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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
J
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Nice FE from Canada Winter Camp
AshAuktober   0
31 minutes ago
Source: Canada Winter (please provide a link, I can't use search function well on a train)
Find all functions $f:\mathbb{R}\to\mathbb{Z}$ such that $f(x+y)<f(x)+f(y)$ and $f(f(x))=\lfloor x\rfloor+2$ for all reals $x,y$.
0 replies
AshAuktober
31 minutes ago
0 replies
J
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Nepal TST DAY 1 Problem 1
Bata325   5
N 33 minutes ago by ThatApollo777
Source: Nepal TST 2025 p1
Consider a triangle $\triangle ABC$ and some point $X$ on $BC$. The perpendicular from $X$ to $AB$ intersects the circumcircle of $\triangle AXC$ at $P$ and the perpendicular from $X$ to $AC$ intersects the circumcircle of $\triangle AXB$ at $Q$. Show that the line $PQ$ does not depend on the choice of $X$.(Shining Sun, USA)
5 replies
Bata325
Yesterday at 1:21 PM
ThatApollo777
33 minutes ago
J
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State target p8 sol
EaZ_Shadow   72
N 34 minutes ago by SI113
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!
72 replies
EaZ_Shadow
Apr 6, 2025
SI113
34 minutes ago
J
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A geometry about a parallelogram ABCD
nAalniaOMliO   1
N 37 minutes ago by jrpartty
Source: Belarusian National Olympiad 2025
On the side $CD$ of parallelogram $ABCD$ a point $E$ is chosen. The perpendicular from $C$ to $BE$ and the perpendicular from $D$ to $AE$ intersect at $P$. Point $M$ is the midpoint of $PE$.
Prove that the perpendicular from $M$ to $CD$ passes through the center of parallelogram $ABCD$.
Matsvei Zorka
1 reply
nAalniaOMliO
Mar 28, 2025
jrpartty
37 minutes ago
J
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NEPAL TST DAY 2 PROBLEM 2
Tony_stark0094   3
N an hour ago by User_two
Kritesh manages traffic on a $45 \times 45$ grid consisting of 2025 unit squares. Within each unit square is a car, facing either up, down, left, or right. If the square in front of a car in the direction it is facing is empty, it can choose to move forward. Each car wishes to exit the $45 \times 45$ grid.

Kritesh realizes that it may not always be possible for all the cars to leave the grid. Therefore, before the process begins, he will remove $k$ cars from the $45 \times 45$ grid in such a way that it becomes possible for all the remaining cars to eventually exit the grid.

What is the minimum value of $k$ that guarantees that Kritesh's job is possible?
3 replies
Tony_stark0094
3 hours ago
User_two
an hour ago
J
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Unusual Hexagon Geo
oVlad   1
N an hour ago by kokcio
Source: Romania Junior TST 2025 Day 1 P4
Let $ABCDEF$ be a convex hexagon, such that the triangles $ABC$ and $DEF$ are equilateral and the diagonals $AD, BE$ and $CF$ are concurrent. Prove that $AC\parallel DF$ or $BE=AD+CF.$
1 reply
oVlad
2 hours ago
kokcio
an hour ago
J
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JBMO Shortlist 2020 N1
Lukaluce   7
N an hour ago by MATHS_ENTUSIAST
Source: JBMO Shortlist 2020
Determine whether there is a natural number $n$ for which $8^n + 47$ is prime.
7 replies
Lukaluce
Jul 4, 2021
MATHS_ENTUSIAST
an hour ago
J
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Almost Squarefree Integers
oVlad   1
N an hour ago by Tintarn
Source: Romania Junior TST 2025 Day 1 P1
A positive integer $n\geqslant 3$ is almost squarefree if there exists a prime number $p\equiv 1\bmod 3$ such that $p^2\mid n$ and $n/p$ is squarefree. Prove that for any almost squarefree positive integer $n$ the ratio $2\sigma(n)/d(n)$ is an integer.
1 reply
oVlad
2 hours ago
Tintarn
an hour ago
J
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Number Theory Chain!
JetFire008   29
N 2 hours ago by Primeniyazidayi
I will post a question and someone has to answer it. Then they have to post a question and someone else will answer it and so on. We can only post questions related to Number Theory and each problem should be more difficult than the previous. Let's start!

Question 1
29 replies
JetFire008
Apr 7, 2025
Primeniyazidayi
2 hours ago
J
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Navid FE on R+
Assassino9931   2
N 2 hours ago by internationalnick123456
Source: Bulgaria Balkan MO TST 2025
Determine all functions $f: \mathbb{R}^{+} \to \mathbb{R}^{+}$ such that
\[ f(x)f\left(x + 4f(y)\right) = xf\left(x + 3y\right) + f(x)f(y) \]for any positive real numbers $x,y$.
2 replies
Assassino9931
Apr 9, 2025
internationalnick123456
2 hours ago
J
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Determining Integers From Sums
oVlad   0
2 hours ago
Source: Romania Junior TST 2025 Day 1 P3
Let $n\geqslant 3$ be a positiv integer. Ana chooses the positive integers $a_1,a_2,\ldots,a_n$ and for any non-empty subset $A\subseteq\{1,2,\ldots,n\}$ she computes the sum \[s_A=\sum_{k \in A}a_k.\]She orders these sums $s_1\leqslant s_2\leqslant\cdots\leqslant s_{2^n-1}.$ Prove that there exists a subset $B\subseteq\{1,2,\ldots,2^n-1\}$ with $2^{n-2}+1$ elements such that, regardless of the integers $a_1,a_2,\ldots,a_n$ chosen by Ana, these can be determined by only knowing the sums $s_i$ with $i\in B.$
0 replies
oVlad
2 hours ago
0 replies
J
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Bogus Proof Marathon
pifinity   7553
N 6 hours ago by dstanz5
Hi!
I'd like to introduce the Bogus Proof Marathon.

In this marathon, simply post a bogus proof that is middle-school level and the next person will find the error. You don't have to post the real solution :P

Use classic Marathon format: 
[hide=P#]a1b2c3[/hide]
[hide=S#]a1b2c3[/hide]


Example posts:

P(x)
-----
S(x)
P(x+1)
-----
Let's go!! Just don't make it too hard!
7553 replies
pifinity
Mar 12, 2018
dstanz5
6 hours ago
J
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Nice Combinatorics Problem
RabtejKalra   9
N Today at 3:21 AM by maxamc
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?
9 replies
RabtejKalra
Yesterday at 10:16 PM
maxamc
Today at 3:21 AM
J
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Facts About 2025!
Existing_Human1   240
N Yesterday at 11:58 PM by Robert00
Hello AOPS,

As we enter the New Year, the most exciting part is figuring out the mathematical connections to the number we have now temporally entered

Here are some facts about 2025:
$$2025 = 45^2 = (20+25)(20+25)$$$$2025 = 1^3 + 2^3 +3^3 + 4^3 +5^3 +6^3 + 7^3 +8^3 +9^3 = (1+2+3+4+5+6+7+8+9)^2 = {10 \choose 2}^2$$
If anyone has any more facts about 2025, enlighted the world with a new appreciation for the year


(I got some of the facts from this video)
240 replies
Existing_Human1
Jan 1, 2025
Robert00
Yesterday at 11:58 PM
J
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J
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amc10 chances?
aoh11   29
N Apr 5, 2025 by avyaank
if i got a 55.5 on amc10, what are my chances of making aime???
29 replies
aoh11
Apr 4, 2025
avyaank
Apr 5, 2025
J
amc10 chances?
G H J
Reveal topic tags
AMC
AMC 10
AIME
L
G H BBookmark kLocked kLocked NReply
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aoh11
205 posts
aoh11
#1 h  Apr 4, 2025, 4:03 AM • 2 Y
Y by PikaPika999, Exponent11
if i got a 55.5 on amc10, what are my chances of making aime???
Z K Y
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giratina3
485 posts
giratina3
#2 h  Apr 4, 2025, 4:06 AM • 1 Y
Y by PikaPika999
It really depends on how devoted you are to math… I would recommend editing your original post and include how long you can study, some other scores from other test, and books and tests you’ve done, so we have a better idea how to answer your question.
This post has been edited 3 times. Last edited by giratina3, Apr 4, 2025, 4:08 AM
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jkim0656
688 posts
jkim0656
#3 h  Apr 4, 2025, 4:26 AM • 1 Y
Y by PikaPika999
also we need ur age too
a 55 isn't too good but if ur young enough u could pull it off
andyluo had like a 90 point jump over a year i think
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jb2015007
1834 posts
jb2015007
#4 h  Apr 4, 2025, 4:30 AM • 1 Y
Y by PikaPika999
super possible i got around that score this year but im mocking 130's on older tests
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Andyluo
915 posts
Andyluo
#5 h  Apr 4, 2025, 11:28 AM • 1 Y
Y by PikaPika999
jb2015007 wrote:
super possible i got around that score this year but im mocking 130's on older tests

130 on old tests is like equivalent to a 100 on 2022 test
Z K Y
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Dream9
82 posts
Dream9
#6 h  Apr 4, 2025, 12:15 PM • 1 Y
Y by PikaPika999
how do people make these jumps. like I got a 70 first time for 8th grade and all i need is like 25 more pts but I can't up my score
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jb2015007
1834 posts
jb2015007
#7 h  Apr 4, 2025, 6:54 PM • 1 Y
Y by PikaPika999
Andyluo wrote:
jb2015007 wrote:
super possible i got around that score this year but im mocking 130's on older tests

130 on old tests is like equivalent to a 100 on 2022 test

bro u js gotta put the work in
Z K Y
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anticodon
136 posts
anticodon
#8 h  Apr 4, 2025, 7:33 PM
Y by
a raw score of 55.5 will not make aime.
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jb2015007
1834 posts
jb2015007
#9 h  Apr 4, 2025, 7:37 PM • 1 Y
Y by Exponent11
no hes talking about next year :skull:
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Dream9
82 posts
Dream9
#10 h  Apr 4, 2025, 8:30 PM
Y by
jb2015007 wrote:
no hes talking about next year :skull:

I thought he was talking about in general like all the remaining years he has.
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sadas123
1168 posts
sadas123
#11 h  Apr 4, 2025, 9:37 PM
Y by
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?
This post has been edited 1 time. Last edited by sadas123, Apr 4, 2025, 10:21 PM
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BrocSoc
19 posts
BrocSoc
#12 h  Apr 4, 2025, 9:41 PM
Y by
146.5 is not a possible score
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jb2015007
1834 posts
jb2015007
#13 h  Apr 4, 2025, 10:11 PM
Y by
bruh i sold on 2021 AMC 10A
so hard
i only got 100.5
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sadas123
1168 posts
sadas123
#14 h  Apr 4, 2025, 10:21 PM
Y by
jb2015007 wrote:
bruh i sold on 2021 AMC 10A
so hard
i only got 100.5

that's pretty good.
Z K Y
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Catcumber
162 posts
Catcumber
#15 h  Apr 4, 2025, 10:31 PM
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

i guess for you it really just comes down to how much you silly on the test
if you dont silly much, you'll probably get hr, but if you do silly a lot, you wont.
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Bigtree
201 posts
Bigtree
#16 h  Apr 4, 2025, 10:56 PM
Y by
I got 228.5 index my first yr it really just depends on the person
This post has been edited 1 time. Last edited by Bigtree, Apr 4, 2025, 11:00 PM
Reason: .
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mathprodigy2011
286 posts
mathprodigy2011
#17 h  Apr 4, 2025, 11:14 PM
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

if your saying rn, then not very high especially since 2023 amc 10a was a very considerably easy test compared to any past test(other than 2024 amc 10b). Also how did u do worse on amc 10a 2023 than 2022(p=one of the hardest past amcs). anyways if you spend enough time on math then you could probably get in, also pls pm me if u have discord

EDIT: i thought u said DHR lol, u probably have a good chance at hr
This post has been edited 1 time. Last edited by mathprodigy2011, Apr 4, 2025, 11:44 PM
Reason: .
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aoh11
205 posts
aoh11
#18 h  Apr 5, 2025, 3:12 AM
Y by
i am in 8th grade right now btw so am I cooked??
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elizhang101412
1203 posts
elizhang101412
#19 h  Apr 5, 2025, 3:27 AM
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

didnt you make dhr already
Z K Y
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jb2015007
1834 posts
jb2015007
#20 h  Apr 5, 2025, 3:45 AM
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

bruh whyd u edit the 96 on AMC 10A 2021 to a 105 this is such cap bro
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sadas123
1168 posts
sadas123
#21 h  Apr 5, 2025, 11:01 AM
Y by
elizhang101412 wrote:
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

didnt you make dhr already

Nope I missed it on A by 4 points :(
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elizhang101412
1203 posts
elizhang101412
#22 h  Apr 5, 2025, 2:47 PM
Y by
sadas123 wrote:
elizhang101412 wrote:
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

didnt you make dhr already

Nope I missed it on A by 4 points :(

ok then why are you worried about it when you almost made dhr
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jb2015007
1834 posts
jb2015007
#23 h  Apr 5, 2025, 3:05 PM
Y by
no i think he thinks u said hr not dhr
but sadas why change the 96 to a 105 on 2021 AMC 10A Fall
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Dream9
82 posts
Dream9
#24 h  Apr 5, 2025, 6:29 PM • 1 Y
Y by PikaPika999
aoh11 wrote:
if i got a 55.5 on amc10, what are my chances of making aime???

Is this amc 10a or b or highest out of both? Also, 8th grade rn means 2 more years of amc10 and 4 more of amc 12 so I mean it can really go either way. Most people can't turn that score around very well but idrk what you'll do so like personally, maybe 8%?
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cheltstudent
566 posts
cheltstudent
#25 h  Apr 5, 2025, 6:34 PM • 1 Y
Y by PikaPika999
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.
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c_double_sharp
308 posts
c_double_sharp
#26 h  Apr 5, 2025, 7:00 PM • 2 Y
Y by PikaPika999, MathPerson12321
cheltstudent wrote:
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.

*loud incorrect buzzer*
no one trolls about divisibility by 3 and half the problems are sqing’s inequalities

also because this is aops hsm problems are way too hard if you got a 55.5
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MathPerson12321
3684 posts
MathPerson12321
#27 h  Apr 5, 2025, 7:09 PM
Y by
c_double_sharp wrote:
cheltstudent wrote:
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.

*loud incorrect buzzer*
no one trolls about divisibility by 3 and half the problems are sqing’s inequalities

also because this is aops hsm problems are way too hard if you got a 55.5

if you can get the first 15 then hsm is good
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MathPerson12321
3684 posts
MathPerson12321
#28 h  Apr 5, 2025, 7:10 PM
Y by
Dream9 wrote:
aoh11 wrote:
if i got a 55.5 on amc10, what are my chances of making aime???

Is this amc 10a or b or highest out of both? Also, 8th grade rn means 2 more years of amc10 and 4 more of amc 12 so I mean it can really go either way. Most people can't turn that score around very well but idrk what you'll do so like personally, maybe 8%?

you are so wrong
i got a low 60 in 6th grade and was close to aime in 8th, not everyone can, but with effort you can and you cannot put a percentage on this @op
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cheltstudent
566 posts
cheltstudent
#29 h  Apr 5, 2025, 7:12 PM • 1 Y
Y by MathPerson12321
c_double_sharp wrote:
cheltstudent wrote:
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.

*loud incorrect buzzer*
no one trolls about divisibility by 3 and half the problems are sqing’s inequalities

also because this is aops hsm problems are way too hard if you got a 55.5

i forgot about the stupid div 3 though lol, also MSM is more active
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avyaank
53 posts
avyaank
#30 h  Apr 5, 2025, 11:28 PM
Y by
aoh11 wrote:
i am in 8th grade right now btw so am I cooked??

uh if you put in effort then ya sure
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