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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Wednesday at 3:18 PM
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 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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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
Wednesday at 3:18 PM
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
J
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2025 MATHCOUNTS State Hub
SirAppel   242
N 6 minutes ago by ethan2011
Previous Years' "Hubs": (2022) (2023) (2024)Please Read

Now that it's April and we're allowed to discuss, and no one else has made this yet ...
[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) *
[*] 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 41? 38 38)
[*] PA: 38 (41 40 40 38 38 37 36 36 34 34) *
[*] MD: 37 (43 39 39 37 37 37)
[*] CT: 36 (44 39? 38 36 34 34 34 34)
[*] 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)
[*] WI: 34 (40 37 37 34 35 30 28 29 29 29) *
[*] 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!
As per last year's guidelines, refrain from problem discussion until their official release on the MATHCOUNTS website.
242 replies
SirAppel
Apr 1, 2025
ethan2011
6 minutes ago
J
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inequality ( 4 var
SunnyEvan   2
N an hour ago by ektorasmiliotis
Let $ a,b,c,d \in R $ , such that $ a+b+c+d=4 . $ Prove that :
$$ a^4+b^4+c^4+d^4+3 \geq \frac{7}{4}(a^3+b^3+c^3+d^3) $$$$ a^4+b^4+c^4+d^4+ \frac{252}{25} \geq \frac{88}{25}(a^3+b^3+c^3+d^3) $$equality cases : ?
2 replies
SunnyEvan
6 hours ago
ektorasmiliotis
an hour ago
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Inspired by JK1603JK
sqing   6
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 0 $ and $ab+bc+ca=1.$ Prove that$$\frac{abc-2}{abc-1}\ge \frac{4(a^2b+b^2c+c^2a)}{a^3b+b^3c+c^3a+1} $$
6 replies
sqing
Today at 3:31 AM
sqing
an hour ago
J
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Geometry problem
kjhgyuio   1
N 2 hours ago by Mathzeus1024
Source: smo
In trapezium ABCD,AD is parallel to BC and points E and F are midpoints of AB and DC respectively. If
Area of AEFD/Area of EBCF =√3 + 1/3-√3 and the area of triangle ABD is √3 .find the area of trapezium ABCD
1 reply
kjhgyuio
Apr 1, 2025
Mathzeus1024
2 hours ago
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D1018 : Can you do that ?
Dattier   1
N 2 hours ago by Dattier
Source: les dattes à Dattier
We can find $A,B,C$, such that $\gcd(A,B)=\gcd(C,A)=\gcd(A,2)=1$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$.

For example :

$C=20$
$A=47650065401584409637777147310342834508082136874940478469495402430677786194142956609253842997905945723173497630499054266092849839$

$B=238877301561986449355077953728734922992395532218802882582141073061059783672634737309722816649187007910722185635031285098751698$

Can you find $A,B,C$ such that $A>3$ is prime, $C,B \in (\mathbb Z/A\mathbb Z)^*$ with $o(C)=(A-1)/2$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$?
1 reply
Dattier
Mar 24, 2025
Dattier
2 hours ago
J
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2025 Caucasus MO Juniors P3
BR1F1SZ   1
N 2 hours ago by FarrukhKhayitboyev
Source: Caucasus MO
Let $K$ be a positive integer. Egor has $100$ cards with the number “$2$” written on them, and $100$ cards with the number “$3$” written on them. Egor wants to paint each card red or blue so that no subset of cards of the same color has the sum of the numbers equal to $K$. Find the greatest $K$ such that Egor will not be able to paint the cards in such a way.
1 reply
BR1F1SZ
Mar 26, 2025
FarrukhKhayitboyev
2 hours ago
J
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1 area = 2025 points
giangtruong13   0
2 hours ago
In a plane give a set $H$ that has 8097 distinct points with area of a triangle that has 3 points belong to $H$ all $ \leq 1$. Prove that there exists a triangle $G$ that has the area $\leq 1 $ contains at least 2025 points that belong to $H$( each of that 2025 points can be inside the triangle or lie on the edge of triangle $G$)X
0 replies
giangtruong13
2 hours ago
0 replies
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Burak0609
Burak0609   0
2 hours ago
So if $2 \nmid n\implies$ $2d_2+d_4+d_5=d_7$ is even it's contradiction. I mean $2 \mid n and d_2=2$.
If $3\mid n \implies d_3=3$ and $(d_6+d_7)^2=n+1,3d_6d_7=n \implies d_6^2-d_6d_7+d_7^2=1$,we can see the only solution is$d_6=d_7=1$ and it is contradiction.
If $4 \mid n d_3=4$ and $(d_6+d_7)^2-4d_6d_7=1 \implies d_7=d_6+1$. So $n=4d_6(d_6+1)$.İt means $8 \mid n$.
If $d_6=8 n=4.8.9=288$ but $3 \nmid n$.İt is contradiction.
If $d_5=8$ we have 2 option. Firstly $d_4=5 \implies 2d_2+d_4+d_5=17=d_7 d_6=16$ but $10 \mid n$ is contradiction. Secondly $d_4=7 \implies d_7=2.2+7+8=19 and d_6=18$ but $3 \nmid n$ is contradiction. I mean $d_4=8 \implies d_7=d_5+12, n=4(d_5+11)(d_5+12) and d_5 \mid n=4(d_5+11)(d_5+12)$. So $d_5 \mid 4.11.12 \implies d_5 \mid 16.11$. If $d_5=16 d_6=27$ but $3 \nmid n$ is contradiction. I mean $d_5=11,d_6=22,d_7=23$. The only solution is $n=2024$.
0 replies
Burak0609
2 hours ago
0 replies
J
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skibidi dop
DhruvJha   22
N 3 hours ago by giangtruong13
Kai is singing the skibidi dop dop dop yes yes yes song 28 times in the span of a fortnite(two weeks). How many times using this rate does kai sing skibidi skibidi dop dop yes yes yes song in a span of 4 days using the rate. Express your answer in terms of sigma.
22 replies
DhruvJha
Today at 12:40 AM
giangtruong13
3 hours ago
J
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Good Partitions
va2010   25
N 3 hours ago by lelouchvigeo
Source: 2015 ISL C3
For a finite set $A$ of positive integers, a partition of $A$ into two disjoint nonempty subsets $A_1$ and $A_2$ is $\textit{good}$ if the least common multiple of the elements in $A_1$ is equal to the greatest common divisor of the elements in $A_2$. Determine the minimum value of $n$ such that there exists a set of $n$ positive integers with exactly $2015$ good partitions.
25 replies
va2010
Jul 7, 2016
lelouchvigeo
3 hours ago
J
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An inequality on triangles sides
nAalniaOMliO   7
N 4 hours ago by navier3072
Source: Belarusian National Olympiad 2025
Numbers $a,b,c$ are lengths of sides of some triangle. Prove the inequality$$\frac{a}{b+c-a}+\frac{b}{c+a-b}+\frac{c}{a+b-c} \geq \frac{a+b}{2c}+\frac{b+c}{2a}+\frac{c+a}{2b}$$
7 replies
nAalniaOMliO
Mar 28, 2025
navier3072
4 hours ago
J
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D is incenter
Layaliya   3
N 4 hours ago by rong2020
Source: From my friend in Indonesia
Given an acute triangle \( ABC \) where \( AB > AC \). Point \( O \) is the circumcenter of triangle \( ABC \), and \( P \) is the projection of point \( A \) onto line \( BC \). The midpoints of \( BC \), \( CA \), and \( AB \) are \( D \), \( E \), and \( F \), respectively. The line \( AO \) intersects \( DE \) and \( DF \) at points \( Q \) and \( R \), respectively. Prove that \( D \) is the incenter of triangle \( PQR \).
3 replies
Layaliya
Yesterday at 11:03 AM
rong2020
4 hours ago
J
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Quadratics problem I came up with
V0305   2
N 6 hours ago by Dixit1
$P(x)$ is a quadratic polynomial such that $P(1) = 2$ and $P(2) = 5$. Find all possible values of $P(7) - P(-4)$.
2 replies
V0305
Nov 3, 2024
Dixit1
6 hours ago
J
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amc10 chances?
aoh11   3
N Today at 4:30 AM by jb2015007
if i got a 55.5 on amc10, what are my chances of making aime???
3 replies
aoh11
Today at 4:03 AM
jb2015007
Today at 4:30 AM
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J
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mathcounts state discussion
Soupboy0   59
N Today at 12:31 AM by Pi_isCool31415
les goo its finally april
59 replies
Soupboy0
Apr 1, 2025
Pi_isCool31415
Today at 12:31 AM
J
mathcounts state discussion
G H J
Reveal topic tags
MATHCOUNTS
L
G H BBookmark kLocked kLocked NReply
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Soupboy0
273 posts
Soupboy0
#46 h  Yesterday at 6:05 PM
Y by
ilikemath247365 wrote:
Tell me if I'm correct for number 24(high change I may be wrong)
If we consider integers with 4 digits and only 2 even digits or 3 even digits exactly, we can have:
EEOO
EOEO
OEEO
EEEO

where E denotes even digits and O denotes odd digits.
We can just simply count up how many even digits are possible or how many odd digits are possible and get that: 4*5*5*5 + 4*5*5*5 + 5*5*5*5 + 4*5*5*5 = 500 + 500 + 625 + 500 = 2125.

If we consider integers with 3 digits that can only have 2 even digits max, we can have:
EEO which results in 4*5*5 = 100.
So 2125 + 100 = 2225(we can't have two-digit integers or one-digit integers for obvious reasons). So is the answer 2225? Can somebody confirm? Thanks.

bro I'm such a bot i gotta start reading books :skul:
2125 moment
Z K Y
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c_double_sharp
301 posts
c_double_sharp
#47 h  Yesterday at 6:15 PM
Y by
Soupboy0 wrote:
ilikemath247365 wrote:
Tell me if I'm correct for number 24(high change I may be wrong)
If we consider integers with 4 digits and only 2 even digits or 3 even digits exactly, we can have:
EEOO
EOEO
OEEO
EEEO

where E denotes even digits and O denotes odd digits.
We can just simply count up how many even digits are possible or how many odd digits are possible and get that: 4*5*5*5 + 4*5*5*5 + 5*5*5*5 + 4*5*5*5 = 500 + 500 + 625 + 500 = 2125.

If we consider integers with 3 digits that can only have 2 even digits max, we can have:
EEO which results in 4*5*5 = 100.
So 2125 + 100 = 2225(we can't have two-digit integers or one-digit integers for obvious reasons). So is the answer 2225? Can somebody confirm? Thanks.

bro I'm such a bot i gotta start reading books :skul:
2125 moment

same i hate reading
Z K Y
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Soupboy0
273 posts
Soupboy0
#48 h  Yesterday at 6:22 PM
Y by
was tthe answer to 23 216
Z K Y
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gamma_pi
153 posts
gamma_pi
#49 h  Yesterday at 6:25 PM
Y by
EPSCE wrote:
Yeah, the sprint was about chapter level. Unfortunately, I didn't get target #6, my friend got 2024. What did you guys get for target #8?

my friedns 21/2 i think
they got it right
This post has been edited 1 time. Last edited by gamma_pi, Yesterday at 6:25 PM
Z K Y
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jb2015007
1777 posts
jb2015007
#50 h  Yesterday at 6:46 PM
Y by
nah it was 27/2 if i remember correctly
Z K Y
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Elodie-AW
234 posts
Elodie-AW
#51 h  Yesterday at 6:52 PM
Y by
I got pretty nervous and messed up kind of badly :oops:
Z K Y
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iwastedmyusername
64 posts
iwastedmyusername
#52 h  Yesterday at 7:22 PM
Y by
was there a non bashy way to do target #4
Z K Y
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jb2015007
1777 posts
jb2015007
#53 h  Yesterday at 7:23 PM
Y by
yes js let the side lengths be a and b, and the hypotneuse is 40-a-b, and then solve
Z K Y
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iwastedmyusername
64 posts
iwastedmyusername
#54 h  Yesterday at 7:26 PM
Y by
wouldnt you have to square 40-a-b though
Z K Y
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jb2015007
1777 posts
jb2015007
#55 h  Yesterday at 7:28 PM
Y by
i js timed myself and did it in 15 secs
its not that big of a deal
Z K Y
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Bummer12345
123 posts
Bummer12345
#56 h  Yesterday at 8:28 PM
Y by
cheese sol
Z K Y
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gamma_pi
153 posts
gamma_pi
#57 h  Yesterday at 9:14 PM • 1 Y
Y by Eddie_tiger
jb2015007 wrote:
nah it was 27/2 if i remember correctly

yeah i think it is
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EightYearLetterman
14 posts
EightYearLetterman
#58 h  Yesterday at 9:17 PM
Y by
iwastedmyusername wrote:
wouldnt you have to square 40-a-b though

a^2 + b^2 = 1600 - 80(a+b) + (a+b)^2
0 = 1600 - 80(40-c) + 2ab
-80c = 1600 - 80*40 + 80
c = -20 + 40 - 1
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Pi_isCool31415
25 posts
Pi_isCool31415
#59 h  Today at 12:30 AM
Y by
target 6 u could just induct and not prove it lol
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Pi_isCool31415
25 posts
Pi_isCool31415
#60 h  Today at 12:31 AM
Y by
Bummer12345 wrote:
cheese sol

bruh even worse sol, calc bash and guess based on answer form
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