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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Jul 1, 2025
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
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Are you tired of the heat and thinking about Fall? You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US.

Our full course list for upcoming classes is below:
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0 replies
jwelsh
Jul 1, 2025
0 replies
J
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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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Sunny lines
sarjinius   20
N 39 minutes ago by EeEeRUT
Source: 2025 IMO P1
A line in the plane is called $sunny$ if it is not parallel to any of the $x$–axis, the $y$–axis, or the line $x+y=0$.

Let $n\ge3$ be a given integer. Determine all nonnegative integers $k$ such that there exist $n$ distinct lines in the plane satisfying both of the following:
[list]
[*] for all positive integers $a$ and $b$ with $a+b\le n+1$, the point $(a,b)$ lies on at least one of the lines; and
[*] exactly $k$ of the $n$ lines are sunny.
[/list]
20 replies
+2 w
sarjinius
Today at 3:35 AM
EeEeRUT
39 minutes ago
J
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IMO 2025 P2
sarjinius   33
N an hour ago by Assassino9931
Source: 2025 IMO P2
Let $\Omega$ and $\Gamma$ be circles with centres $M$ and $N$, respectively, such that the radius of $\Omega$ is less than the radius of $\Gamma$. Suppose $\Omega$ and $\Gamma$ intersect at two distinct points $A$ and $B$. Line $MN$ intersects $\Omega$ at $C$ and $\Gamma$ at $D$, so that $C, M, N, D$ lie on $MN$ in that order. Let $P$ be the circumcentre of triangle $ACD$. Line $AP$ meets $\Omega$ again at $E\neq A$ and meets $\Gamma$ again at $F\neq A$. Let $H$ be the orthocentre of triangle $PMN$.

Prove that the line through $H$ parallel to $AP$ is tangent to the circumcircle of triangle $BEF$.
33 replies
+4 w
sarjinius
Today at 3:38 AM
Assassino9931
an hour ago
J
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D1051 : A general result on prime number
Dattier   4
N an hour ago by Dattier
Source: les dattes à Dattier
Let $p>3$ prime number.

Is it true that exists $q$ prime number with $q< p$ and $p \mod q> \sqrt p-1$ ?
4 replies
Dattier
2 hours ago
Dattier
an hour ago
J
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Inspired by the slimshadyyy.3.60's one.
arqady   8
N an hour ago by Mathzeus1024
Let $a\geq b\geq c\geq0$ and $a^2+b^2+c^2+abc=4$. Prove that:
$$a+b+c+\frac{1}{\sqrt2}\left(\sqrt{a}-\sqrt{c}\right)^2\geq3.$$
8 replies
arqady
Apr 1, 2025
Mathzeus1024
an hour ago
J
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Non cyclic inequality
Nguyenhuyen_AG   0
an hour ago
Let $a,\,b,\,c$ be non-negative real numbers such that $a+b+c>0.$ Prove that
\[\frac{10-\sqrt2}{294} \leqslant \frac{(a+b+c)(a^2+b^2+c^2)}{(a+2b+3c)^3} \leqslant 1.\]When does equality hold?
0 replies
Nguyenhuyen_AG
an hour ago
0 replies
J
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NICE Planimetry 3
prof.   0
2 hours ago
A circle is inscribed in triangle $ABC$, and tangents are drawn to this circle parallel to the sides of the triangle. In this way, three smaller triangles are cut off from triangle $ABC$, each with an incircle of radius $r_1,r_2,r_3$, respectively. If $r$ the radius of the incircle of triangle $ABC$, prove that $$r=r_1+r_2+r_3.$$
0 replies
prof.
2 hours ago
0 replies
J
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inequality
SunnyEvan   4
N 2 hours ago by Kittycat12370
Source: Own
Let $ x \in (\frac{\pi}{2}-arcsin(\frac{1}{\sqrt[4]{2}}), arcsin(\frac{1}{\sqrt[4]{2}})) $, try to prove or disprove that :
$$ \frac{(\sqrt2 cosx -1)^2}{cos2x+tan\frac{\pi}{8}}-\frac{(\sqrt2 sinx -1)^2}{cos2x-tan\frac{\pi}{8}} \geq \frac{1}{2}(\frac{tanx-1}{tanx+1})^2 $$
4 replies
SunnyEvan
Sunday at 1:24 PM
Kittycat12370
2 hours ago
J
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2^a 3^b + 9 = c^2
delegat   16
N 2 hours ago by Baimukh
Source: JBMO 2009 Problem 2
Solve in non-negative integers the equation $ 2^{a}3^{b} + 9 = c^{2}$
16 replies
delegat
Jun 27, 2009
Baimukh
2 hours ago
J
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R->R functional equation
fukano_2   4
N 2 hours ago by Mathzeus1024
Find all functions $ f: \mathbb{R} \to \mathbb{R} $ that satisfy $ f(x^2+yf(x))+f(y^2+xf(y))=f(x+y)^2 $ and $ f(0)=2 $.
4 replies
fukano_2
Apr 16, 2020
Mathzeus1024
2 hours ago
J
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Number of solutions to strange exponent/log equation
NamelyOrange   1
N 2 hours ago by Mathzeus1024
Source: 2022 National Taiwan University STEM Development Program Admissions Test, P2
Find (with proof) the number of real solutions to the system $\begin{cases}3^x+5^y=52\\ \log_3x-\log_5y=1\end{cases}$.

Edit: what is my luck, and why is my post sandwiched between two posts on the newest IMO problems?
1 reply
NamelyOrange
Today at 3:40 AM
Mathzeus1024
2 hours ago
J
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LaTeX TeXeR did not save...
PikaPika999   2
N Today at 1:27 AM by PikaPika999
1. So I was creating this game for my forum on LaTeX TeXeR with my friend
2. spent 2 hours working on it
3. I clicked save
4. I didn't touch it for ~1 week
5. I went to work on it today
6. none of my work was there :( :noo: :mad: :wallbash: :wallbash_red:
2 replies
PikaPika999
Today at 12:45 AM
PikaPika999
Today at 1:27 AM
J
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Video not working
AndyYangZhang   3
N Yesterday at 11:53 PM by KangarooPrecise
Hello!

It seems that the videos in the Prealgebra course are not working for me? The website directs me to YouTube kids, but it does not point me to the video and I cannot find it through searching YouTube kids? Any help would be appreciated!

Thanks,
Andrew
3 replies
AndyYangZhang
Yesterday at 11:12 PM
KangarooPrecise
Yesterday at 11:53 PM
J
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k Alcumus and For the win
Demetri   5
N Yesterday at 8:20 PM by Demetri
What is the reasoning for the alcumus and for the win forums not being searchable? Also why are their threads hidden after a certain amount of time?
5 replies
Demetri
Yesterday at 7:46 PM
Demetri
Yesterday at 8:20 PM
J
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k Cannot post Latex, Account is already 23 days old
lrnnz   4
N Yesterday at 2:26 PM by melloncandy
Hello, a class i'm in requires us to post problems in the High School Math section, but the posts I make are hard to read as they don't contain any Latex. I was told my account needs to at least be 2 weeks old before I can start making posts with Latex, but i still can't
4 replies
lrnnz
Sunday at 5:22 PM
melloncandy
Yesterday at 2:26 PM
J
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J
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k Hide tag workaround
char0221   23
N Jun 10, 2025 by jlacosta
Summary of the problem: When quoting a tip tag, hovering over it causes a glitch where the tip tag's inner contents are "stuck" below the quotes.
Page URL: Any community message boards.
Steps to reproduce:
1. Create a message.
2. Insert a quote.
3. Inside the quote, put a tip tag.
4. Submit/preview, then hover over the tip tag.
Expected behavior: Tip tag does not stay when mouse is removed.
Frequency: 100%
Operating system(s): macOS Sequoia
Browser(s), including version: Safari 18.4
Additional information:
IMAGE
Also, make sure that the quote+tip is last.
[quote=char0221]
Try to close me!
[/quote]
23 replies
char0221
May 26, 2025
jlacosta
Jun 10, 2025
J
Hide tag workaround
G H J
Reveal topic tags
L
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
char0221
170 posts
char0221
#1 h  May 26, 2025, 4:03 PM • 1 Y
Y by PikaPika999
Summary of the problem: When quoting a tip tag, hovering over it causes a glitch where the tip tag's inner contents are "stuck" below the quotes.
Page URL: Any community message boards.
Steps to reproduce:
1. Create a message.
2. Insert a quote.
3. Inside the quote, put a tip tag.
4. Submit/preview, then hover over the tip tag.
Expected behavior: Tip tag does not stay when mouse is removed.
Frequency: 100%
Operating system(s): macOS Sequoia
Browser(s), including version: Safari 18.4
Additional information:
https://cdn.artofproblemsolving.com/attachments/7/5/4658fcc169e89b5f480a7ef8815ed107093d5e.png
Also, make sure that the quote+tip is last.
char0221 wrote:
Try to close me!
This post has been edited 1 time. Last edited by char0221, May 26, 2025, 4:04 PM
Z Y
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SlyOwl45
160 posts
SlyOwl45
#2 h  May 26, 2025, 4:16 PM • 1 Y
Y by PikaPika999
I can't reproduce . . . that's weird that yours does it! :( Maybe it's a problem on your end?
Socrates wrote:
I only know
Z Y
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Demetri
1599 posts
Demetri
#3 h  May 26, 2025, 4:20 PM • 2 Y
Y by MusicalHorse18, PikaPika999
I can't reproduce the bug, it dissapears after I hover off it.
This post has been edited 1 time. Last edited by Demetri, May 26, 2025, 4:21 PM
Z Y
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InsightfulHawk16
3791 posts
InsightfulHawk16
#4 h  May 26, 2025, 4:21 PM • 1 Y
Y by PikaPika999
i think that is how it supposed to be?
hover for tip
Z Y
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Demetri
1599 posts
Demetri
#5 h  May 26, 2025, 4:22 PM • 2 Y
Y by KSH31415, PikaPika999
InsightfulHawk16 wrote:
i think that is how it supposed to be?
hover for tip
They are saying that hovering over the tip, it won't dissapear after putting your mouse somewhere else.
Z Y
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InsightfulHawk16
3791 posts
InsightfulHawk16
#6 h  May 26, 2025, 4:25 PM • 1 Y
Y by PikaPika999
oh sorry $ $
i know that on my ipad it stays there but thats just how ipad touch works
Z Y
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jlacosta
671 posts
jlacosta
#7 h  May 27, 2025, 10:56 PM • 1 Y
Y by PikaPika999
Hi char0221! Can you provide a screenrecording of the issue that you're experiencing? I'm unable to replicate it on my end either.
Z Y
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Yiyj
430 posts
Yiyj
#10 h  Jun 2, 2025, 2:38 AM • 1 Y
Y by ShrewdBunny
cant reproduce
This post has been edited 1 time. Last edited by Yiyj, Jun 2, 2025, 3:29 AM
Z Y
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ShrewdBunny
747 posts
ShrewdBunny
#11 h  Jun 2, 2025, 2:52 AM
Y by
If you copy when its stuck this happened
Attachments:
This post has been edited 1 time. Last edited by ShrewdBunny, Jun 2, 2025, 2:54 AM
Reason: spelling
Z Y
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ahxun2006
1143 posts
ahxun2006
#12 h  Jun 2, 2025, 3:26 AM • 1 Y
Y by ShrewdBunny
Can reproduce system mac
Only if its in quotes
This post has been edited 1 time. Last edited by ahxun2006, Jun 2, 2025, 3:39 AM
Z Y
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ShrewdBunny
747 posts
ShrewdBunny
#13 h  Jun 2, 2025, 3:38 AM • 1 Y
Y by ahxun2006
ahxun2006 wrote:
Can reproduce system mac

Same
Z Y
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Yiyj
430 posts
Yiyj
#14 h  Jun 2, 2025, 3:42 AM
Y by
can't reproduce for mac
Z Y
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Yrock
1471 posts
Yrock
#15 h  Jun 2, 2025, 5:00 AM • 2 Y
Y by ahxun2006, ShrewdBunny
can reproduce
Z Y
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CurlyFalcon55
1397 posts
CurlyFalcon55
#16 h  Jun 2, 2025, 1:56 PM
Y by
My Operating system(s): macOS Sequoia

My Browser(s), including version: Chrome, I don't know what version

Let’s see if I can reproduce…
This test quote wrote:
Try to close me!
Z Y
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Yrock
1471 posts
Yrock
#17 h  Jun 4, 2025, 5:10 AM
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$~~~~~~$
I'm sure the same problem occurs in a hide tag.

It closes if you ignore it for a while.
This post has been edited 1 time. Last edited by Yrock, Jun 4, 2025, 5:11 AM
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CurlyFalcon55
1397 posts
CurlyFalcon55
#18 h  Jun 4, 2025, 4:54 PM
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Sorry, I never said if it worked. I cannot reproduce. :(
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ShrewdBunny
747 posts
ShrewdBunny
#19 h  Jun 5, 2025, 2:20 AM
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nvm it works on my laptop but not PC
This post has been edited 1 time. Last edited by ShrewdBunny, Jun 5, 2025, 1:27 PM
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miles888
1101 posts
miles888
#20 h  Jun 5, 2025, 5:59 PM
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Yiyj wrote:
can't reproduce for mac
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char0221
170 posts
char0221
#21 h  Jun 7, 2025, 5:21 PM
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Screen recording for clarification: https://drive.google.com/file/d/1MRFOzCskSVmhqMNpWU8HAal8wyI4qvsY/view?usp=share_link
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FunnyKoala17
337 posts
FunnyKoala17
#22 h  Jun 7, 2025, 5:26 PM
Y by
char0221 wrote:
Screen recording for clarification: https://drive.google.com/file/d/1MRFOzCskSVmhqMNpWU8HAal8wyI4qvsY/view?usp=share_link

I can reproduce. It's pretty strange.
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A7456321
409 posts
A7456321
#23 h  Jun 7, 2025, 5:57 PM
Y by
same, but only sometimes
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Yiyj
430 posts
Yiyj
#24 h  Jun 7, 2025, 10:12 PM • 1 Y
Y by PikaPika999
sus can't reproduce
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MusicalPanda94
1226 posts
MusicalPanda94
#25 h  Jun 10, 2025, 3:47 AM • 1 Y
Y by PikaPika999
char0221 wrote:
Summary of the problem: When quoting a tip tag, hovering over it causes a glitch where the tip tag's inner contents are "stuck" below the quotes.
Page URL: Any community message boards.
Steps to reproduce:
1. Create a message.
2. Insert a quote.
3. Inside the quote, put a tip tag.
4. Submit/preview, then hover over the tip tag.
Expected behavior: Tip tag does not stay when mouse is removed.
Frequency: 100%
Operating system(s): macOS Sequoia
Browser(s), including version: Safari 18.4
Additional information:
https://cdn.artofproblemsolving.com/attachments/7/5/4658fcc169e89b5f480a7ef8815ed107093d5e.png
Also, make sure that the quote+tip is last.
char0221 wrote:
Try to close me!

I can reproduce on my Mac
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jlacosta
671 posts
jlacosta
#26 h  Jun 10, 2025, 7:06 PM • 1 Y
Y by PikaPika999
Thanks so much for the screenrecording and the screenshot! We still weren't able to replicate the issue on our end, but I'll be sure to pass it along to the appropriate teams to look into this in more detail for you!
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