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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.

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[*]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
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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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AMC 10 Preparation over 6 months
raresillypanther   30
N 13 minutes ago by derekwang2048
Hi, I'm currently in 8th grade and I have about 6 months left to prepare for the AMC 10, and I really want to qualify for AIME and get above a 100. I took the AMC 8 this year and did really bad, with a score of 16, and a 35 on the MATHCOUNTS Chapter test. I have a feeling I would get about a 70 on the AMC 10 now, so I want to be able to improve by 30 points in 6 months. Is that possible? I have summer break coming up so I feel like I could study for about 4 hours a day every single day, and I'm willing to if that's what it takes. Do you have any ideas for what resources I should use? I know about Alcumus and I have some of the AOPS books, but not all of them. If you have any tips, let me know. Thank you so much!
30 replies
raresillypanther
Yesterday at 10:18 PM
derekwang2048
13 minutes ago
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nice system of equations
outback   4
N 44 minutes ago by Raj_singh1432
Solve in positive numbers the system

$ x_1+\frac{1}{x_2}=4, x_2+\frac{1}{x_3}=1, x_3+\frac{1}{x_4}=4, ..., x_{99}+\frac{1}{x_{100}}=4, x_{100}+\frac{1}{x_1}=1$
4 replies
outback
Oct 8, 2008
Raj_singh1432
44 minutes ago
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Two circles, a tangent line and a parallel
Valentin Vornicu   103
N an hour ago by zuat.e
Source: IMO 2000, Problem 1, IMO Shortlist 2000, G2
Two circles $ G_1$ and $ G_2$ intersect at two points $ M$ and $ N$. Let $ AB$ be the line tangent to these circles at $ A$ and $ B$, respectively, so that $ M$ lies closer to $ AB$ than $ N$. Let $ CD$ be the line parallel to $ AB$ and passing through the point $ M$, with $ C$ on $ G_1$ and $ D$ on $ G_2$. Lines $ AC$ and $ BD$ meet at $ E$; lines $ AN$ and $ CD$ meet at $ P$; lines $ BN$ and $ CD$ meet at $ Q$. Show that $ EP = EQ$.
103 replies
Valentin Vornicu
Oct 24, 2005
zuat.e
an hour ago
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Inequalities
idomybest   3
N 2 hours ago by damyan
Source: The Interesting Around Technical Analysis Three Variable Inequalities
The problem is in the attachment below.
3 replies
idomybest
Oct 15, 2021
damyan
2 hours ago
J
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Function on positive integers with two inputs
Assassino9931   2
N 2 hours ago by Assassino9931
Source: Bulgaria Winter Competition 2025 Problem 10.4
The function $f: \mathbb{Z}_{>0} \times \mathbb{Z}_{>0} \to \mathbb{Z}_{>0}$ is such that $f(a,b) + f(b,c) = f(ac, b^2) + 1$ for any positive integers $a,b,c$. Assume there exists a positive integer $n$ such that $f(n, m) \leq f(n, m + 1)$ for all positive integers $m$. Determine all possible values of $f(2025, 2025)$.
2 replies
Assassino9931
Jan 27, 2025
Assassino9931
2 hours ago
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Normal but good inequality
giangtruong13   4
N 2 hours ago by IceyCold
Source: From a province
Let $a,b,c> 0$ satisfy that $a+b+c=3abc$. Prove that: $$\sum_{cyc} \frac{ab}{3c+ab+abc} \geq \frac{3}{5} $$
4 replies
giangtruong13
Mar 31, 2025
IceyCold
2 hours ago
J
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Math and AI 4 Girls
mkwhe   25
N 2 hours ago by WhitePhoenix
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!
25 replies
1 viewing
mkwhe
Apr 5, 2025
WhitePhoenix
2 hours ago
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9 Did you get into Illinois middle school math Olympiad?
Gavin_Deng   9
N 2 hours ago by K1mchi_
I am simply curious of who got in.
9 replies
Gavin_Deng
Apr 19, 2025
K1mchi_
2 hours ago
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Tiling rectangle with smaller rectangles.
MarkBcc168   61
N 2 hours ago by YaoAOPS
Source: IMO Shortlist 2017 C1
A rectangle $\mathcal{R}$ with odd integer side lengths is divided into small rectangles with integer side lengths. Prove that there is at least one among the small rectangles whose distances from the four sides of $\mathcal{R}$ are either all odd or all even.

Proposed by Jeck Lim, Singapore
61 replies
MarkBcc168
Jul 10, 2018
YaoAOPS
2 hours ago
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A magician has one hundred cards numbered 1 to 100
Valentin Vornicu   49
N 2 hours ago by YaoAOPS
Source: IMO 2000, Problem 4, IMO Shortlist 2000, C1
A magician has one hundred cards numbered 1 to 100. He puts them into three boxes, a red one, a white one and a blue one, so that each box contains at least one card. A member of the audience draws two cards from two different boxes and announces the sum of numbers on those cards. Given this information, the magician locates the box from which no card has been drawn.

How many ways are there to put the cards in the three boxes so that the trick works?
49 replies
Valentin Vornicu
Oct 24, 2005
YaoAOPS
2 hours ago
J
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Nice inequality
sqing   2
N 2 hours ago by Seungjun_Lee
Source: WYX
Let $a_1,a_2,\cdots,a_n (n\ge 2)$ be real numbers . Prove that : There exist positive integer $k\in \{1,2,\cdots,n\}$ such that $$\sum_{i=1}^{n}\{kx_i\}(1-\{kx_i\})<\frac{n-1}{6}.$$Where $\{x\}=x-\left \lfloor x \right \rfloor.$
2 replies
sqing
Apr 24, 2019
Seungjun_Lee
2 hours ago
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Concurrency
Dadgarnia   27
N 2 hours ago by zuat.e
Source: Iranian TST 2020, second exam day 2, problem 4
Let $ABC$ be an isosceles triangle ($AB=AC$) with incenter $I$. Circle $\omega$ passes through $C$ and $I$ and is tangent to $AI$. $\omega$ intersects $AC$ and circumcircle of $ABC$ at $Q$ and $D$, respectively. Let $M$ be the midpoint of $AB$ and $N$ be the midpoint of $CQ$. Prove that $AD$, $MN$ and $BC$ are concurrent.

Proposed by Alireza Dadgarnia
27 replies
Dadgarnia
Mar 12, 2020
zuat.e
2 hours ago
J
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nice geo
Melid   1
N 3 hours ago by Melid
Source: 2025 Japan Junior MO preliminary P9
Let ABCD be a cyclic quadrilateral, which is AB=7 and BC=6. Let E be a point on segment CD so that BE=9. Line BE and AD intersect at F. Suppose that A, D, and F lie in order. If AF=11 and DF:DE=7:6, find the length of segment CD.
1 reply
Melid
3 hours ago
Melid
3 hours ago
J
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easy olympiad problem
kjhgyuio   7
N 3 hours ago by Charizard_637
Find all positive integer values of \( x \) such that
\[ \sqrt{x - 2011} + \sqrt{2011 - x} + 10 \]is an integer.
7 replies
kjhgyuio
Apr 17, 2025
Charizard_637
3 hours ago
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J
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Quadratics problem I came up with
V0305   5
N Apr 8, 2025 by Matheron777
$P(x)$ is a quadratic polynomial such that $P(1) = 2$ and $P(2) = 5$. Find all possible values of $P(7) - P(-4)$.
5 replies
V0305
Nov 3, 2024
Matheron777
Apr 8, 2025
J
Quadratics problem I came up with
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Reveal topic tags
quadratics
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V0305
670 posts
V0305
#1 h  Nov 3, 2024, 11:10 PM
Y by
$P(x)$ is a quadratic polynomial such that $P(1) = 2$ and $P(2) = 5$. Find all possible values of $P(7) - P(-4)$.
This post has been edited 2 times. Last edited by V0305, Nov 3, 2024, 11:26 PM
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Rabbit47
780 posts
Rabbit47
#2 h  Nov 4, 2024, 1:48 AM • 2 Y
Y by aidan0626, HockeyMaster85
We represent $P(x)$ as $ax^2+bx+c$. From the first equation, we have $a+b+c=2$ and from the second we have $4a+2b+c=5$. Note we are trying to find, $49a+7b-16a+4b-c$ which simplifies to $33a+11b$. We also have from the first two equations $3a+b=3$, and multiplying on both sides by $11$ we have $33a+11b=\boxed{33}$, which is our answer.
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Dixit1
11 posts
Dixit1
#3 h  Apr 4, 2025, 4:56 AM
Y by
Since p(1)=2 and p(2)=5, we have the equations

a+b+c=2 and 4a+2b+c=5
Equating both, we will get
b=3(1-a) and c=2a-1
Then p(7) would be 30a+20 and p(-4) would be 30a-13. Subtracting both the equations, we get the answer to be 33.

Hence the answer is 33
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jb2015007
1918 posts
jb2015007
#4 h  Apr 5, 2025, 12:59 AM
Y by
Sol

Also hi V0305!
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Apple_maths60
24 posts
Apple_maths60
#5 h  Apr 7, 2025, 4:56 PM
Y by
Let P(x)= ax²+bx+c
Then, P(1)=a+b+c =2 ....(i)
P(2)=4a+2b+c=5....(ii)
Now (ii)-(i) gives 3a+b =3....(iii)

Now P(7)-P(-4)=11b+33a=11(b+3a) = 33 (from (iii))
Done !!
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Matheron777
1 post
Matheron777
#6 h  Apr 8, 2025, 4:03 PM
Y by
Let the quadratic poly be k(x-1)(x-2)+3x-1 .... {where k is the leading coefficient and poly is made by obersving pattern of provided values}
Now p(7)=30k+20
And p(-4)=30k-13
P(7)-P(-4) = 33 which is our answer
This post has been edited 1 time. Last edited by Matheron777, Apr 8, 2025, 4:10 PM
Reason: Spelling mistake
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