was way too good

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281 posts

#5 h Apr 6, 2025, 4:01 PM • 1 Y

Y by PikaPika999

EaZ_Shadow wrote:

This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!

our team got p1 team wrong :noo:

:noo:

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1214 posts

#7 h Apr 6, 2025, 7:39 PM • 1 Y

Y by PikaPika999

It is actually a good solution and I am not being sarcastic skull

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542 posts

maxamc

#8 h Apr 6, 2025, 7:47 PM • 1 Y

Y by PikaPika999

i did all 10 team round in 19 min but failed target p8 and i am not being sarcastic skull

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1214 posts

#9 h Apr 6, 2025, 8:19 PM • 1 Y

Y by PikaPika999

maxamc wrote:

i did all 10 team round in 19 min but failed target p8 and i am not being sarcastic skull

skull i did 11 team rounds and got a perfect on target and sprint to get 46 overall ¿como estas?

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DottedCaculator

7334 posts

DottedCaculator

#10 h Apr 6, 2025, 8:41 PM • 3 Y

Y by PikaPika999, jkim0656, scannose

https://www.eecs.qmul.ac.uk/~norman/papers/probability_puzzles/equal_sequences.shtml

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542 posts

maxamc

#11 h Apr 6, 2025, 9:03 PM • 1 Y

Y by PikaPika999

DottedCaculator wrote:

https://www.eecs.qmul.ac.uk/~norman/papers/probability_puzzles/equal_sequences.shtml

https://www.youtube.com/watch?v=t8xqMxlZz9Y

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61 posts

#12 h Apr 6, 2025, 9:44 PM • 1 Y

Y by PikaPika999

Quote:

The probability of getting consecutive coin tosses with the pattern HTT is (2/3)(1/3)(1/3)=2/27 . The expectation value of the number of tosses needed to first achieve that pattern is the reciprocal of that probability, thus 27/2.

I don't get the solution (why can you just reciprocate it?)

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Craftybutterfly

368 posts

Craftybutterfly

#13 h Apr 6, 2025, 9:51 PM • 1 Y

Y by PikaPika999

Is MATHCOUNTS only for middle school students or also high school students or elementary students as well?

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DottedCaculator

7334 posts

DottedCaculator

#14 h Apr 6, 2025, 9:56 PM • 4 Y

Y by PikaPika999, huajun78, iwastedmyusername, vincentwant

huajun78 wrote:

Quote:

The probability of getting consecutive coin tosses with the pattern HTT is (2/3)(1/3)(1/3)=2/27 . The expectation value of the number of tosses needed to first achieve that pattern is the reciprocal of that probability, thus 27/2.

I don't get the solution (why can you just reciprocate it?)

Consider doing many coin tosses. Each appearance of HTT is disjoint, and the total number of HTTs is 2/27 times the number of tosses, so the expected distance to the next one is 27/2.

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599 posts

#15 h Apr 7, 2025, 12:19 AM

Y by

i did it like dottedcaculator did, everyone was like did you p8 and they were like god that problem was actually hard, and i was like bruh its just that the probability is 2/3*1/3*1/3= 2/27 so the expected number is 27/2 lol you guys shouldve seen my friends expression when i told him that

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7551 posts

#16 h Apr 7, 2025, 12:27 AM

Y by

DottedCaculator wrote:

Consider doing many coin tosses. Each appearance of HTT is disjoint, and the total number of HTTs is 2/27 times the number of tosses, so the expected distance to the next one is 27/2.

I like how this solution fails if HTT is replaced with, say, TT. The expected number of flips is not 4 in this case.

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