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omg tysmmmm
by
pupitrethebean, May 10, 2025, 3:16 AM
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hola bro
by
Staragon, May 10, 2025, 3:16 AM
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haiiiiiii cute blog <3
by
yaxuan, May 8, 2025, 8:29 AM
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done!
by
pupitrethebean, Mar 19, 2025, 2:05 PM
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Hi! Contrib?
by
RandomeMids, Mar 13, 2025, 2:22 PM
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aww tysmmmm
by
pupitrethebean, Feb 3, 2025, 10:19 PM
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revive the shoutbox lol
i like your blog : )
by
witchofblackbirdpond, Feb 3, 2025, 7:56 PM
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revive the shoutbox
by
pupitrethebean, Jan 20, 2025, 4:42 AM
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d
e
d
.
by
ujulee, Nov 26, 2024, 11:37 PM
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bruhhh nahhhh
by
pupitrethebean, Oct 13, 2024, 3:22 PM
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this blog is so aesthetic it's crazy
by
Technodoggo, Oct 12, 2024, 11:16 PM
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ehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh soon :>
by
pupitrethebean, Oct 12, 2024, 1:29 AM
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pupitre you should totally promote meee
by
CC_chloe, Oct 11, 2024, 7:34 PM
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admins and contribs r different colors
by
pupitrethebean, Oct 8, 2024, 3:01 PM
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why are certain usernames different colors :thonk:
by
Technodoggo, Oct 8, 2024, 12:44 AM
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oh my good lord
by
pupitrethebean, Apr 11, 2023, 6:43 PM
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bALLSS
in myyyyyyy
by
teasang, Apr 11, 2023, 6:38 PM
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schoooolllllll
by
pupitrethebean, Apr 11, 2023, 4:21 PM
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NOOO DONT REMIND ME
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addyc, Apr 11, 2023, 2:18 PM
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yes happy new day
congrats on grades being teleported to powerschool
by
pupitrethebean, Apr 11, 2023, 4:29 AM
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HAPPY NEW DAY
by
addyc, Apr 11, 2023, 4:18 AM
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yoda, i am not
by
pupitrethebean, Apr 11, 2023, 2:59 AM
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yoda are you???
by
addyc, Apr 10, 2023, 11:57 PM
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correct you are
by
pupitrethebean, Apr 10, 2023, 7:17 PM
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poop
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addyc, Apr 9, 2023, 3:25 AM
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hmm how can i make this shout box more interesting
by
pupitrethebean, Apr 8, 2023, 3:42 PM
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shhhhh we dont talk about that
that was before everything was done so it never happened
by
pupitrethebean, Apr 5, 2023, 10:41 PM
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NO U DELTED MY FIRST SHOUT, COMMENT, AND POST
by
addyc, Apr 5, 2023, 9:52 PM
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lets gooooo first shout
by
pupitrethebean, Apr 5, 2023, 7:12 AM
by danilorj, May 14, 2025, 9:08 PM 
be nonnegative real numbers such that 
. Prove that![\[
\frac{a}{4 - b} + \frac{b}{4 - c} + \frac{c}{4 - a} + \frac{1}{16}(1 - a)^2(1 - b)^2(1 - c)^2 \leq 1,
\]](http://latex.artofproblemsolving.com/5/b/d/5bd3349071e075519bd986c845c500125b7d46f8.png)
and determine all such triples 
where the equality holds.
in this order. Prove that![\[a_1a_3+a_3a_5+a_5a_7+a_7a_9+a_9a_1=a_2a_4+a_4a_6+a_6a_8+a_8a_{10}+a_{10}a_2.\]](http://latex.artofproblemsolving.com/9/e/e/9ee73bbdc4b4f2cad2eb3fcfb3dbdf76b6200b4d.png)
with 
.![$P(x,y) \in \mathbb Q[x,y]$](http://latex.artofproblemsolving.com/b/3/7/b37942b05292a493c8e350322adc122205bc778d.png)
?
be a triangle and let 
be its circumcenter and 
its incenter.
be the radical center of its three mixtilinears and let 
be the isogonal conjugate of 
be the Gergonne point of the triangle 
is parallel with line 
.
. Let the incenter of triangle 
, which touches 
at 
, respectively. Let 
be the midpoint of 
. Let the circle centered at 
intersect 
at 
, respecively. Let line 
meet 
, line 
meet 
at 
. Prove that the three lines 
are concurrent.
boxes 
, 
, 
,..,
. The 
-th box 
contains 
greater than 
and choose 
a multiple of 
, 
, 
and move the 
balls to the box 
.
be a cyclic quadrilateral with circumcircle 
.Lines 
and 
intersect at point 
,and lines 
,
.Circle 
is tangent to segments 
at points 
respectively,and intersects with circle 
.Lines 
intersect line 
at 
respectively.Show that 
are concyclic.
be an acute triangle, and let 
be its circumcenter and orthocenter, respectively. For 
, points 
and 
lie on lines 
and 
(where 
), respectively, such that 
is a parallelogram. Prove that![\[\frac{OQ_{1}}{OP_{1}}+\frac{OQ_{2}}{OP_{2}}+\frac{OQ_{3}}{OP_{3}}\geq 3.\]](http://latex.artofproblemsolving.com/b/a/5/ba563336236b6a04fc9ef661760fa1251bfb07d6.png)
April 2025
December 2024
.
such that
for all 
.