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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jun 2, 2025
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this 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 a transformative 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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[list][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
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0 replies
jlacosta
Jun 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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Linetown Mayor Admits Orz
Rijul saini   1
N 28 minutes ago by YaoAOPS
Source: LMAO 2025 Day 1 Problem 2
Having won the elections in Linetown, Turbo the Snail has become mayor, and one of the most pressing issues he needs to work on is the road network. Linetown can be represented as a configuration of $2025$ lines
in the plane, of which no two are parallel and no three are concurrent.

There is one house in Linetown for each pairwise intersection of two lines. The $2025$ lines are used as roads by the townsfolk. In the past, the roads in Linetown used to be two-way, but this often led to residents accidentally cycling back to where they started.

Turbo wants to make each of the $2025$ roads one-way such that it is impossible for any resident to start at a house, follow the roads in the correct directions, and end up back at the original house. In how many ways can Turbo achieve this?

Proposed by Archit Manas
1 reply
1 viewing
Rijul saini
Yesterday at 6:59 PM
YaoAOPS
28 minutes ago
J
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Functional equation: f(xf(y)+f(x)f(y))=xf(y)+f(xy)
Behappy0918   2
N 37 minutes ago by Behappy0918
Find all function $f: \mathbb{R} \to \mathbb{R}$ such that for all $x, y\in\mathbb{R}$, $$f(xf(y)+f(x)f(y))=xf(y)+f(xy)$$
2 replies
Behappy0918
Tuesday at 12:24 PM
Behappy0918
37 minutes ago
J
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Painting Beads on Necklace
amuthup   47
N an hour ago by ezpotd
Source: 2021 ISL C2
Let $n\ge 3$ be a fixed integer. There are $m\ge n+1$ beads on a circular necklace. You wish to paint the beads using $n$ colors, such that among any $n+1$ consecutive beads every color appears at least once. Find the largest value of $m$ for which this task is $\emph{not}$ possible.

Carl Schildkraut, USA
47 replies
amuthup
Jul 12, 2022
ezpotd
an hour ago
J
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Onto the altitude'
TheUltimate123   4
N an hour ago by EpicBird08
Source: Extension of nukelauncher's and my Mock AIME #15 (https://artofproblemsolving.com/community/c875089h1825979p12212193)
In triangle $ABC$, let $D$, $E$, and $F$ denote the feet of the altitudes from $A$, $B$, and $C$, respectively, and let $O$ denote the circumcenter of $\triangle ABC$. Points $X$ and $Y$ denote the projections of $E$ and $F$, respectively, onto $\overline{AD}$, and $Z=\overline{AO}\cap\overline{EF}$. There exists a point $T$ such that $\angle DTZ=90^\circ$ and $AZ=AT$. If $P=\overline{AD}\cap\overline{ZT}$ and $Q$ lies on $\overline{EF}$ such that $\overline{PQ}\parallel\overline{BC}$, prove that line $AQ$ bisects $\overline{BC}$.
4 replies
TheUltimate123
May 19, 2019
EpicBird08
an hour ago
J
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The Bank of Oslo
mathisreaI   60
N an hour ago by ezpotd
Source: IMO 2022 Problem 1
The Bank of Oslo issues two types of coin: aluminum (denoted A) and bronze (denoted B). Marianne has $n$ aluminum coins and $n$ bronze coins arranged in a row in some arbitrary initial order. A chain is any subsequence of consecutive coins of the same type. Given a fixed positive integer $k \leq 2n$, Gilberty repeatedly performs the following operation: he identifies the longest chain containing the $k^{th}$ coin from the left and moves all coins in that chain to the left end of the row. For example, if $n=4$ and $k=4$, the process starting from the ordering $AABBBABA$ would be $AABBBABA \to BBBAAABA \to AAABBBBA \to BBBBAAAA \to ...$

Find all pairs $(n,k)$ with $1 \leq k \leq 2n$ such that for every initial ordering, at some moment during the process, the leftmost $n$ coins will all be of the same type.
60 replies
mathisreaI
Jul 13, 2022
ezpotd
an hour ago
J
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2-var inequality
sqing   2
N an hour ago by Rohit-2006
Source: Own
Let $ a,b\geq 0 $ and $\frac{1}{a^2+3} + \frac{1}{b^2+3} -ab\leq \frac{1}{2}.$ Prove that
$$ a^2+ab+b^2 \geq \frac{3(\sqrt{57}-7)}{4}$$Let $ a,b\geq 0 $ and $\frac{a}{b^2+3} + \frac{b}{a^2+3} +ab\leq \frac{1}{2}.$ Prove that
$$ a^2+ab+b^2 \leq \frac{9}{4}$$Let $ a,b\geq 0 $ and $ \frac{a}{b^3+3}+\frac{b}{a^3+3}-ab\leq \frac{1}{2}.$ Prove that
$$ a^2+ab+b^2 \geq \frac{9}{4}$$
2 replies
sqing
Yesterday at 12:55 PM
Rohit-2006
an hour ago
J
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Problem 5
blug   4
N 2 hours ago by Sir_Cumcircle
Source: Czech-Polish-Slovak Junior Match 2025 Problem 5
For every integer $n\geq 1$ prove that
$$\frac{1}{n+1}-\frac{2}{n+2}+\frac{3}{n+3}-\frac{4}{n+4}+...+\frac{2n-1}{3n-1}>\frac{1}{3}.$$
4 replies
blug
May 19, 2025
Sir_Cumcircle
2 hours ago
J
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Cool integer FE
Rijul saini   2
N 2 hours ago by ZVFrozel
Source: LMAO Revenge 2025 Day 1 Problem 1
Alice has a function $f : \mathbb N \rightarrow \mathbb N$ such that for all naturals $a, b$ the function satisfies:
\[a + b \mid a^{f(a)} + b^{f(b)} \]Bob wants to find all possible functions Alice could have. Help Bob and find all functions that Alice could have.
2 replies
Rijul saini
Yesterday at 7:06 PM
ZVFrozel
2 hours ago
J
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star on a quilt
derekwang2048   22
N 2 hours ago by RedFireTruck
Source: 2025 AMC 8 #1
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire $4$-by-$4$ grid is covered by the star?

$\textbf{(A)}\ 40\qquad \textbf{(B)}\ 50\qquad \textbf{(C)}\ 60\qquad \textbf{(D)}\ 75\qquad \textbf{(E)}\ 80$
IMAGE

Thank you @zhenghua for the diagram!
22 replies
derekwang2048
Jan 30, 2025
RedFireTruck
2 hours ago
J
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Frustration with Olympiad Geo
gulab_jamun   18
N 2 hours ago by cooljoseph
Ok, so right now, I am doing the EGMO book by Evan Chen, but when it comes to problems, there are some that just genuinely frustrate me and I don't know how to deal with them. For example, I've spent 1.5 hrs on the second to last question in chapter 2, and used all the hints, and I still am stuck. It just frustrates me incredibly. Any tips on managing this? (or.... am I js crashing out too much?)
18 replies
gulab_jamun
May 29, 2025
cooljoseph
2 hours ago
J
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A beautiful collinearity regarding three wonderful points
math_pi_rate   10
N 2 hours ago by alexanderchew
Source: Own
Let $\triangle DEF$ be the medial triangle of an acute-angle triangle $\triangle ABC$. Suppose the line through $A$ perpendicular to $AB$ meet $EF$ at $A_B$. Define $A_C,B_A,B_C,C_A,C_B$ analogously. Let $B_CC_B \cap BC=X_A$. Similarly define $X_B$ and $X_C$. Suppose the circle with diameter $BC$ meet the $A$-altitude at $A'$, where $A'$ lies inside $\triangle ABC$. Define $B'$ and $C'$ similarly. Let $N$ be the circumcenter of $\triangle DEF$, and let $\omega_A$ be the circle with diameter $X_AN$, which meets $\odot (X_A,A')$ at $A_1,A_2$. Similarly define $\omega_B,B_1,B_2$ and $\omega_C,C_1,C_2$.
1) Show that $X_A,X_B,X_C$ are collinear.
2) Prove that $A_1,A_2,B_1,B_2,C_1,C_2$ lie on a circle centered at $N$.
3) Prove that $\omega_A,\omega_B,\omega_C$ are coaxial.
4) Show that the line joining $X_A,X_B,X_C$ is perpendicular to the radical axis of $\omega_A,\omega_B,\omega_C$.
10 replies
math_pi_rate
Nov 8, 2018
alexanderchew
2 hours ago
J
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Tricky FE
Rijul saini   4
N 2 hours ago by YaoAOPS
Source: LMAO 2025 Day 1 Problem 1
Let $\mathbb{R}$ denote the set of all real numbers. Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$f(xy) + f(f(y)) = f((x + 1)f(y))$$for all real numbers $x$, $y$.

Proposed by MV Adhitya and Kanav Talwar
4 replies
Rijul saini
Yesterday at 6:58 PM
YaoAOPS
2 hours ago
J
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MOP Emails Out! (2025)
Mathandski   121
N 3 hours ago by Schintalpati
What an emotional roller coaster the past 34 days have been.

Congrats to all that qualified!
121 replies
Mathandski
Apr 22, 2025
Schintalpati
3 hours ago
J
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Solutions to Challenging Problems in Middle School Math by Ertan Kay
BlisterBud7S   1
N 4 hours ago by Gavin_Deng
Hi,

I have purchased this book, however cannot locate a copy of their solutions manual. Could someone please help wit this?
1 reply
BlisterBud7S
Yesterday at 2:22 AM
Gavin_Deng
4 hours ago
J
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J
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MathCamp Decisions 2025
hellohannah   55
N Apr 18, 2025 by ninjaforce
Post relevant details if you want, also timestamp of email if you want
55 replies
hellohannah
Apr 17, 2025
ninjaforce
Apr 18, 2025
J
MathCamp Decisions 2025
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Reveal topic tags
summer program
Mathcamp
email
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G H BBookmark kLocked kLocked NReply
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mineric
62 posts
mineric
#42 h  Apr 17, 2025, 11:40 PM
Y by
plang2008 wrote:
mineric wrote:
Whats the chance that waitlist gets in :sob:
i'm not sure how long the waitlist is but i would guess not very long because i've barely seen any waitlists
last year 72/77 people went so ig 5 people got off the waitlist
so don't expect to get off (especially since mop doesn't conflict with mcsp) but congrats and good luck!

:noo: (im cooked)
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freshestcheese
41 posts
freshestcheese
#43 h  Apr 17, 2025, 11:54 PM
Y by
it says i got accepted in the system however I have not received an email (first time applicant in 11th)

i solved only 4/6 (1,2,3,5) and my only comp experience is horrendously failing the AIME this year so I think the essays carried [but i had some really "unique" experiences to write about, idt i will say it here tho]
This post has been edited 1 time. Last edited by freshestcheese, Apr 17, 2025, 11:55 PM
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Alex-131
5404 posts
Alex-131
#44 h  Apr 17, 2025, 11:56 PM
Y by
freshestcheese wrote:
it says i got accepted in the system however I have not received an email (first time applicant in 11th)

i solved only 4/6 (1,2,3,5) and I horrendously failed the AIME so I think the essays carried [but i had some really "unique" experiences to write about, idt i will say it here tho]

Congrats! I suppose it is time to get some "unique" experiences too
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freshestcheese
41 posts
freshestcheese
#45 h  Apr 17, 2025, 11:57 PM
Y by
Alex-131 wrote:
freshestcheese wrote:
it says i got accepted in the system however I have not received an email (first time applicant in 11th)

i solved only 4/6 (1,2,3,5) and I horrendously failed the AIME so I think the essays carried [but i had some really "unique" experiences to write about, idt i will say it here tho]

Congrats! I suppose it is time to get some "unique" experiences too

lmao thanks but nah bro you do not want to do that my high school career is beyond normal
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NoSignOfTheta
1752 posts
NoSignOfTheta
#46 h  Apr 18, 2025, 12:16 AM
Y by
napwyj wrote:
i also took calc in 8th grade

What? Do you mean that you got a calc in 8th grade?
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martianrunner
212 posts
martianrunner
#47 h  Apr 18, 2025, 12:30 AM • 1 Y
Y by Pengu14
no i think they mean that they took calculus in 8th

which isn't like totally unfeasible, you can self-study it if you are good enough
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NoSignOfTheta
1752 posts
NoSignOfTheta
#48 h  Apr 18, 2025, 12:30 AM • 1 Y
Y by scannose
But... calc is slang for calculator
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martianrunner
212 posts
martianrunner
#49 h  Apr 18, 2025, 12:31 AM • 1 Y
Y by Pengu14
is it? I've seen it used more commonly to refer to calculus

nonetheless in this case it stands for calculus
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joeym2011
503 posts
joeym2011
#50 h  Apr 18, 2025, 1:48 AM
Y by
Still didn't receive the email, only website showed acceptance
2nd time application, 8th grade, JMO last year, AMO this year
solved all problems and sillied 5b
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lovematch13
672 posts
lovematch13
#51 h  Apr 18, 2025, 2:11 AM • 8 Y
Y by Alex-131, Danielzh, RollingPanda4616, hsuya1, Ilikeminecraft, aidan0626, ninjaforce, cappucher
I worked many hours on my application, hoping I would get in, but I slacked off halfway through. I always wanted to come to Mathcamp after attending MathPath the previous summer, but you apply to a summer camp with a 7% acceptance rate of very talented individuals, things won't go your way more often than not.

I don't regret my application and I certainly don't think they should reconsider any application unless something crazy happened (like someone was confirmed to cheat). After looking at the page in the morning and seeing the words "not accepted" bolded at the top, i didn't really feel anything. Just "emptiness" or "nothing." The rest of the day was painful, and I kept thinking the fact that the decision letter was copypasted was a personal attack (it isn't).

Once I got home from school, that "emptiness" transitioned into a whole slew of negative emotions. I trudged through an Evan Chen handout about Functional Equations, telling myself "I'm going to lock in this year." I checked my grades for the biology test I took first period in the morning and was surprised that i didn't bomb it and got a 95.5% somehow, despite my nonexistent emotional stability and self-control.

I wrote in my About Me that competitions and applications can make people feel inadequate. But I've never experienced it as firsthand as this—being rejected from a camp that I spent hundreds of hours working on an application for. I will almost certainly apply next year, and am not sure what will happen next year. I would like to tell myself that I'm going to lock in and make it next year, but in all honesty I have no idea where I'll be one year from now.

I've never been the top player at any competitions or math in general. I'm only a kid who likes solving math problems. I will always find joy in solving problems, like I did seeing my first AMC 8 test, but Mathcamp 2025 will not be part of my life story, but the scars from its application will be.

This is all cope, just needed a place to put my sadness. If you disagree, please spare the hate and just don't comment, I know what this community is like.
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freshestcheese
41 posts
freshestcheese
#52 h  Apr 18, 2025, 3:19 AM
Y by
lovematch13 wrote:
I worked many hours on my application, hoping I would get in, but I slacked off halfway through. I always wanted to come to Mathcamp after attending MathPath the previous summer, but you apply to a summer camp with a 7% acceptance rate of very talented individuals, things won't go your way more often than not.

I don't regret my application and I certainly don't think they should reconsider any application unless something crazy happened (like someone was confirmed to cheat). After looking at the page in the morning and seeing the words "not accepted" bolded at the top, i didn't really feel anything. Just "emptiness" or "nothing." The rest of the day was painful, and I kept thinking the fact that the decision letter was copypasted was a personal attack (it isn't).

Once I got home from school, that "emptiness" transitioned into a whole slew of negative emotions. I trudged through an Evan Chen handout about Functional Equations, telling myself "I'm going to lock in this year." I checked my grades for the biology test I took first period in the morning and was surprised that i didn't bomb it and got a 95.5% somehow, despite my nonexistent emotional stability and self-control.

I wrote in my About Me that competitions and applications can make people feel inadequate. But I've never experienced it as firsthand as this—being rejected from a camp that I spent hundreds of hours working on an application for. I will almost certainly apply next year, and am not sure what will happen next year. I would like to tell myself that I'm going to lock in and make it next year, but in all honesty I have no idea where I'll be one year from now.

I've never been the top player at any competitions or math in general. I'm only a kid who likes solving math problems. I will always find joy in solving problems, like I did seeing my first AMC 8 test, but Mathcamp 2025 will not be part of my life story, but the scars from its application will be.

This is all cope, just needed a place to put my sadness. If you disagree, please spare the hate and just don't comment, I know what this community is like.

its ok bro we're here for you, there is many years for you to come, just keep pushing and a great opportunity will present itself to you eventually
This post has been edited 1 time. Last edited by freshestcheese, Apr 18, 2025, 3:19 AM
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profhong
8 posts
profhong
#53 h  Apr 18, 2025, 3:36 AM
Y by
hellohannah wrote:
waitlisted :(

app:
almost full solve (except 2 vs 3 on 6c and the bonus on 2)
solid essay i think? not really sure

stats:
9th grade
2x jmo
1x red mop
solid resume for higher math? taken a bunch of "college level classes" for whatever that means at my school
AP calc 5 in 7th grade

This is likely a top 3 profile (in competition math) among 9th graders in the US. The camp admission officers waitlisted you probably because they thought you are going to MOP again this year. It does not mean that you are not as strong as the other applicants.
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ninjaforce
96 posts
ninjaforce
#54 h  Apr 18, 2025, 4:08 AM
Y by
profhong wrote:
hellohannah wrote:
waitlisted :(

app:
almost full solve (except 2 vs 3 on 6c and the bonus on 2)
solid essay i think? not really sure

stats:
9th grade
2x jmo
1x red mop
solid resume for higher math? taken a bunch of "college level classes" for whatever that means at my school
AP calc 5 in 7th grade

This is likely a top 3 profile (in competition math) among 9th graders in the US. The camp admission officers waitlisted you probably because they thought you are going to MOP again this year. It does not mean that you are not as strong as the other applicants.

You can attend both MOP and MCSP in the same summer—they do not conflict.
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MathPerson12321
3801 posts
MathPerson12321
#55 h  Apr 18, 2025, 4:17 AM
Y by
ninjaforce wrote:
profhong wrote:
hellohannah wrote:
waitlisted :(

app:
almost full solve (except 2 vs 3 on 6c and the bonus on 2)
solid essay i think? not really sure

stats:
9th grade
2x jmo
1x red mop
solid resume for higher math? taken a bunch of "college level classes" for whatever that means at my school
AP calc 5 in 7th grade

This is likely a top 3 profile (in competition math) among 9th graders in the US. The camp admission officers waitlisted you probably because they thought you are going to MOP again this year. It does not mean that you are not as strong as the other applicants.

You can attend both MOP and MCSP in the same summer—they do not conflict.

i think its because if youve already mopped then the curriculum wouldnt be good for you
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ninjaforce
96 posts
ninjaforce
#56 h  Apr 18, 2025, 4:19 AM • 2 Y
Y by MathPerson12321, cappucher
MathPerson12321 wrote:
i think its because if youve already mopped then the curriculum wouldnt be good for you

MOP and MCSP focus on different things, and there is always a plethora of MOPpers who attend.
This post has been edited 1 time. Last edited by ninjaforce, Apr 18, 2025, 4:21 AM
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