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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

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Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 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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Arrange positive divisors of n in rectangular table!
cjquines0   42
N 39 minutes ago by SimplisticFormulas
Source: 2016 IMO Shortlist C2
Find all positive integers $n$ for which all positive divisors of $n$ can be put into the cells of a rectangular table under the following constraints:
[list]
[*]each cell contains a distinct divisor;
[*]the sums of all rows are equal; and
[*]the sums of all columns are equal.
[/list]
42 replies
cjquines0
Jul 19, 2017
SimplisticFormulas
39 minutes ago
J
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Find min
hunghd8   0
44 minutes ago
Let $a,b,c$ be nonnegative real numbers such that $ a+b+c\geq 2+abc $. Find min
$$P=a^2+b^2+c^2.$$
0 replies
hunghd8
44 minutes ago
0 replies
J
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postaffteff
JetFire008   16
N an hour ago by JetFire008
Source: Internet
Let $P$ be the Fermat point of a $\triangle ABC$. Prove that the Euler line of the triangles $PAB$, $PBC$, $PCA$ are concurrent and the point of concurrence is $G$, the centroid of $\triangle ABC$.
16 replies
JetFire008
Mar 15, 2025
JetFire008
an hour ago
J
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2025 USAMO Problems
Nippon2283   1
N an hour ago by ohiorizzler1434
Can someone post the 2025 USAMO problems?

Thanks.
1 reply
Nippon2283
2 hours ago
ohiorizzler1434
an hour ago
J
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Cubic function from Olymon
Adywastaken   4
N an hour ago by Adywastaken
Source: Olymon Volume 11 2010 663
Find all $f:\mathbb{R}\rightarrow\mathbb{R}$ such that
$x^2y^2(f(x+y)-f(x)-f(y))=3(x+y)f(x)f(y)$ $\forall$ $x,y \in \mathbb{R}$
4 replies
Adywastaken
Today at 5:25 AM
Adywastaken
an hour ago
J
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Inspired by Titu Andreescu
sqing   1
N 2 hours ago by MS_asdfgzxcvb
Source: Own
Let $ a,b,c>0 $ and $ a+b+c\geq 3abc . $ Prove that
$$a^2+b^2+c^2+1\geq \frac{4}{3}(ab+bc+ca) $$
1 reply
sqing
3 hours ago
MS_asdfgzxcvb
2 hours ago
J
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Incircle
PDHT   1
N 2 hours ago by luutrongphuc
Source: Nguyen Minh Ha
Given a triangle \(ABC\) that is not isosceles at \(A\), let \((I)\) be its incircle, which is tangent to \(BC, CA, AB\) at \(D, E, F\), respectively. The lines \(DE\) and \(DF\) intersect the line passing through \(A\) and parallel to \(BC\) at \(M\) and \(N\), respectively. The lines passing through \(M, N\) and perpendicular to \(MN\) intersect \(IF\) and \(IE\) at \(Q\) and \(P\), respectively.

Prove that \(D, P, Q\) are collinear and that \(PF, QE, DI\) are concurrent.
1 reply
PDHT
Yesterday at 6:14 PM
luutrongphuc
2 hours ago
J
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IMO ShortList 2001, number theory problem 4
orl   43
N 2 hours ago by Zany9998
Source: IMO ShortList 2001, number theory problem 4
Let $p \geq 5$ be a prime number. Prove that there exists an integer $a$ with $1 \leq a \leq p-2$ such that neither $a^{p-1}-1$ nor $(a+1)^{p-1}-1$ is divisible by $p^2$.
43 replies
orl
Sep 30, 2004
Zany9998
2 hours ago
J
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squares in dots - MATHCOUNTS challenge problem
rrusczyk   6
N 2 hours ago by DhruvJha
. . . . .
. . . . .
. . . . .
. . . . .

(That should be a 4x5 grid of dots.) Assuming each point is exactly one unit from its nearest neighbors, how many squares can be formed by connecting groups of four points?
6 replies
rrusczyk
May 27, 2003
DhruvJha
2 hours ago
J
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Inspired by my own results
sqing   2
N 3 hours ago by cazanova19921
Source: Own
Let $ a,b,c\geq \frac{1}{2} . $ Prove that
$$ (a+1)(b+2)(c +1)-15 abc\leq \frac{15}{4}$$$$ (a+1)(b+3)(c +1)-21abc\leq \frac{21}{4}$$$$(a+2)(b+1)(c +2)-25a b c \leq \frac{25}{4}$$$$ (a+2)(b+3)(c +2)-35a b c \leq \frac{35}{2}$$$$ (a+3)(b+1)(c +3)-49a b c \leq \frac{49}{4}$$$$ (a+3)(b+2)(c +3)-49a b c \leq \frac{49}{2}$$
2 replies
sqing
4 hours ago
cazanova19921
3 hours ago
J
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Line through incenter tangent to a circle
Kayak   32
N 3 hours ago by L13832
Source: Indian TST D1 P1
In an acute angled triangle $ABC$ with $AB < AC$, let $I$ denote the incenter and $M$ the midpoint of side $BC$. The line through $A$ perpendicular to $AI$ intersects the tangent from $M$ to the incircle (different from line $BC$) at a point $P$> Show that $AI$ is tangent to the circumcircle of triangle $MIP$.

Proposed by Tejaswi Navilarekallu
32 replies
Kayak
Jul 17, 2019
L13832
3 hours ago
J
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MATHCOUNTS on ESPN
rrusczyk   24
N Today at 4:21 AM by aidan0626
ESPN noon EST - the Countdown round of Nationals.

(Disclaimer: yours truly is an 'analyst' for the broadcast.)
24 replies
rrusczyk
May 27, 2003
aidan0626
Today at 4:21 AM
J
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Chances of mathcounts nats qual
stjwyl   81
N Today at 4:19 AM by mathelvin
Info:
In 8th grade so I'm really hoping I can make nats now

I currently mock around 38 - 40 on nationals questions from 2015+
I mock anywhere from 37 - 42 on state questons from 2020+

For the sprint round I also have noticed that the difficulty jump from questions around 19 and 20 to questions around 22 and 23 has been really large (starting from 2023). I've also noticed that the last three questions (also from 2023 ->) are IMO impossible to do in the 40 minutes.

On target I can get 7/8 or even 8/8 if I'm lucky but it's possible for me to get 6/8

I'm in MA :sob: really hard state so do I have a chance

Edit: Just mocked the 2022 state round and got a 41 (29 sprint, 12 target :sob:)

Currently putting around 3 hrs or so a day and I have been for the past 2 months
States is 3/1 for me :sob:

so am i cooked
81 replies
stjwyl
Feb 21, 2025
mathelvin
Today at 4:19 AM
J
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Mathcounts STRATEGIES
Existing_Human1   17
N Today at 3:54 AM by mathenrichmentaops
Hello commuinty!

I am wondering what your strategies are for mathcounts. Please note I do not mean tips. These can be for all rounds, but please specify. BTW, this is for state, but it can apply to any competition.

Ex:
Team - sit in a specific order
Target - do the easiest first
Sprint - go as fast as possible

I just made up the examples, and you will probably have better strategies, so if you want to help out, please do
17 replies
Existing_Human1
Yesterday at 7:27 PM
mathenrichmentaops
Today at 3:54 AM
J
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J
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Chances of mathcounts nats qual
stjwyl   81
N Today at 4:19 AM by mathelvin
Info:
In 8th grade so I'm really hoping I can make nats now

I currently mock around 38 - 40 on nationals questions from 2015+
I mock anywhere from 37 - 42 on state questons from 2020+

For the sprint round I also have noticed that the difficulty jump from questions around 19 and 20 to questions around 22 and 23 has been really large (starting from 2023). I've also noticed that the last three questions (also from 2023 ->) are IMO impossible to do in the 40 minutes.

On target I can get 7/8 or even 8/8 if I'm lucky but it's possible for me to get 6/8

I'm in MA :sob: really hard state so do I have a chance

Edit: Just mocked the 2022 state round and got a 41 (29 sprint, 12 target :sob:)

Currently putting around 3 hrs or so a day and I have been for the past 2 months
States is 3/1 for me :sob:

so am i cooked
81 replies
stjwyl
Feb 21, 2025
mathelvin
Today at 4:19 AM
J
Chances of mathcounts nats qual
G H J
Reveal topic tags
MATHCOUNTS
L
G H BBookmark kLocked kLocked NReply
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stjwyl
1228 posts
stjwyl
#1 h  Feb 21, 2025, 12:56 AM
Y by
Info:
In 8th grade so I'm really hoping I can make nats now

I currently mock around 38 - 40 on nationals questions from 2015+
I mock anywhere from 37 - 42 on state questons from 2020+

For the sprint round I also have noticed that the difficulty jump from questions around 19 and 20 to questions around 22 and 23 has been really large (starting from 2023). I've also noticed that the last three questions (also from 2023 ->) are IMO impossible to do in the 40 minutes.

On target I can get 7/8 or even 8/8 if I'm lucky but it's possible for me to get 6/8

I'm in MA :sob: really hard state so do I have a chance

Edit: Just mocked the 2022 state round and got a 41 (29 sprint, 12 target :sob:)

Currently putting around 3 hrs or so a day and I have been for the past 2 months
States is 3/1 for me :sob:

so am i cooked
This post has been edited 2 times. Last edited by stjwyl, Feb 22, 2025, 8:51 PM
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chesskingaops
58 posts
chesskingaops
#2 h  Feb 21, 2025, 1:08 AM
Y by
i dont know mathcounts, but you look pretty good
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stjwyl
1228 posts
stjwyl
#3 h  Feb 21, 2025, 1:33 AM
Y by
/bump :D
@above ty for response :D
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DhruvJha
730 posts
DhruvJha
#4 h  Feb 21, 2025, 1:38 AM
Y by
stjwyl wrote:
/bump :D
@above ty for response :D

2022 state was very easy, notoriously easy state round. Your scores are still ectremely high. I can give you access to 2018-2024 Nats, and maybe time yourself like it would be at the real states. I'd say you would need to mock 33+ on those nats round to be a safe "in" (adding 3 for extra pressure due to comp pressure).

Or just move to Arkansas and get in with a 25 like me last year.


And also I would reccomend to amc 10 last 5 problems from those aops mocks user-created. Those tend to be similar to 27-30 on mathcounts states which tends to biggest struggle for someone in ur situation.





Hope I helped!
This post has been edited 3 times. Last edited by DhruvJha, Feb 21, 2025, 1:40 AM
Reason: swsw
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stjwyl
1228 posts
stjwyl
#5 h  Feb 21, 2025, 1:40 AM
Y by
wild fr

I have nats problems, but thanks for the offer
Currently mocking 2021 :P

MA is really hard tho which is why im so unsure
like 2022 cutoff was 42 :/
last year cutoff was 38 :/ and i mocked a 37 on it :/ D:
Z K Y
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stjwyl
1228 posts
stjwyl
#6 h  Feb 21, 2025, 1:41 AM
Y by
DhruvJha wrote:
stjwyl wrote:
/bump :D
@above ty for response :D

2022 state was very easy, notoriously easy state round. Your scores are still ectremely high. I can give you access to 2018-2024 Nats, and maybe time yourself like it would be at the real states. I'd say you would need to mock 33+ on those nats round to be a safe "in" (adding 3 for extra pressure due to comp pressure).

Or just move to Arkansas and get in with a 25 like me last year.


And also I would reccomend to amc 10 last 5 problems from those aops mocks user-created. Those tend to be similar to 27-30 on mathcounts states which tends to biggest struggle for someone in ur situation.





Hope I helped!

dam are last 3 rlly that hard lol
thx for help :D
Z K Y
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DhruvJha
730 posts
DhruvJha
#7 h  Feb 21, 2025, 1:42 AM
Y by
yeah, i solve a lot of them in mocks but the ones at real test are hard. I guess it varies. 2019, 2022 were pretty easy but 2024, 2017, 2023 were tough.







I could've prob been better but I didn't grind too hard and i basically had free nats qual being in arkansas.
This post has been edited 1 time. Last edited by DhruvJha, Feb 21, 2025, 1:43 AM
Reason: n
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DhruvJha
730 posts
DhruvJha
#8 h  Feb 21, 2025, 1:45 AM
Y by
Also, when you're practicing put yourself on 25 min time limit for sprint and 4 per set for target. That tends to simulate real competition stress.


And correct me if i'm wrong, MA should be significantly less competitive this year with the leaving of orz people like selena. So just try to make sure youve got all the first 25 correct, before attempting the last 5. I think you can do it.
This post has been edited 1 time. Last edited by DhruvJha, Feb 21, 2025, 1:47 AM
Reason: j
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chesskingaops
58 posts
chesskingaops
#9 h  Feb 21, 2025, 1:48 AM
Y by
What did you get for AMC 8 @ stjwyl (sorry if irrelevant)
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stjwyl
1228 posts
stjwyl
#10 h  Feb 21, 2025, 1:49 AM
Y by
24 :<
i basically sillied 50+55 :facepalm:
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DhruvJha
730 posts
DhruvJha
#11 h  Feb 21, 2025, 1:49 AM
Y by
just curious what were you at states lastyear
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stjwyl
1228 posts
stjwyl
#12 h  Feb 21, 2025, 1:50 AM
Y by
DhruvJha wrote:
Also, when you're practicing put yourself on 25 min time limit for sprint and 4 per set for target. That tends to simulate real competition stress.


And correct me if i'm wrong, MA should be significantly less competitive this year with the leaving of orz people like selena. So just try to make sure youve got all the first 25 correct, before attempting the last 5. I think you can do it.

im pretty sure selena's last year was like 2022

also i was in canada for ayear in 7th grade so i wasnt able to do
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DhruvJha
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DhruvJha
#13 h  Feb 21, 2025, 1:51 AM
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stjwyl wrote:
DhruvJha wrote:
Also, when you're practicing put yourself on 25 min time limit for sprint and 4 per set for target. That tends to simulate real competition stress.


And correct me if i'm wrong, MA should be significantly less competitive this year with the leaving of orz people like selena. So just try to make sure youve got all the first 25 correct, before attempting the last 5. I think you can do it.

im pretty sure selena's last year was like 2022

also i was in canada for ayear in 7th grade so i wasnt able to do


Selena was runner-up last year

but if im being honest your probably gonna have to try to get 23 of the first 25 right, and a 6-7 on target to make it.
This post has been edited 1 time. Last edited by DhruvJha, Feb 21, 2025, 1:52 AM
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pingpongmerrily
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pingpongmerrily
#14 h  Feb 21, 2025, 1:55 AM
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stjwyl wrote:
Info:
In 8th grade so I'm really hoping I can make nats now

I currently mock around 38 - 40 on nationals questions from 2015+
I mock anywhere from 37 - 42 on state questons from 2020+

For the sprint round I also have noticed that the difficulty jump from questions around 19 and 20 to questions around 22 and 23 has been really large (starting from 2023). I've also noticed that the last three questions (also from 2023 ->) are IMO impossible to do in the 40 minutes.

On target I can get 7/8 or even 8/8 if I'm lucky but it's possible for me to get 6/8

I'm in MA :sob: really hard state so do I have a chance

Edit: Just mocked the 2022 state round and got a 41 (29 sprint, 12 target :sob:)

bro target is so easy to sell
also btw the last 3 questions aren't that deep
for last year, Q30 was trivial in like 2 minutes, #28 was solvable in 5 minutes, #29 was a bit harder but definitely doable
you will need to cook here
i mock like a 30 which should be good for first :coolspeak:
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stjwyl
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stjwyl
#15 h  Feb 21, 2025, 1:55 AM
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wait rlly
omg wait that means she and her brother r leavin right
thats 2 orz ppl

but then again there was a 6th grader who qualed for nats last year
and he got 3rd in his chapter :/
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