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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.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

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]
Our full course list for upcoming classes is below:
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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
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The REAL reason for high cutoffs (HINT: It's not USAMTS or Cheating)
jcoons91   61
N 2 minutes ago by mhgelgi
AoPS,

Everyone has been blaming USAMTS or leaks for the sky-high cutoffs this year. These may have played a factor, but do you know the elephant in the room?

It's not cheating. It's not USAMTS. It's LETTING CANADIAN STUDENTS QUALIFY FOR THE USA(J)MO.

Last year, DOZENS of Canadian students won medals and awards at the USA(J)MO. DOZENS. Including Gold medals on USAMO and Top Honors on JMO.

Now think, if DOZENS of Canadians won awards, and the Olympiads honor about 40% of participants, guess how many canadians qualified?

Our sources indicate that 60+ Canadians qualified for oly this year. That's a huge amount! Doing the calculations show that the cutoffs should've been ~10 points lower if Canadian students were removed from the pool.

How is that fair? Why are we letting Canadian Nationals take the UNITED STATES Math Olympiad?

People have been saying Canada leaked the AIME I and II in response to our tariffs-- not sure if this is true or not, but it certainly checks out!! They are the only foreign nation who was permitted to take the AIME I.

And last year, the leaks of USAMO came from Canada too!! China wasn't even allowed to take the USAMO, but it was leaked anyway! Why do you think?

Ban Canadians from the USAMO, and treat them like all other foreigners!
61 replies
+3 w
jcoons91
2 hours ago
mhgelgi
2 minutes ago
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Mathcounts States
RMarri_1018   6
N 8 minutes ago by mathlover3141
As Mathcounts States has not started yet, I would like to ask a quick question. What would be the target goal to get to nationals in the state of Pennslyvania. I mock 34-38, so I want to know would that be enough to get me to CDR?
6 replies
+1 w
RMarri_1018
Feb 24, 2025
mathlover3141
8 minutes ago
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If you're Canadian: DO NOT TAKE THE USAMO
jcoons91   10
N 16 minutes ago by SpeedCuber7
You cannot in good conscience participate in TWO nations' MATH OLYMPIADS

10 replies
jcoons91
an hour ago
SpeedCuber7
16 minutes ago
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Geo is back??
GoodMorning   134
N 37 minutes ago by Ilikeminecraft
Source: 2023 USAJMO Problem 2/USAMO Problem 1
In an acute triangle $ABC$, let $M$ be the midpoint of $\overline{BC}$. Let $P$ be the foot of the perpendicular from $C$ to $AM$. Suppose that the circumcircle of triangle $ABP$ intersects line $BC$ at two distinct points $B$ and $Q$. Let $N$ be the midpoint of $\overline{AQ}$. Prove that $NB=NC$.

Proposed by Holden Mui
134 replies
GoodMorning
Mar 23, 2023
Ilikeminecraft
37 minutes ago
J
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Divisibility of a triple
goodar2006   52
N an hour ago by zuat.e
Source: Iran TST 2013-First exam-2nd day-P5
Do there exist natural numbers $a, b$ and $c$ such that $a^2+b^2+c^2$ is divisible by $2013(ab+bc+ca)$?

Proposed by Mahan Malihi
52 replies
goodar2006
Apr 19, 2013
zuat.e
an hour ago
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Rectangle EFGH in incircle, prove that QIM = 90
v_Enhance   61
N 2 hours ago by daixiahu
Source: Taiwan 2014 TST1, Problem 3
Let $ABC$ be a triangle with incenter $I$, and suppose the incircle is tangent to $CA$ and $AB$ at $E$ and $F$. Denote by $G$ and $H$ the reflections of $E$ and $F$ over $I$. Let $Q$ be the intersection of $BC$ with $GH$, and let $M$ be the midpoint of $BC$. Prove that $IQ$ and $IM$ are perpendicular.
61 replies
v_Enhance
Jul 18, 2014
daixiahu
2 hours ago
J
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USAMO PYQ
JetFire008   1
N 2 hours ago by v_Enhance
Source: USAMO 1993
Let $ABCD$ be a convex quadrilateral with perpendicular diagonals intersecting at $O$. Prove that the reflections of $O$ across $AB$, BC, CD, DA$ are concyclic.
1 reply
JetFire008
4 hours ago
v_Enhance
2 hours ago
J
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ABC is similar to XYZ
Amir Hossein   50
N 2 hours ago by daixiahu
Source: China TST 2011 - Quiz 2 - D2 - P1
Let $AA',BB',CC'$ be three diameters of the circumcircle of an acute triangle $ABC$. Let $P$ be an arbitrary point in the interior of $\triangle ABC$, and let $D,E,F$ be the orthogonal projection of $P$ on $BC,CA,AB$, respectively. Let $X$ be the point such that $D$ is the midpoint of $A'X$, let $Y$ be the point such that $E$ is the midpoint of $B'Y$, and similarly let $Z$ be the point such that $F$ is the midpoint of $C'Z$. Prove that triangle $XYZ$ is similar to triangle $ABC$.
50 replies
Amir Hossein
May 20, 2011
daixiahu
2 hours ago
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{x_i-a}+{x_{i+1}-b} at most 1/2024
navi_09220114   1
N 2 hours ago by YaoAOPS
Source: Malaysian SST 2023 P5
Find the maximal value of $c>0$ such that for any $n\ge 1$, and for any $n$ real numbers $x_1, \cdots, x_n$ there exists real numbers $a ,b$ such that $$\{x_i-a\}+\{x_{i+1}-b\}\le \frac{1}{2024}$$for at least $cn$ indices $i$. Here, $x_{n+1}=x_1$ and $\{x\}$ denotes the fractional part of $x$.

Proposed by Wong Jer Ren
1 reply
navi_09220114
Aug 27, 2023
YaoAOPS
2 hours ago
J
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Nice, simple geo
MathSaiyan   1
N 2 hours ago by Double07
Source: PErA 2025/4
Let \( ABC \) be an acute-angled scalene triangle. Let \( B_1 \) and \( B_2 \) be points on the rays \( BC \) and \( BA \), respectively, such that \( BB_1 = BB_2 = AC \). Similarly, let \( C_1 \) and \( C_2 \) be points on the rays \( CB \) and \( CA \), respectively, such that \( CC_1 = CC_2 = AB \). Prove that if \( B_1B_2 \) and \( C_1C_2 \) intersect at \( K \), then \( AK \) is parallel to \( BC \).
1 reply
MathSaiyan
Today at 1:50 PM
Double07
2 hours ago
J
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A geometry problem from the TOT
Invert_DOG_about_centre_O   8
N 2 hours ago by daixiahu
Source: Tournament of towns Spring 2018 A-level P4
Let O be the center of the circumscribed circle of the triangle ABC. Let AH be the altitude in this triangle, and let P be the base of the perpendicular drawn from point A to the line CO. Prove that the line HP passes through the midpoint of the side AB. (6 points)

Egor Bakaev
8 replies
Invert_DOG_about_centre_O
Mar 10, 2020
daixiahu
2 hours ago
J
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IMO Shortlist 2013, Geometry #2
lyukhson   76
N 2 hours ago by imagien_bad
Source: IMO Shortlist 2013, Geometry #2
Let $\omega$ be the circumcircle of a triangle $ABC$. Denote by $M$ and $N$ the midpoints of the sides $AB$ and $AC$, respectively, and denote by $T$ the midpoint of the arc $BC$ of $\omega$ not containing $A$. The circumcircles of the triangles $AMT$ and $ANT$ intersect the perpendicular bisectors of $AC$ and $AB$ at points $X$ and $Y$, respectively; assume that $X$ and $Y$ lie inside the triangle $ABC$. The lines $MN$ and $XY$ intersect at $K$. Prove that $KA=KT$.
76 replies
lyukhson
Jul 9, 2014
imagien_bad
2 hours ago
J
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IMO Shortlist 2013, Number Theory #3
lyukhson   46
N 3 hours ago by hgomamogh
Source: IMO Shortlist 2013, Number Theory #3
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.
46 replies
1 viewing
lyukhson
Jul 10, 2014
hgomamogh
3 hours ago
J
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Functional equation in three variables
mavropnevma   17
N 3 hours ago by Ilikeminecraft
Source: Balkan MO 2013, Problem 3
Let $S$ be the set of positive real numbers. Find all functions $f\colon S^3 \to S$ such that, for all positive real numbers $x$, $y$, $z$ and $k$, the following three conditions are satisfied:

(a) $xf(x,y,z) = zf(z,y,x)$,

(b) $f(x, ky, k^2z) = kf(x,y,z)$,

(c) $f(1, k, k+1) = k+1$.

(United Kingdom)
17 replies
mavropnevma
Jun 30, 2013
Ilikeminecraft
3 hours ago
J
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J
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2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   10
N 5 hours ago by RainbowSquirrel53B
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary

Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


10 replies
audio-on
Jan 26, 2025
RainbowSquirrel53B
5 hours ago
J
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
G H J
Reveal topic tags
Math Competitions
math contests
middle school math contests
Middle School contests
AI
artificial intel
computer science
L
G H BBookmark kLocked kLocked NReply
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audio-on
507 posts
audio-on
#1 h  Jan 26, 2025, 1:34 AM • 6 Y
Y by stuffedmath, christinaa.luu, manaleec, KevinYang2.71, EveningDawn, KnowingAnt
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary

Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!
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Ruegerbyrd
1032 posts
Ruegerbyrd
#6 h  Jan 26, 2025, 11:25 PM • 1 Y
Y by ChampionGirl
why only middle school :(
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christinaa.luu
2 posts
christinaa.luu
#7 h  Jan 27, 2025, 1:50 AM
Y by
Will the online award ceremony be recorded if I can’t attend live?
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audio-on
507 posts
audio-on
#8 h  Feb 1, 2025, 1:53 AM
Y by
christinaa.luu wrote:
Will the online award ceremony be recorded if I can’t attend live?

Yes, we will record the online award ceremony :)
You can access recordings from previous years on our YouTube channel or on our website under the result from each year (for example, the slide presentation and recording link for 2024 are under "Additional Links")
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SanrioSmarties05
149 posts
SanrioSmarties05
#9 h  Feb 1, 2025, 1:59 AM
Y by
How exactly will this work?
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mirzakhani12
3 posts
mirzakhani12
#10 h  Feb 8, 2025, 7:22 PM
Y by
This sounds like a great initiative! What steps can students take to prepare?
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audio-on
507 posts
audio-on
#12 h  Feb 10, 2025, 7:29 PM
Y by
SanrioSmarties05 wrote:
How exactly will this work?

After applications open on 3/22, you'll have about a month to complete the application!
We will post a Submittable link closer to the competition on our website, and you can find the problem set + essay questions there.
Applications will be filled out on Submittable.
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audio-on
507 posts
audio-on
#13 h  Feb 10, 2025, 7:32 PM
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mirzakhani12 wrote:
This sounds like a great initiative! What steps can students take to prepare?

Students will be tested on a variety of topics. The problem set is mainly math, although having a bit of computer science knowledge could help.
I would recommend looking at the past competitions under our past contests tab here where you can find the problem set + solutions for 2021 - 2023. You can find the problems and solutions from last year's competition here.

Hope this helps!
This post has been edited 1 time. Last edited by audio-on, Feb 10, 2025, 7:33 PM
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christinaa.luu
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christinaa.luu
#14 h  Mar 9, 2025, 12:25 AM
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Do I need a lot of experience in AI and programming to be able to participate?
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angie.
314 posts
angie.
#15 h  Today at 3:04 AM
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christinaa.luu wrote:
Do I need a lot of experience in AI and programming to be able to participate?

No, you don't need any experience in AI or programming to participate! Most of the contest is logic based, and the CS involves simple pseudocode designed to be accessible for everyone.
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RainbowSquirrel53B
583 posts
RainbowSquirrel53B
#16 h  5 hours ago
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How many contestants are there usually?
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