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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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3D Geometry Problem
ReticulatedPython   15
N 5 minutes ago by Soupboy0
A sphere with radius $1$ is centered at the apex of a right square pyramid with base length $2$ and height $1.$ The volume of the space where the sphere overlaps with the pyramid can be expressed in the form $k\pi.$ Find $k.$

Hint

Formulas
15 replies
+1 w
ReticulatedPython
Yesterday at 4:05 PM
Soupboy0
5 minutes ago
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Chessboard problem
Ecrin_eren   1
N 5 minutes ago by Soupboy0
On an 8×8 checkerboard, what is the minimum number of squares that must be marked (including the marked ones) so that every square has exactly one marked neighbor? (We define neighbors as squares that share a common edge, and a square is not considered a neighbor of itself.)
1 reply
Ecrin_eren
an hour ago
Soupboy0
5 minutes ago
J
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Math Question
somerandomkid32   2
N 7 minutes ago by Dream9
I was looking to get better at math overall but don't know where to start. For context I am taking geometry as an 8th grader and have gotten a 18 on AMC 8. I have some background in Algebra 2 already such as factoring polynomials etc. reply if you need more info.
2 replies
somerandomkid32
Today at 12:31 AM
Dream9
7 minutes ago
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AMC 8 Help
krish6_9   21
N 22 minutes ago by krish6_9
Hey guys
im in new jersey a third grader who got 12 on amc 8. I want to make mop in high school and mathcounts nationals in 6th grade is that realistic how should I get better
21 replies
krish6_9
Mar 17, 2025
krish6_9
22 minutes ago
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Proof Question
MathRook7817   3
N 5 hours ago by Jack_w
Prove or disprove the assertion that when $1/n$ is written in decimal form with n being a natural number, that it's decimal either terminates or is eventually periodic.

I saw this question somewhere and I thinks it's interesting.
3 replies
MathRook7817
Today at 2:19 AM
Jack_w
5 hours ago
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Inequalities
lgx57   2
N 6 hours ago by sqing
Let $0 < a,b,c < 1$. Prove that

$$a(1-b)+b(1-c)+c(1-a)<1$$
2 replies
lgx57
Today at 7:43 AM
sqing
6 hours ago
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solve the system of equations
Havu   1
N 6 hours ago by Mathzeus1024
Solve the system of equations:
\[\begin{cases} 3x^2-2xy+3y^2+\dfrac{2}{x^2-2xy+y^2}=8\\ 2x+\dfrac{1}{x-y}=4 \end{cases}\]
1 reply
Havu
Today at 7:52 AM
Mathzeus1024
6 hours ago
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Inequalities
sqing   7
N Today at 8:12 AM by sqing
Let $a,b,c\ge \frac{1}{2}$ and $\left(\frac{1}{a}+\frac{1}{b}-\frac{1}{c}\right)\left(\frac{1}{a}-\frac{1}{b}+\frac{1}{c}\right)\le 1. $ Prove that
$$a+b+c\geq 2$$Let $a,b,c\ge \frac{1}{2}$ and $ \left(a+\frac{1}{a}+\frac{1}{b}-\frac{1}{c}\right)\left(a+\frac{1}{a}-\frac{1}{b}+\frac{1}{c}\right)\le \frac{9}{2}. $ Prove that
$$a^2+b^2+c^2\geq 1$$Let $a,b\ge \frac{1}{2}$ and $ \left( \frac{1}{a}-\frac{1}{b}+2\right)\left( \frac{1}{b}-\frac{1}{a}+2\right) \le \frac{20}{9}. $ Prove that
$$ a+b\geq 2$$Let $a,b\ge \frac{1}{2}$ and $a^2+b^2=1. $ Prove that
$$\left(\frac{2}{a}+\frac{1}{b}-1\right)\left(\frac{2}{a}-\frac{1}{b}+1\right)\ge \frac{13}{3}$$
7 replies
sqing
Mar 15, 2025
sqing
Today at 8:12 AM
J
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Quadratic Equation Problems
Saucepan_man02   7
N Today at 5:53 AM by soryn
P1) Let $\alpha < \beta < \gamma$ be the roots of $ax^3+bx^2+cx+d=0$ with $7a+3b>0, 3a+2b<0$ and $\alpha(\beta+1)+\beta(\gamma+1)+\gamma(1+\alpha)=0$.
If [.] denotes the greatest integer function, then the number of possible values of $[|3 \alpha |] + [|6 \beta|] + [|9 \gamma |]$ is equal to
7 replies
Saucepan_man02
Mar 3, 2025
soryn
Today at 5:53 AM
J
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Trash Trig Sum
P_Groudon   4
N Today at 5:41 AM by invisibleman
Find the smallest positive integer $n$ such that $$\sum_{k=0}^{298}\sin(k^2 + 2k + 2)\sin(2k + 2) = \frac{\cos(1) - \cos(n)}{2},$$where degrees are used.
4 replies
P_Groudon
Monday at 5:34 PM
invisibleman
Today at 5:41 AM
J
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Chessboard
Ecrin_eren   2
N Today at 5:24 AM by Ecrin_eren
On an 8×8 checkerboard, what is the minimum number of squares that must be marked (including the marked ones) so that every square has exactly one marked neighbor? (We define neighbors as squares that share a common edge, and a square is not considered a neighbor of itself.)

2 replies
Ecrin_eren
Yesterday at 8:55 PM
Ecrin_eren
Today at 5:24 AM
J
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Inequality
BaCaPhe   1
N Today at 4:43 AM by lbh_qys
$\begin{array}{l} a,b,c \ge 1,ab + bc + ca \ge 4 + abc\\ {a^2} + {b^2} + {c^2} \ge 9? \end{array}$
I tried:
$\begin{array}{l} * {\text{In three numbers }}a,b,c \ge 1,{\text{ at least 2 numbers }} \ge {\text{2 or}} \le {\text{2}}\\ {\text{WLOG assume they are }}a{\text{ and }}b \Rightarrow \left( {a - 2} \right)\left( {b - 2} \right) \ge 0 \Leftrightarrow 4c + abc \ge 2ac + 2bc\\ \Leftrightarrow 2ac + 2bc \le 4c - 4 + 4 + abc \le 4c - 4 + ab + bc + ca \Leftrightarrow ac + bc \le 4c - 4 + ab \end{array}$
How do I process further?
1 reply
BaCaPhe
Today at 3:13 AM
lbh_qys
Today at 4:43 AM
J
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Inequalities
sqing   21
N Today at 4:36 AM by sqing
Let $ a,b>0 $ and $ \frac{1}{a}+\frac{1}{b}=1. $ Prove that
$$(a^2-a+1)(b^2-b+1) \geq 9$$$$ (a^2-a+b+1)(b^2-b+a+1) \geq 25$$Let $ a,b>0 $ and $ \frac{1}{a}+\frac{1}{b}=\frac{2}{3}. $ Prove that
$$(a+8)(a^2-a+b+2)(b^2-b+5)\geq1331$$$$(a+10)(a^2-a+b+4)(b^2-b+7)\geq2197$$
21 replies
sqing
Mar 10, 2025
sqing
Today at 4:36 AM
J
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Inequalities
sqing   6
N Today at 4:16 AM by sqing
Let $ a,b $ be real numbers such that $ a + b \geq |ab + 1|. $ Prove that$$ a^3 + b^3 \geq |a^3 b^3 + 1|$$Let $ a,b $ be real numbers such that $ 2(a + b ) \geq |ab + 1|. $ Prove that$$26( a^3 + b^3) \geq |a^3 b^3 + 1|$$Let $ a,b $ be real numbers such that $ 4(a + b) \geq 3|ab + 1|. $ Prove that$$148(a^3 + b^3) \geq27 |a^3 b^3 + 1|$$
6 replies
sqing
Mar 8, 2025
sqing
Today at 4:16 AM
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MATHCOUNTS Chapter Score Thread
apex304   103
N Mar 17, 2025 by captainnobody
$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ \end{tabular}$
103 replies
apex304
Mar 1, 2025
captainnobody
Mar 17, 2025
J
MATHCOUNTS Chapter Score Thread
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Reveal topic tags
MATHCOUNTS
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apex304
519 posts
apex304
#1 h  Mar 1, 2025, 5:20 PM • 2 Y
Y by GlitchyBoy, BigOrca
$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ \end{tabular}$
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Jaxman8
95 posts
Jaxman8
#2 h  Mar 1, 2025, 5:23 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ Jaxman8 & 8 & 39(27+12) \\ \end{tabular}$
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mathprodigy2011
223 posts
mathprodigy2011
#3 h  Mar 1, 2025, 5:34 PM
Y by
Jaxman8 wrote:
$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ mathprodigy2011 & 8 & 43 \\ Jaxman8 & 8 & 39(27+12) \\ \end{tabular}$
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Existing_Human1
182 posts
Existing_Human1
#4 h  Mar 1, 2025, 5:39 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Target & Sprint & Final Score \\ \hline apex304 & 8 & 16 & 30 & 46\\ Jaxman8 & 8 & 12 & 27 & 39 \\ ExistingHuman1 & 8 & 14 & 29 & 43\\ \end{tabular}$

Added more columns
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jb2015007
1703 posts
jb2015007
#5 h  Mar 1, 2025, 5:39 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ mathprodigy2011 & 8 & 43 \\ Jaxman8 & 8 & 39(27+12) \\ jb2015007 & 7 & 35 :facepalm: \end{tabular}$
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luckyrabbit11
379 posts
luckyrabbit11
#6 h  Mar 1, 2025, 5:40 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ mathprodigy2011 & 8 & 43 \\ Jaxman8 & 8 & 39(27+12) \\ luckyrabbit11 & 8 & 41 \\ jb2015007 & 7 & 35 :facepalm: \end{tabular}$
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Soupboy0
159 posts
Soupboy0
#8 h  Mar 1, 2025, 5:58 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ mathprodigy2011 & 8 & 43 \\ Jaxman8 & 8 & 39(27+12) \\ luckyrabbit11 & 8 & 41 \\ jb2015007 & 7 & 35 :facepalm: \\ Soupboy0 & 7 & 39 \end{tabular}$
4 sillies btw
This post has been edited 1 time. Last edited by Soupboy0, Mar 1, 2025, 5:59 PM
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Existing_Human1
182 posts
Existing_Human1
#9 h  Mar 1, 2025, 6:04 PM
Y by
Can you guys put sprint and target, then I'll add you to the table with more columns
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Soupboy0
159 posts
Soupboy0
#10 h  Mar 1, 2025, 6:05 PM • 1 Y
Y by nmlikesmath
sprint: 25 target: 14 (MASSIVE SELL)
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Existing_Human1
182 posts
Existing_Human1
#11 h  Mar 1, 2025, 6:09 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Target & Sprint & Final Score \\ \hline apex304 & 8 & 16 & 30 & 46\\ Jaxman8 & 8 & 12 & 27 & 39 \\ Mathprodigy2011 & 8 & idk & idk & 43\\ ExistingHuman1 & 8 & 14 & 29 & 43\\ jb2015007 & 7 & idk & idk & 35 :facepalm: \\ luckyrabbit11 & 8 & idk & idk & 41\\ Soupboy0 & 7 & 14 & 25 & 39 \\ \end{tabular}$
This post has been edited 2 times. Last edited by Existing_Human1, Mar 1, 2025, 6:10 PM
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jb2015007
1703 posts
jb2015007
#12 h  Mar 1, 2025, 6:11 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Target & Sprint & Final Score \\ \hline apex304 & 8 & 16 & 30 & 46\\ Jaxman8 & 8 & 12 & 27 & 39 \\ Mathprodigy2011 & 8 & idk & idk & 43\\ ExistingHuman1 & 8 & 14 & 29 & 43\\ jb2015007 & 7 & 14 & 21 & 35 :facepalm: \\ luckyrabbit11 & 8 & idk & idk & 41\\ Soupboy0 & 7 & 14 & 25 & 39 \\ \end{tabular}$
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elizhang101412
1184 posts
elizhang101412
#13 h  Mar 1, 2025, 6:14 PM
Y by
a
$\begin{tabular}{c|c|c|c|c}Username & Grade & Target & Sprint & Final Score \\ \hline apex304 & 8 & 16 & 30 & 46\\ Jaxman8 & 8 & 12 & 27 & 39 \\ Mathprodigy2011 & 8 & idk & idk & 43\\ ExistingHuman1 & 8 & 14 & 29 & 43\\ jb2015007 & 7 & 14 & 21 & 35 :facepalm: \\ luckyrabbit11 & 8 & idk & idk & 41\\ Soupboy0 & 7 & 14 & 25 & 39 \\ elizhang101412 & 6 & 12 & 27 & 39 \\ \end{tabular}$
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derekwang2048
1188 posts
derekwang2048
#14 h  Mar 1, 2025, 6:58 PM
Y by
idk my real score tho (this is what i think i got)
$\begin{tabular}{c|c|c|c|c}Username & Grade & Target & Sprint & Final Score \\ \hline apex304 & 8 & 16 & 30 & 46\\ Jaxman8 & 8 & 12 & 27 & 39 \\ Mathprodigy2011 & 8 & idk & idk & 43\\ ExistingHuman1 & 8 & 14 & 29 & 43\\ jb2015007 & 7 & 14 & 21 & 35 :facepalm: \\ luckyrabbit11 & 8 & idk & idk & 41\\ Soupboy0 & 7 & 14 & 25 & 39 \\ elizhang101412 & 6 & 12 & 27 & 39 \\ derekwang2048 & 6 & 14 & 26-29? & 40-43? \\ \end{tabular}$
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martianrunner
122 posts
martianrunner
#15 h  Mar 1, 2025, 7:31 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Target & Sprint & Final Score \\ \hline apex304 & 8 & 16 & 30 & 46\\ Jaxman8 & 8 & 12 & 27 & 39 \\ Mathprodigy2011 & 8 & idk & idk & 43\\ ExistingHuman1 & 8 & 14 & 29 & 43\\ jb2015007 & 7 & 14 & 21 & 35 :facepalm: \\ luckyrabbit11 & 8 & idk & idk & 41\\ Soupboy0 & 7 & 14 & 25 & 39 \\ elizhang101412 & 6 & 12 & 27 & 39 \\ derekwang2048 & 6 & 14 & 26-29? & 40-43? \\ martianrunner & 8 & 14 & 26-27 & 40-41 \\ \end{tabular}$
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ilikemath247365
220 posts
ilikemath247365
#16 h  Mar 1, 2025, 7:36 PM
Y by
$\begin{tabular}{c|c|c|c|c}Username & Grade & Target & Sprint & Final Score \\ \hline apex304 & 8 & 16 & 30 & 46\\ Jaxman8 & 8 & 12 & 27 & 39 \\ Mathprodigy2011 & 8 & idk & idk & 43\\ ExistingHuman1 & 8 & 14 & 29 & 43\\ jb2015007 & 7 & 14 & 21 & 35 :facepalm: \\ luckyrabbit11 & 8 & idk & idk & 41\\ Soupboy0 & 7 & 14 & 25 & 39 \\ elizhang101412 & 6 & 12 & 27 & 39 \\ derekwang2048 & 6 & 14 & 26-29? & 40-43? \\ martianrunner & 8 & 14 & 26-27 & 40-41 \\ ilikemath247365 & 7 & 14 & 26 & 40 \\ \end{tabular}$
If I didn't silly, I would've gotten a 44 or even a 45(Sillied numbers 27, 28 on sprint, almost solved 29, sillied number 4 on target)
This post has been edited 1 time. Last edited by ilikemath247365, Mar 1, 2025, 7:37 PM
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