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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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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)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]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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All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
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
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
Alcumus vs books
UnbeatableJJ   14
N 24 minutes ago by GallopingUnicorn45
If I am aiming for AIME, then JMO afterwards, is Alcumus adequate, or I still need to do the problems on AoPS books?

I got AMC 23 this year, and never took amc 10 before. If I master the alcumus of intermediate algebra (making all of the bars blue). How likely I can qualify for AIME 2026?
14 replies
1 viewing
UnbeatableJJ
Apr 23, 2025
GallopingUnicorn45
24 minutes ago
strange geometry problem
Zavyk09   0
an hour ago
Source: own
Let $ABC$ be a triangle with circumcenter $O$ and internal bisector $AD$. Let $AD$ cuts $(O)$ again at $M$ and $MO$ cuts $(O)$ again at $N$. Point $L$ lie on $AD$ such that $(AD, LM) = -1$. The line pass through $L$ and perpendicular to $AD$ intersects $NC, NB$ at $P, Q$ respectively. Let circumcircle of $\triangle NPQ$ cuts $(O)$ at $G \ne N$. Prove that $\angle AGD = 90^{\circ}$.
0 replies
Zavyk09
an hour ago
0 replies
A sharp one with 3 var (3)
mihaig   3
N an hour ago by JARP091
Source: Own
Let $a,b,c\geq0$ satisfying
$$\left(a+b+c-2\right)^2+8\leq3\left(ab+bc+ca\right).$$Prove
$$a^2+b^2+c^2+5abc\geq8.$$
3 replies
mihaig
Yesterday at 5:17 PM
JARP091
an hour ago
Dophantine equation
MENELAUSS   2
N an hour ago by Assassino9931
Solve for $x;y \in \mathbb{Z}$ the following equation :
$$3^x-8^y =2xy+1 $$
2 replies
MENELAUSS
Yesterday at 11:35 PM
Assassino9931
an hour ago
Serbian selection contest for the IMO 2025 - P6
OgnjenTesic   11
N an hour ago by JARP091
Source: Serbian selection contest for the IMO 2025
For an $n \times n$ table filled with natural numbers, we say it is a divisor table if:
- the numbers in the $i$-th row are exactly all the divisors of some natural number $r_i$,
- the numbers in the $j$-th column are exactly all the divisors of some natural number $c_j$,
- $r_i \ne r_j$ for every $i \ne j$.

A prime number $p$ is given. Determine the smallest natural number $n$, divisible by $p$, such that there exists an $n \times n$ divisor table, or prove that such $n$ does not exist.

Proposed by Pavle Martinović
11 replies
OgnjenTesic
May 22, 2025
JARP091
an hour ago
Shortest number theory you might've seen in your life
AlperenINAN   9
N an hour ago by Assassino9931
Source: Turkey JBMO TST 2025 P4
Let $p$ and $q$ be prime numbers. Prove that if $pq(p+1)(q+1)+1$ is a perfect square, then $pq + 1$ is also a perfect square.
9 replies
AlperenINAN
May 11, 2025
Assassino9931
an hour ago
Wrong Answer on a Street Math Challenge
miguel00   17
N an hour ago by miguel00
Hello AoPS Community,

I was just watching this video link (those of you that are Korean, you should watch it!) but I came across a pretty hard vector geometry problem (keep in mind contestants have to solve this problem in 5 minutes). No one got this problem (no surprise there) but I am posting because I actually think the answer he gave is wrong.

So the problem goes like this: Referencing the diagram attached, there are three externally tangent unit circles $C_1, C_2, C_3$ on a plane with centers $O_1, O_2, O_3$, respectively. $H$ is feet of the perpendicular from $O_1$ to $O_2O_3$ and $A$ and $B$ are intersections of line $O_1H$ with circle $C_1$. Points $P$ and $Q$ can move around the circle $C_2$ and $C_3$, respectively. Find the maximum possible value of $|\overrightarrow{AQ}+\overrightarrow{PB}|$.


I got my answer but the video said their 1st answer but they later corrected it on the comments to their 2nd answer. I'll let you guys attempt the problem and will give my solution shortly after. Thanks in advance!

-miguel00
17 replies
miguel00
Today at 1:37 AM
miguel00
an hour ago
Inequality about number of spanning trees of graph
CBMaster   0
an hour ago
Let \( k(G) \) be the number of spanning trees in a graph \( G \), where \( G \) may have multiple edges and loops.

For two edges \( e \) and \( f \) of \( G \), let \( G/e \), \( G/f \), and \( G/\{e,f\} \) denote the graphs obtained by contracting the edges \( e \), \( f \), and both \( e \) and \( f \) in $G$, respectively.

Find a combinatorial proof of the following inequality:
\[
k(G/\{e,f\}) \cdot k(G) \leq k(G/e) \cdot k(G/f)
\]
0 replies
CBMaster
an hour ago
0 replies
1,2,...,2011 around circle such that 8 of 25 successive multiples of 5 and/or 7
parmenides51   1
N 2 hours ago by ririgggg
Source: 2011 Belarus TST 2.1
Is it possible to arrange the numbers $1,2,...,2011$ over the circle in some order so that among any $25$ successive numbers at least $8$ numbers are multiplies of $5$ or $7$ (or both $5$ and $7$) ?

I. Gorodnin
1 reply
parmenides51
Nov 8, 2020
ririgggg
2 hours ago
Sipnayan JHS 2021 F-9
PikaVee   1
N 2 hours ago by PikaVee
Matt and Sai are playing a game of darts together. Matt has a slightly more accurate aim than Sai. In
fact, Matt can hit the bullseye 80% of the time while Sai can only hit it 60% of the time. They take turns
in playing and the first player is determined by a flip of a fair coin. If the probability that Sai scores the
first bullseye is given by $ \frac {a}{b} $ where a and b are relatively prime integers, what is b − a?
1 reply
PikaVee
2 hours ago
PikaVee
2 hours ago
Standart looking FE
Kimchiks926   13
N 2 hours ago by math-olympiad-clown
Source: Baltic Way 2022, Problem 5
Let $\mathbb{R}$ be the set of real numbers. Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(0)+1=f(1)$ and for any real numbers $x$ and $y$,
$$ f(xy-x)+f(x+f(y))=yf(x)+3 $$
13 replies
1 viewing
Kimchiks926
Nov 12, 2022
math-olympiad-clown
2 hours ago
A sharp one with 3 var (2)
mihaig   4
N 2 hours ago by mihaig
Source: Own
Let $a,b,c\geq0$ satisfying
$$\left(a+b+c-2\right)^2+8\leq3\left(ab+bc+ca\right).$$Prove
$$a+b+c+\sqrt{abc}\geq4.$$
4 replies
mihaig
May 26, 2025
mihaig
2 hours ago
Introducing a math summer program for middle school students
harry133   0
Today at 12:52 AM
Introducing IITSP, an online math summer program designed for middle school students over summer.

The program is designed by Professor Shubhrangshu Dasgupta from the Department of Physics at the Indian Institute of Technology Ropar (IIT Ropar).

Please check out the webpage if you are interested in.

https://www.imc-impea.org/IMC/bbs/content.php?co_id=iitsp
0 replies
harry133
Today at 12:52 AM
0 replies
2 headed arrows usage
mathprodigy2011   1
N Yesterday at 11:30 PM by alcumusftwgrind
Source: 2003 USAMO 4
I can't upload the file but I was working with someone on 2003 USAMO p4. When we saw "if and only if" I thought it meant we have to prove it both directions. However, when we looked at Evan Chen's solution after writing it out; Evan Chen used double headed arrows and left it at that. My question is, how did he use them and how do I know when I can or can not use them?
1 reply
mathprodigy2011
Yesterday at 11:09 PM
alcumusftwgrind
Yesterday at 11:30 PM
Mathcounts state
happymoose666   40
N May 8, 2025 by ZMB038
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure
40 replies
happymoose666
Mar 24, 2025
ZMB038
May 8, 2025
Mathcounts state
G H J
G H BBookmark kLocked kLocked NReply
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happymoose666
343 posts
#1 • 2 Y
Y by PikaPika999, nmlikesmath
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure
Z K Y
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programjames1
3046 posts
#2 • 2 Y
Y by PikaPika999, nmlikesmath
Pennsylvania is about median in difficulty. See the cutoff map from last year.
This post has been edited 1 time. Last edited by programjames1, Mar 24, 2025, 10:38 PM
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Andyluo
1003 posts
#3 • 3 Y
Y by programjames1, PikaPika999, nmlikesmath
programjames1 wrote:
Pennsylvania is about median in difficulty. See the cutoff map from last year.

this data is skewed because generally bad states wouldn't post their scores.

Here, Ohio and PA are both shown to be slightly below average, but they both placed 14th and 18th out of 50 states and 6 territories.
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BossLu99
1398 posts
#4 • 1 Y
Y by nmlikesmath
happymoose666 wrote:
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure

hey yo whats ur name im in PA too
Z K Y
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programjames1
3046 posts
#5 • 1 Y
Y by nmlikesmath
Andyluo wrote:
this data is skewed because generally bad states wouldn't post their scores.

Here, Ohio and PA are both shown to be slightly below average, but they both placed 14th and 18th out of 50 states and 6 territories.

Cutoffs are different from top scorers though. I did MATHCOUNTS in two states, each of which typically ranked between 20th and 30th, and had cutoffs one or two points lower than Pennsylvanias. The difference between those states and Pennsylvania is the scores were much closer together.
This post has been edited 2 times. Last edited by programjames1, Mar 24, 2025, 11:06 PM
Z K Y
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happymoose666
343 posts
#7 • 1 Y
Y by nmlikesmath
BossLu99 wrote:
happymoose666 wrote:
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure

hey yo whats ur name im in PA too

Is your name benjamin Lu
Z K Y
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Math-lover1
354 posts
#8 • 1 Y
Y by nmlikesmath
happymoose666 wrote:
BossLu99 wrote:
happymoose666 wrote:
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure

hey yo whats ur name im in PA too

Is your name benjamin Lu

yes he is
Benorz the GOAT

btw I'm the norz viktor wang
Z K Y
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happymoose666
343 posts
#9 • 1 Y
Y by nmlikesmath
he got second
Z K Y
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Pengu14
637 posts
#10 • 1 Y
Y by nmlikesmath
viktorz :omighty:
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ethan2011
349 posts
#11 • 1 Y
Y by nmlikesmath
happymoose666 wrote:
he got second

he got 1st written, 2nd cdr, so i'd say he got 1st
Z K Y
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nmlikesmath
523 posts
#12
Y by
the amount of orzness coming from this post is so high its dangerous
Z K Y
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nmlikesmath
523 posts
#13
Y by
bruh my california chapter is so hard I got 39 and was like 1 away from state qual :wallbash_red:
Z K Y
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fxx11
51 posts
#14 • 1 Y
Y by nmlikesmath
@happymoose666 what grade are you in
Z K Y
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Math-lover1
354 posts
#15 • 1 Y
Y by nmlikesmath
ethan2011 wrote:
happymoose666 wrote:
he got second

he got 1st written, 2nd cdr, so i'd say he got 1st

wait are you Ethan qi
Z K Y
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ethan2011
349 posts
#16 • 1 Y
Y by nmlikesmath
Math-lover1 wrote:
ethan2011 wrote:
happymoose666 wrote:
he got second

he got 1st written, 2nd cdr, so i'd say he got 1st

wait are you Ethan qi

no
I don't live in pa
Z K Y
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fxx11
51 posts
#17 • 1 Y
Y by nmlikesmath
happymoose666 wrote:
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure

r u Shawn Ruan?
Z K Y
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orangebear
724 posts
#18 • 1 Y
Y by nmlikesmath
Pengu14 wrote:
viktorz :omighty:

You mean you orz
Z K Y
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Cerberusman
317 posts
#19 • 1 Y
Y by nmlikesmath
orangebear wrote:
Pengu14 wrote:
viktorz :omighty:

You mean you orz

Off topic but I love your pfp :10:
Z K Y
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Math-lover1
354 posts
#20 • 1 Y
Y by nmlikesmath
fxx11 wrote:
happymoose666 wrote:
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure

r u Shawn Ruan?

no he isn't based off chapter score
Z K Y
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BossLu99
1398 posts
#22
Y by
who is happy moose bro
Z K Y
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ZMB038
286 posts
#23
Y by
@Bosslu99 good luck at nats, you were really good in states.
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happymoose666
343 posts
#24
Y by
ZMB038 wrote:
@Bosslu99 good luck at nats, you were really good in states.

Who are you???
I'm from springhouse
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ZMB038
286 posts
#25
Y by
I'm just a random 6th grader who went to states but did not make cdr :wallbash: .
My chapter is SUPER easy.
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ZMB038
286 posts
#26 • 1 Y
Y by Math-lover1
happy moose are you John Xie, or Robert Zhou?
This post has been edited 1 time. Last edited by ZMB038, Apr 23, 2025, 7:39 PM
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Math-lover1
354 posts
#27
Y by
ZMB038 wrote:
happy moose are you John Xie, or Robert Zhou?

Pretty sure orangebear is John Xie, I know he got CDR (9th-10th) range
This post has been edited 1 time. Last edited by Math-lover1, Apr 25, 2025, 12:29 AM
Reason: edit edit
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ZMB038
286 posts
#28
Y by
Math-lover1 wrote:
ZMB038 wrote:
happy moose are you John Xie, or Robert Zhou?

Pretty sure orangebear is John Xie, I know he got CDR (9th-10th) range

Thanks math-lover1/vicktor wamg
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BossLu99
1398 posts
#29
Y by
ZMB038 wrote:
@Bosslu99 good luck at nats, you were really good in states.

thanks bro
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ZMB038
286 posts
#30
Y by
yeah ofc
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LostRiptide
29 posts
#31
Y by
happymoose666 wrote:
Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure

I'd say the best 2-3 people are quite competitive but the competitiveness generally falls off fast for PA.
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tikachaudhuri
84 posts
#32
Y by
Nice I’m from PA too and I also didn’t make nats :D

Afaik BossLu, orangebear, and MathLover are all cdr people
This post has been edited 1 time. Last edited by tikachaudhuri, Apr 29, 2025, 8:02 PM
Reason: s
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tikachaudhuri
84 posts
#33
Y by
ZMB038 wrote:
happy moose are you John Xie, or Robert Zhou?

not Robert Zhou… :skull: \jk
This post has been edited 1 time. Last edited by tikachaudhuri, Apr 29, 2025, 8:03 PM
Reason: s
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orangebear
724 posts
#34
Y by
tikachaudhuri wrote:
ZMB038 wrote:
happy moose are you John Xie, or Robert Zhou?

not Robert Zhou… :skull: \jk

Oh now I know who you are.
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neeyakkid23
131 posts
#35
Y by
Math-lover1 wrote:
happymoose666 wrote:
Is your name benjamin Lu
yes he is
Benorz the GOAT
why are you glazing this ben jit so hard
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tikachaudhuri
84 posts
#36
Y by
Robert Zhou beat me in cdr chapter and then he beat me at cdr state :skull
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ZMB038
286 posts
#37
Y by
tikachaudhuri wrote:
Robert Zhou beat me in cdr chapter and then he beat me at cdr state :skull

Tika Chaudhuri, Ben Lu, and Robert Zhou are all from the same chapter. Delaware County Chapter in PA is goated.
This post has been edited 1 time. Last edited by ZMB038, May 3, 2025, 6:26 PM
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fxx11
51 posts
#38 • 1 Y
Y by happypi31415
trust in centre county chapter
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happypi31415
755 posts
#39
Y by
fxx11 wrote:
trust in centre county chapter

i can confirm that central will be pretty strong next year :maybe:
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Math-lover1
354 posts
#40
Y by
LostRiptide wrote:

I'd say the best 2-3 people are quite competitive but the competitiveness generally falls off fast for PA.

ouch that hurt
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tikachaudhuri
84 posts
#41
Y by
Math-lover1 wrote:
LostRiptide wrote:

I'd say the best 2-3 people are quite competitive but the competitiveness generally falls off fast for PA.

ouch that hurt

(Math-lover1 got 7th so that's why he's saying that)

Viktorz
This post has been edited 1 time. Last edited by tikachaudhuri, May 7, 2025, 1:40 AM
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Inaaya
423 posts
#42
Y by
ZMB038 wrote:
tikachaudhuri wrote:
Robert Zhou beat me in cdr chapter and then he beat me at cdr state :skull

Tika Chaudhuri, Ben Lu, and Robert Zhou are all from the same chapter. Delaware County Chapter in PA is goated.

i can personally confirm that Tika Chaudhuri is goated
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ZMB038
286 posts
#44
Y by
Inaaya wrote:
ZMB038 wrote:
tikachaudhuri wrote:
Robert Zhou beat me in cdr chapter and then he beat me at cdr state :skull

Tika Chaudhuri, Ben Lu, and Robert Zhou are all from the same chapter. Delaware County Chapter in PA is goated.

i can personally confirm that Tika Chaudhuri is goated

YES! Like I know her, and she thinks she is a failure! If she is a failure what am I?
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