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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
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
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]
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.

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0 replies
jlacosta
Apr 2, 2025
0 replies
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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
J
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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
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2025 MATHCOUNTS State Hub
SirAppel   563
N 2 minutes ago by sadas123
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!
563 replies
SirAppel
Apr 1, 2025
sadas123
2 minutes ago
J
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Three-player money transfer game with unique winner per round
rilarfer   1
N 32 minutes ago by Lankou
Source: ASJTNic 2005
Ana, Bárbara, and Cecilia play a game with the following rules:
[list]
[*] In each round, exactly one player wins.
[*] The two losing players each give half of their current money to the winner.
[/list]
The game proceeds as follows:

[list=1]
[*] Ana wins the first round.
[*] Bárbara wins the second round.
[*] Cecilia wins the third round.
[/list]
At the end of the game, the players have the following amounts:
[list]
[*] Ana: C$35
[*] Bárbara: C$75
[*] Cecilia: C$150
[/list]
How much money did each of them have at the beginning?
1 reply
rilarfer
an hour ago
Lankou
32 minutes ago
J
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Find all integer solutions to an exponential equation involving powers of 2 and
rilarfer   2
N 41 minutes ago by teomihai
Source: ASJTNic 2005
Find all integer pairs $(x, y)$ such that:
$$ 2^x + 3^y = 3^{y + 2} - 2^{x + 1}. $$
2 replies
rilarfer
an hour ago
teomihai
41 minutes ago
J
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9 What is the most important topic in maths competition?
AVIKRIS   13
N 42 minutes ago by Yihangzh
I think arithmetic is the most the most important topic in math competitions.
13 replies
AVIKRIS
3 hours ago
Yihangzh
42 minutes ago
J
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Winning strategy in a two-player subtraction game starting with 65 tokens
rilarfer   1
N an hour ago by CHESSR1DER
Source: ASJTNic 2005
Juan and Pedro play the following game:
[list]
[*] There are initially 65 tokens.
[*] The players alternate turns, starting with Juan.
[*] On each turn, a player may remove between 1 and 7 tokens.
[*] The player who removes the last token wins.
[/list]
Describe and justify a strategy that guarantees Juan a win.
1 reply
rilarfer
an hour ago
CHESSR1DER
an hour ago
J
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Radius of circle tangent to two equal circles and a common line
rilarfer   1
N an hour ago by Lankou
Source: ASJTNic 2005
Two circles of radius 2 are tangent to each other and to a straight line. A third circle is placed so that it is tangent to both of the other circles and also tangent to the same straight line.

What is the radius of the third circle?

IMAGE
1 reply
rilarfer
an hour ago
Lankou
an hour ago
J
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Four-variable FE mod n
TheUltimate123   2
N an hour ago by cosmicgenius
Source: PRELMO 2023/3 (http://tinyurl.com/PRELMO)
Let \(n\) be a positive integer, and let \(\mathbb Z/n\mathbb Z\) denote the integers modulo \(n\). Determine the number of functions \(f:(\mathbb Z/n\mathbb Z)^4\to\mathbb Z/n\mathbb Z\) satisfying \begin{align*} &f(a,b,c,d)+f(a+b,c,d,e)+f(a,b,c+d,e)\\ &=f(b,c,d,e)+f(a,b+c,d,e)+f(a,b,c,d+e). \end{align*}for all \(a,b,c,d,e\in\mathbb Z/n\mathbb Z\).
2 replies
TheUltimate123
Jul 11, 2023
cosmicgenius
an hour ago
J
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Functional divisibility for large arguments
Assassino9931   3
N an hour ago by Assassino9931
Source: Bulgaria Winter Mathematical Competition 2025 12.3
Determine all functions $f: \mathbb{Z}_{\geq 2025} \to \mathbb{Z}_{>0}$ such that $mn+1$ divides $f(m)f(n) + 1$ for any integers $m,n \geq 2025$ and there exists a polynomial $P$ with integer coefficients, such that $f(n) \leq P(n)$ for all $n\geq 2025$.
3 replies
Assassino9931
Jan 27, 2025
Assassino9931
an hour ago
J
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Preparing for Higher AIME+
PhoenixMathClub   6
N an hour ago by sadas123
Hello, I am going to be a 7th grader next year and I really want to qualify for USAJMO in 8th grade, so far I have these goals reached

1. AMC 10 Honor Roll A and B 2025
2. AMC 8 DHR and HR
3. AIME 3 :(

This year on AIME something happened and I got a 3 :( on the AMC's I got a 105 on AMC 10 A and I got a 114 on AMC 10 B. I want to improve mostly on AIME but since the AMC 10 is coming up quicker what would you guys recommend for getting 110+ on both of the AMC 10's and getting a 6+ on AIME? So far I am only doing Alcumus and have no books so far.... Checking the table of contents on the books Alcumus provides the same topics. I was thinking to take WOOT 1 and AMC 10 Problem Series.
6 replies
PhoenixMathClub
Today at 1:51 PM
sadas123
an hour ago
J
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Max integer divisible by 25 with leftover equal to one-fourth of a share
rilarfer   0
an hour ago
Source: ASJTNic 2005
In preparation for a piñata, a certain number of candies was bought to be equally distributed among 25 guests. However, during the distribution, it was noticed that one-fourth of the amount each guest should receive was always left over.

What is the greatest number of candies that could have been originally purchased?
0 replies
rilarfer
an hour ago
0 replies
J
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Combinatorics
TUAN2k8   2
N an hour ago by soryn
A sequence of integers $a_1,a_2,...,a_k$ is call $k-balanced$ if it satisfies the following properties:
$i) a_i \neq a_j$ and $a_i+a_j \neq 0$ for all indices $i \neq j$.
$ii) \sum_{i=1}^{k} a_i=0$.
Find the smallest integer $k$ for which: Every $k-balanced$ sequence, there always exist two terms whose diffence is not less than $n$. (where $n$ is given positive integer)
2 replies
TUAN2k8
Today at 8:22 AM
soryn
an hour ago
J
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source own
Bet667   5
N 2 hours ago by GeoMorocco
Let $x,y\ge 0$ such that $2(x+y)=1+xy$ then find minimal value of $$x+\frac{1}{x}+\frac{1}{y}+y$$
5 replies
Bet667
4 hours ago
GeoMorocco
2 hours ago
J
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Cross-ratio Practice!
shanelin-sigma   3
N 2 hours ago by MENELAUSS
Source: 2024 imocsl G3 (Night 6-G)
Triangle $ABC$ has circumcircle $\Omega$ and incircle $\omega$, where $\omega$ is tangent to $BC, CA, AB$ at $D,E,F$, respectively. $T$ is an arbitrary point on $\omega$. $EF$ meets $BC$ at $K$, $AT$ meets $\Omega$ again at $P$, $PK$ meets $\Omega$ again at $S$. $X$ is a point on $\Omega$ such that $S, D, X$ are colinear. Let $Y$ be the intersection of $AX$ and $EF$, prove that $YT$ is tangent to $\omega$.

Proposed by chengbilly
3 replies
shanelin-sigma
Aug 8, 2024
MENELAUSS
2 hours ago
J
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Website to learn math
hawa   34
N 4 hours ago by iwastedmyusername
Hi, I'm kinda curious what website do yall use to learn math, like i dont find any website thats fun to learn math
34 replies
1 viewing
hawa
Apr 9, 2025
iwastedmyusername
4 hours ago
J
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J
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Nice Combinatorics Problem
RabtejKalra   10
N Apr 12, 2025 by sadas123
A number is considered happy if it contains at least one digit exactly twice. For instance, the numbers 2020 and 2024 are happy, but the numbers 2019 and 2022 are not. How many happy counting numbers are there that are less than 10,000?
10 replies
RabtejKalra
Apr 11, 2025
sadas123
Apr 12, 2025
J
Nice Combinatorics Problem
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Reveal topic tags
combinatorics
IMC
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RabtejKalra
64 posts
RabtejKalra
#1 h  Apr 11, 2025, 10:16 PM
Y by
A number is considered happy if it contains at least one digit exactly twice. For instance, the numbers 2020 and 2024 are happy, but the numbers 2019 and 2022 are not. How many happy counting numbers are there that are less than 10,000?
Z K Y
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HacheB2031
368 posts
HacheB2031
#2 h  Apr 11, 2025, 10:32 PM
Y by
ez sol
This post has been edited 1 time. Last edited by HacheB2031, Apr 11, 2025, 10:36 PM
Reason: imagine having a computational error wouldnt be me
Z K Y
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Bummer12345
132 posts
Bummer12345
#3 h  Apr 11, 2025, 10:38 PM
Y by
@above there can also be numbers with a digit that repeats more than twice
Z K Y
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HacheB2031
368 posts
HacheB2031
#4 h  Apr 11, 2025, 10:42 PM
Y by
Bummer12345 wrote:
@above there can also be numbers with a digit that repeats more than twice

oops yeah i didn't count $0043$ and stuff let me fix that
HacheB2031 wrote:
idoit sol
Z K Y
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RabtejKalra
64 posts
RabtejKalra
#5 h  Apr 11, 2025, 11:03 PM
Y by
No, 0043 and stuf like that would just be considered 43, so they're sad numbers
Z K Y
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maxamc
547 posts
maxamc
#6 h  Apr 11, 2025, 11:05 PM
Y by
sol
This post has been edited 1 time. Last edited by maxamc, Apr 12, 2025, 12:19 AM
Reason: mistake
Z K Y
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iwastedmyusername
88 posts
iwastedmyusername
#7 h  Apr 12, 2025, 12:00 AM
Y by
maxamc wrote:
sol

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383
Z K Y
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maxamc
547 posts
maxamc
#8 h  Apr 12, 2025, 12:18 AM
Y by
iwastedmyusername wrote:
maxamc wrote:
sol

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383

oops, edited my post
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sadas123
1220 posts
sadas123
#9 h  Apr 12, 2025, 2:08 AM
Y by
Bashy 3 minute solution

I took a bit of inspiration from you @maxamc
This post has been edited 2 times. Last edited by sadas123, Apr 12, 2025, 1:23 PM
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maxamc
547 posts
maxamc
#10 h  Apr 12, 2025, 3:21 AM
Y by
sadas123 wrote:
Bashy 3 minute solution

I took a bit of inspiration from you @maxamc

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383
Z K Y
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sadas123
1220 posts
sadas123
#11 h  Apr 12, 2025, 1:22 PM
Y by
maxamc wrote:
sadas123 wrote:
Bashy 3 minute solution

I took a bit of inspiration from you @maxamc

You overcounted 243 4 digit numbers (aabb is the same as a permutation of bbaa). So I think the actual answer should be 4626-243=4383

oh woops wait I am dumb :( I should have saw that updating my thingie
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