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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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2025 RAMC 10
Andyluo   40
N 38 minutes ago by Inaaya
We, andyluo, MC_ADe, Arush Krisp, pengu14, mathkiddus, vivdax present...

IMAGE

About Errata(0) Test Taking Discussion Test Integrity Notes/Credits

Test: RAMC 10
Leaderboard Yet to be released

mods can you keep this in c & p until it finishes please

To gain access to the private discussion forum, either private message me on AOPS with your Mathdash account, or simply ask and label your AOPS on the Mathdash discussion page.
Forum
40 replies
Andyluo
Apr 26, 2025
Inaaya
38 minutes ago
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MOP Emails Out! (not clickbait)
Mathandski   95
N an hour ago by Potato2017
What an emotional roller coaster the past 34 days have been.

Congrats to all that qualified!
95 replies
Mathandski
Apr 22, 2025
Potato2017
an hour ago
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How many approaches you got? (A lot)
IAmTheHazard   85
N 2 hours ago by S.G
Source: USAMO 2023/2
Let $\mathbb{R}^+$ be the set of positive real numbers. Find all functions $f \colon \mathbb{R}^+ \to \mathbb{R}^+$ such that, for all $x,y \in \mathbb{R}^+$,
$$f(xy+f(x))=xf(y)+2.$$
85 replies
IAmTheHazard
Mar 23, 2023
S.G
2 hours ago
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How many people get waitlisted st promys?
dragoon   29
N 3 hours ago by dragoon
Asking for a friend here
29 replies
dragoon
Apr 18, 2025
dragoon
3 hours ago
J
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Generating Functions
greenplanet2050   7
N 3 hours ago by rchokler
So im learning generating functions and i dont really understand why $1+2x+3x^2+4x^3+5x^4+…=\dfrac{1}{(1-x)^2}$

can someone help

thank you :)
7 replies
greenplanet2050
Yesterday at 10:42 PM
rchokler
3 hours ago
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Algebraic Manipulation
Darealzolt   1
N 5 hours ago by Soupboy0
Find the number of pairs of real numbers $a, b, c$ that satisfy the equation $a^4 + b^4 + c^4 + 1 = 4abc$.
1 reply
Darealzolt
Today at 1:25 PM
Soupboy0
5 hours ago
J
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BrUMO 2025 Team Round Problem 13
lpieleanu   1
N 5 hours ago by vanstraelen
Let $\omega$ be a circle, and let a line $\ell$ intersect $\omega$ at two points, $P$ and $Q.$ Circles $\omega_1$ and $\omega_2$ are internally tangent to $\omega$ at points $X$ and $Y,$ respectively, and both are tangent to $\ell$ at a common point $D.$ Similarly, circles $\omega_3$ and $\omega_4$ are externally tangent to $\omega$ at $X$ and $Y,$ respectively, and are tangent to $\ell$ at points $E$ and $F,$ respectively.

Given that the radius of $\omega$ is $13,$ the segment $\overline{PQ}$ has a length of $24,$ and $YD=YE,$ find the length of segment $\overline{YF}.$
1 reply
lpieleanu
Apr 27, 2025
vanstraelen
5 hours ago
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Inequlities
sqing   33
N Today at 1:50 PM by sqing
Let $ a,b,c\geq 0 $ and $ a^2+ab+bc+ca=3 .$ Prove that$$\frac{1}{1+a^2}+ \frac{1}{1+b^2}+ \frac{1}{1+c^2} \geq \frac{3}{2}$$$$\frac{1}{1+a^2}+ \frac{1}{1+b^2}+ \frac{1}{1+c^2}-bc \geq -\frac{3}{2}$$
33 replies
sqing
Jul 19, 2024
sqing
Today at 1:50 PM
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Very tasteful inequality
tom-nowy   1
N Today at 1:39 PM by sqing
Let $a,b,c \in (-1,1)$. Prove that $$(a+b+c)^2+3>(ab+bc+ca)^2+3(abc)^2.$$
1 reply
tom-nowy
Today at 10:47 AM
sqing
Today at 1:39 PM
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Inequalities
sqing   8
N Today at 1:31 PM by sqing
Let $x\in(-1,1). $ Prove that
$$ \dfrac{1}{\sqrt{1-x^2}} + \dfrac{1}{2+ x^2} \geq \dfrac{3}{2}$$$$ \dfrac{2}{\sqrt{1-x^2}} + \dfrac{1}{1+x^2} \geq 3$$
8 replies
sqing
Apr 26, 2025
sqing
Today at 1:31 PM
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đề hsg toán
akquysimpgenyabikho   1
N Today at 12:16 PM by Lankou
làm ơn giúp tôi giải đề hsg

1 reply
akquysimpgenyabikho
Apr 27, 2025
Lankou
Today at 12:16 PM
J
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Inequalities
sqing   2
N Today at 10:05 AM by sqing
Let $a,b,c> 0$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1.$ Prove that
$$ (1-abc) (1-a)(1-b)(1-c) \ge 208 $$$$ (1+abc) (1-a)(1-b)(1-c) \le -224 $$$$(1+a^2b^2c^2) (1-a)(1-b)(1-c) \le -5840 $$
2 replies
sqing
Jul 12, 2024
sqing
Today at 10:05 AM
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9 Physical or online
wimpykid   0
Today at 6:49 AM
Do you think the AoPS print books or the online books are better?

0 replies
wimpykid
Today at 6:49 AM
0 replies
J
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Three variables inequality
Headhunter   6
N Today at 6:08 AM by lbh_qys
$\forall a\in R$ ,$~\forall b\in R$ ,$~\forall c \in R$
Prove that at least one of $(a-b)^{2}$, $(b-c)^{2}$, $(c-a)^{2}$ is not greater than $\frac{a^{2}+b^{2}+c^{2}}{2}$.

I assume that all are greater than it, but can't go more.
6 replies
Headhunter
Apr 20, 2025
lbh_qys
Today at 6:08 AM
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Colored Pencils for Math Competitions
Owinner   17
N Apr 1, 2025 by lord_of_the_rook
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.
17 replies
Owinner
Mar 29, 2025
lord_of_the_rook
Apr 1, 2025
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Colored Pencils for Math Competitions
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Reveal topic tags
geometry
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Owinner
53 posts
Owinner
#1 h  Mar 29, 2025, 5:56 PM
Y by
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.
Z K Y
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mathprodigy2011
324 posts
mathprodigy2011
#2 h  Mar 29, 2025, 6:49 PM
Y by
Owinner wrote:
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.

i think colored pencils are more useful for really complicated and involved geometry problems. So I would think they are useful for AMC 10 but mathcounts and amc8 usually have geometry problems with simple-ish solutions
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LearnMath_105
149 posts
LearnMath_105
#3 h  Mar 29, 2025, 7:19 PM
Y by
I would say that they are most helpful for marking concyclic/colinear/concurrent objects so later aime - olyis where its most commonly used
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Andyluo
946 posts
Andyluo
#4 h  Mar 29, 2025, 7:43 PM
Y by
they're useless for the competitions listed, it's way too fast-paced to spend time and color a diagram, maybe on olympiads but you're losing precious time if you do it on those. Maybe the AIME would utilize this? But I highly doubt that it would give any benefits

@below coloring lines is basically the same thing c'mon
This post has been edited 1 time. Last edited by Andyluo, Mar 29, 2025, 7:49 PM
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cheltstudent
617 posts
cheltstudent
#5 h  Mar 29, 2025, 7:48 PM
Y by
Bruh, andyluo, literally not colouring just marking different lines they talked about this in my AMC 10 seminar

@above nah like drawing lines with a colour pencil bro
This post has been edited 1 time. Last edited by cheltstudent, Mar 29, 2025, 7:51 PM
Reason: gg
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ChaitraliKA
1004 posts
ChaitraliKA
#6 h  Mar 29, 2025, 7:57 PM
Y by
It can be useful, but I feel like in the actual competition you would end up not using it because you would be too invested in thinking about how to solve the problem instead of "oh, I should mark this with a different color", and would just end up drawing over your diagram with your regular pencil again. Drawing a specific part of your diagram with harder pressure compared to other areas of your diagram can also help you too, especially if it's just mathcounts or AMC 8.
I brought a ruler, a pen, and a compass to Aime, but didn't use any of those materials. Didn't touch them at all. No time to think ¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯
The only time I've ever used different colors is when I draw my diagrams on my chromebook canvas, and I'm lazy to get paper and pencil.
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mathprodigy2011
324 posts
mathprodigy2011
#7 h  Mar 29, 2025, 10:45 PM
Y by
Andyluo wrote:
they're useless for the competitions listed, it's way too fast-paced to spend time and color a diagram, maybe on olympiads but you're losing precious time if you do it on those. Maybe the AIME would utilize this? But I highly doubt that it would give any benefits

@below coloring lines is basically the same thing c'mon

i mean i used different colors to get aime p14 correct so they are useful just not for faster paced competitions. It really depends on how you think.
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mdk2013
637 posts
mdk2013
#8 h  Mar 29, 2025, 11:38 PM • 1 Y
Y by Exponent11
colored pencils way better for olympiads so you can show your steps, for example, there were a few problems on the BAMO and SDMO that i took that i could have used colored pencils to more accurately show my proofs. however
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Jack_w
109 posts
Jack_w
#9 h  Mar 30, 2025, 5:52 PM
Y by
it’s not very helpful
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resources
748 posts
resources
#10 h  Mar 30, 2025, 5:56 PM
Y by
they can be extremely helpful if used correctly.
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vincentwant
1359 posts
vincentwant
#11 h  Mar 30, 2025, 6:31 PM
Y by
I used colored pencils on jmo p3
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EaZ_Shadow
1234 posts
EaZ_Shadow
#12 h  Mar 30, 2025, 6:37 PM
Y by
Owinner wrote:
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.

Ofc u can use it for those comp if u want
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ChaitraliKA
1004 posts
ChaitraliKA
#13 h  Mar 30, 2025, 7:13 PM
Y by
@op, you're getting a bunch of different responses, but in the end, it's your decision obv, whether you wanna use it or not
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Andyluo
946 posts
Andyluo
#14 h  Mar 30, 2025, 7:23 PM
Y by
the general consensus is using colored pencils is a waste of time unless you're doing AIME/Olympiads, at that point, you choose if you should or should not.
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BS2012
1025 posts
BS2012
#15 h  Mar 30, 2025, 7:28 PM
Y by
for contests AIME difficulty or easier the geo diagrams are usually simple enough that using colored pencils would be useless, for oly could be useful though
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Mr.Sharkman
498 posts
Mr.Sharkman
#16 h  Mar 31, 2025, 8:16 PM
Y by
vincentwant wrote:
I used colored pencils on jmo p3

Lol same; it kinda helped solve it
I also did on #2 of last year but still got it wrong anyway
This post has been edited 1 time. Last edited by Mr.Sharkman, Mar 31, 2025, 8:17 PM
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deduck
215 posts
deduck
#17 h  Mar 31, 2025, 9:48 PM • 1 Y
Y by fake123
colored pencils make me confused but i think on olympiads it's personal preference

i think on mathcounts/amc8/10/12 and other fast paced comeptition it's not worth it. if u cant solve the problem in pencil black/white it probably wont get solved just bc u colored it xd because usually the solutions arent that invovled about concyclic/collinear/etc

just my opinion xd
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lord_of_the_rook
146 posts
lord_of_the_rook
#18 h  Apr 1, 2025, 1:33 AM
Y by
@op I feel like you should try them out at home, and see if you find them useful.
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