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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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)!

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[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 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
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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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Mathcounts Nationals Written Score Hub
DhruvJha   2
N a few seconds ago by iwastedmyusername
Put in your estimated score on the written nats comp on Sunday after the comp so we can get a good idea of the cdr quals are
2 replies
DhruvJha
32 minutes ago
iwastedmyusername
a few seconds ago
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9 What is the best way to learn math???
lovematch13   99
N 4 minutes ago by GallopingUnicorn45
On the contrary, I'm also gonna try to send this to school admins. PLEASE DO NOT TROLL!!!!
99 replies
lovematch13
May 22, 2023
GallopingUnicorn45
4 minutes ago
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A glass is filled with milk. Two-thirds of its content is poured out and replace
Vulch   5
N 12 minutes ago by valisaxieamc
A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is
5 replies
Vulch
Today at 8:53 AM
valisaxieamc
12 minutes ago
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LOTS of recurrence!
SatisfiedMagma   4
N 16 minutes ago by Reacheddreams
Source: Indian Statistical Institute Entrance UGB 2023/5
There is a rectangular plot of size $1 \times n$. This has to be covered by three types of tiles - red, blue and black. The red tiles are of size $1 \times 1$, the blue tiles are of size $1 \times 1$ and the black tiles are of size $1 \times 2$. Let $t_n$ denote the number of ways this can be done. For example, clearly $t_1 = 2$ because we can have either a red or a blue tile. Also $t_2 = 5$ since we could have tiled the plot as: two red tiles, two blue tiles, a red tile on the left and a blue tile on the right, a blue tile on the left and a red tile on the right, or a single black tile.

[list=a]
[*]Prove that $t_{2n+1} = t_n(t_{n-1} + t_{n+1})$ for all $n > 1$.

[*]Prove that $t_n = \sum_{d \ge 0} \binom{n-d}{d}2^{n-2d}$ for all $n >0$.
[/list]
Here,
\[ \binom{m}{r} = \begin{cases} \dfrac{m!}{r!(m-r)!}, &\text{ if $0 \le r \le m$,} \\ 0, &\text{ otherwise} \end{cases}\]for integers $m,r$.
4 replies
SatisfiedMagma
May 14, 2023
Reacheddreams
16 minutes ago
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combi/nt
blug   1
N 18 minutes ago by blug
Prove that every positive integer $n$ can be written in the form
$$n=a_1+a_2+...+a_k,$$where $a_m=2^i3^j$ for some non-negative $i, j$ such that
$$a_x\nmid a_y$$for every $x, y\leq k$.
1 reply
blug
Yesterday at 3:37 PM
blug
18 minutes ago
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Inequality, inequality, inequality...
Assassino9931   9
N 25 minutes ago by ZeroHero
Source: Al-Khwarizmi Junior International Olympiad 2025 P6
Let $a,b,c$ be real numbers such that \[ab^2+bc^2+ca^2=6\sqrt{3}+ac^2+cb^2+ba^2.\]Find the smallest possible value of $a^2 + b^2 + c^2$.

Binh Luan and Nhan Xet, Vietnam
9 replies
Assassino9931
Today at 9:38 AM
ZeroHero
25 minutes ago
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Vectors in a tilted square
mathwizard888   20
N 28 minutes ago by HamstPan38825
Source: 2016 IMO Shortlist A3
Find all positive integers $n$ such that the following statement holds: Suppose real numbers $a_1$, $a_2$, $\dots$, $a_n$, $b_1$, $b_2$, $\dots$, $b_n$ satisfy $|a_k|+|b_k|=1$ for all $k=1,\dots,n$. Then there exists $\varepsilon_1$, $\varepsilon_2$, $\dots$, $\varepsilon_n$, each of which is either $-1$ or $1$, such that
\[ \left| \sum_{i=1}^n \varepsilon_i a_i \right| + \left| \sum_{i=1}^n \varepsilon_i b_i \right| \le 1. \]
20 replies
mathwizard888
Jul 19, 2017
HamstPan38825
28 minutes ago
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Combi Geo
Adywastaken   0
38 minutes ago
Source: NMTC 2024/8
A regular polygon with $100$ vertices is given. To each vertex, a natural number from the set $\{1,2,\dots,49\}$ is assigned. Prove that there are $4$ vertices $A, B, C, D$ such that if the numbers $a, b, c, d$ are assigned to them respectively, then $a+b=c+d$ and $ABCD$ is a parallelogram.
0 replies
Adywastaken
38 minutes ago
0 replies
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9 MathandAI4Girls!!!
Inaaya   20
N 41 minutes ago by Inaaya
How many problems did y'all solve this year?
I clowned and started the pset the week before :oops:
Though I think if i used the time wisely, I could have at least solved 11 of them
ended up with 9 :wallbash_red:
20 replies
Inaaya
May 7, 2025
Inaaya
41 minutes ago
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Japan MO Finals 2023
parkjungmin   1
N 42 minutes ago by EvansGressfield
It's hard. Help me
1 reply
parkjungmin
Yesterday at 2:35 PM
EvansGressfield
42 minutes ago
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Non-homogenous Inequality
Adywastaken   0
an hour ago
Source: NMTC 2024/7
$a, b, c\in \mathbb{R}$ such that $ab+bc+ca=3abc$. Show that $a^2b+b^2c+c^2a \ge 2(a+b+c)-3$. When will equality hold?
0 replies
Adywastaken
an hour ago
0 replies
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Calculus
youochange   1
N an hour ago by youochange
Find the area enclosed by the curves $e^x,e^{-x},x^2+y^2=1$
1 reply
youochange
2 hours ago
youochange
an hour ago
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Classic Diophantine
Adywastaken   0
an hour ago
Source: NMTC 2024/6
Find all natural number solutions to $3^x-5^y=z^2$.
0 replies
Adywastaken
an hour ago
0 replies
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Indian Geo
Adywastaken   0
an hour ago
Source: NMTC 2024/5
$\triangle ABC$ has $\angle A$ obtuse. Let $D$, $E$, $F$ be the feet of the altitudes from $A$, $B$, $C$ respectively. Let $A_1$, $B_1$, $C_1$ be arbitrary points on $BC$, $CA$, $AB$ respectively. The circles with diameter $AA_1$, $BB_1$, $CC_1$ are drawn. Show that the lengths of the tangents from the orthocentre of $ABC$ to these circles are equal.
0 replies
Adywastaken
an hour ago
0 replies
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Can someone explain this one
hawa   10
N Apr 29, 2025 by VivaanKam
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
10 replies
hawa
Apr 29, 2025
VivaanKam
Apr 29, 2025
J
Can someone explain this one
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Reveal topic tags
inequalities
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hawa
2 posts
hawa
#1 h  Apr 29, 2025, 1:36 AM
Y by
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
Z K Y
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FredyCrooger
62 posts
FredyCrooger
#2 h  Apr 29, 2025, 1:45 AM
Y by
So first you find the change in the difference between the numbers and assuming the question is asking to find the largest $n$, you can add them up and continue from there.
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johnnie.walker
2 posts
johnnie.walker
#3 h  Apr 29, 2025, 1:38 PM
Y by
Hint
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fossasor
603 posts
fossasor
#4 h  Apr 29, 2025, 1:48 PM
Y by
Hint #2
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snake2020
4509 posts
snake2020
#5 h  Apr 29, 2025, 1:51 PM
Y by
Hint #3
This post has been edited 1 time. Last edited by snake2020, Apr 29, 2025, 1:51 PM
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snake2020
4509 posts
snake2020
#6 h  Apr 29, 2025, 2:08 PM
Y by
Solution
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Andrew2019
2310 posts
Andrew2019
#7 h  Apr 29, 2025, 5:32 PM
Y by
snake2020 wrote:
Solution

believe this is incorrect, it says $n$ is less that $2021$, not the sum
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VivaanKam
159 posts
VivaanKam
#8 h  Apr 29, 2025, 8:01 PM
Y by
The general term of the sequence is $a_n=\dfrac{3n(n-1))}{2}$
This post has been edited 1 time. Last edited by VivaanKam, Apr 29, 2025, 8:10 PM
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VivaanKam
159 posts
VivaanKam
#9 h  Apr 29, 2025, 8:04 PM
Y by
But I don't get the problem. Are you saying that $3+9+18+30+\dots +n<2021$ and $n<2021$?
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VivaanKam
159 posts
VivaanKam
#10 h  Apr 29, 2025, 8:05 PM
Y by
nvm I figured it out.
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VivaanKam
159 posts
VivaanKam
#11 h  Apr 29, 2025, 8:23 PM
Y by
Solution
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