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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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9 AMC 8 Scores
ChromeRaptor777   112
N a few seconds ago by Chonkachu
As far as I'm certain, I think all AMC8 scores are already out. Vote above.
112 replies
ChromeRaptor777
Apr 1, 2022
Chonkachu
a few seconds ago
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9 Did you get into Illinois middle school math Olympiad?
Gavin_Deng   14
N 28 minutes ago by b2025tyx
I am simply curious of who got in.
14 replies
1 viewing
Gavin_Deng
Apr 19, 2025
b2025tyx
28 minutes ago
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1234th Post!
PikaPika999   180
N 30 minutes ago by jkim0656
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
180 replies
PikaPika999
Apr 21, 2025
jkim0656
30 minutes ago
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Nats 2024 cutoff Map
MathyMathMan   18
N 39 minutes ago by K1mchi_
2024 MATHCOUNTS Nats Cutoff Map

Greetings!

I should first and foremost thank those who helped with this project along the way. This idea is fully inspired by past South Dakota alumni that attended my school. The original ideas were created by @anser and @techguy2. I would also like to thank @peace09 for agreeing to collaborate with me on the scores and ratings during the 2024 state competitions throughout the country.

@peace09's post Cutoffs and Scores

Please state your state and cutoff score. (4th place) You can also provide the 3rd, 2nd, and 1st place scores as well. People from different territories can also provide their state's scores as well. I will try my best to keep this map updated until we get all the scores. You are also free to discuss states and nationals stuff too if you want. :)

(Btw congratulations to everyone who made nationals, I hope to see you guys there too!)

Nats qualification scores
18 replies
MathyMathMan
Apr 4, 2024
K1mchi_
39 minutes ago
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Complex Numbers Question
franklin2013   2
N Today at 1:59 PM by Xx_BABAI_xX
Hello everyone! This is one of my favorite complex numbers questions. Have fun!

$f(z)=z^{720}-z^{120}$. How many complex numbers $z$ are there such that $|z|=1$ and $f(z)$ is an integer.

Hint
2 replies
franklin2013
Apr 20, 2025
Xx_BABAI_xX
Today at 1:59 PM
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Inequalities
sqing   17
N Today at 1:26 PM by sqing
Let $ a,b,c> 0 $ and $ ab+bc+ca\leq 3abc . $ Prove that
$$ a+ b^2+c\leq a^2+ b^3+c^2 $$$$ a+ b^{11}+c\leq a^2+ b^{12}+c^2 $$
17 replies
sqing
Yesterday at 1:54 PM
sqing
Today at 1:26 PM
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Geometric inequality
ReticulatedPython   1
N Today at 12:43 PM by vanstraelen
Let $A$ and $B$ be points on a plane such that $AB=n$, where $n$ is a positive integer. Let $S$ be the set of all points $P$ such that $\frac{AP^2+BP^2}{(AP)(BP)}=c$, where $c$ is a real number. The path that $S$ traces is continuous, and the value of $c$ is minimized. Prove that $c$ is rational for all positive integers $n.$
1 reply
ReticulatedPython
Yesterday at 5:12 PM
vanstraelen
Today at 12:43 PM
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Binomial Sum
P162008   0
Today at 12:34 PM
Compute $\sum_{r=0}^{n} \sum_{k=0}^{r} (-1)^k (k + 1)(k + 2) \binom {n + 5}{r - k}$
0 replies
P162008
Today at 12:34 PM
0 replies
J
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Triple Sum
P162008   0
Today at 12:24 PM
Find the value of

$\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k} \sum_{n=0}^{\infty} \sum_{m=0}^{\infty} \frac{(-1)^m}{k.2^n + 2m + 1}$
0 replies
P162008
Today at 12:24 PM
0 replies
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Binomial Sum
P162008   0
Today at 12:03 PM
The numbers $p$ and $q$ are defined in the following manner:

$p = 99^{98} - \frac{99}{1} 98^{98} + \frac{99.98}{1.2} 97^{98} - \frac{99.98.97}{1.2.3} 96^{98} + .... + 99$

$q = 99^{100} - \frac{99}{1} 98^{100} + \frac{99.98}{1.2} 97^{100} - \frac{99.98.97}{1.2.3} 96^{100} + .... + 99$

If $p + q = k(99!)$ then find the value of $\frac{k}{10}.$
0 replies
P162008
Today at 12:03 PM
0 replies
J
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Polynomial Limit
P162008   0
Today at 11:55 AM
If $P_{n}(x) = \prod_{k=0}^{n} \left(x + \frac{1}{2^k}\right) = \sum_{k=0}^{n} a_{k} x^k$ then find the value of $\lim_{n \to \infty} \frac{a_{n - 2}}{a_{n - 4}}.$
0 replies
P162008
Today at 11:55 AM
0 replies
J
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Telescopic Sum
P162008   0
Today at 11:40 AM
Compute the value of $\Omega = \sum_{r=1}^{\infty} \frac{14 - 9r - 90r^2 - 36r^3}{7^r r(r + 1)(r + 2)(4r^2 - 1)}$
0 replies
P162008
Today at 11:40 AM
0 replies
J
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CHINA TST 2017 P6 DAY1
lingaguliguli   0
Today at 9:03 AM
When i search the china TST 2017 problem 6 day I i crossed out this lemme, but don't know to prove it, anyone have suggestion? tks
Given a fixed number n, and a prime p. Let f(x)=(x+a_1)(x+a_2)...(x+a_n) in which a_1,a_2,...a_n are positive intergers. Show that there exist an interger M so that 0<v_p((f(M))< n + v_p(n!)
0 replies
lingaguliguli
Today at 9:03 AM
0 replies
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Combinatoric
spiderman0   1
N Today at 6:44 AM by MathBot101101
Let $ S = \{1, 2, 3, \ldots, 2024\}.$ Find the maximum positive integer $n \geq 2$ such that for every subset $T \subset S$ with n elements, there always exist two elements a, b in T such that:

$|\sqrt{a} - \sqrt{b}| < \frac{1}{2} \sqrt{a - b}$
1 reply
spiderman0
Yesterday at 7:46 AM
MathBot101101
Today at 6:44 AM
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bracelets
pythagorazz   7
N Yesterday at 4:06 PM by H1u2g4o4
Kat designs circular bead bracelets for kids. Each bracelet has 5 beads, all of which are either yellow or green. If beads of the same color are identical, how many distinct bracelets could Kat make?
7 replies
pythagorazz
Apr 14, 2025
H1u2g4o4
Yesterday at 4:06 PM
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bracelets
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Reveal topic tags
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pythagorazz
378 posts
pythagorazz
#1 h  Apr 14, 2025, 9:09 AM
Y by
Kat designs circular bead bracelets for kids. Each bracelet has 5 beads, all of which are either yellow or green. If beads of the same color are identical, how many distinct bracelets could Kat make?
Z K Y
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Bobelix
40 posts
Bobelix
#2 h  Apr 14, 2025, 10:41 AM
Y by
I could be wrong, but isn’t it 32?
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HungryCalculator
539 posts
HungryCalculator
#3 h  Apr 14, 2025, 12:04 PM • 2 Y
Y by orangefronted, pythagorazz
1+1+2+2+1+1=8
Bobelix wrote:
I could be wrong, but isn’t it 32?

Account for rotations for each case of # of yellow and green beads
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EthanNg6
25 posts
EthanNg6
#4 h  Yesterday at 2:07 AM
Y by
It's 32
2 times 2 times 2 times 2 times 2=32
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DDCN_2011
354 posts
DDCN_2011
#5 h  Yesterday at 2:35 AM
Y by
EthanNg6 wrote:
It's 32
2 times 2 times 2 times 2 times 2=32

like what 2 post ahead said you have to account for rotation as ygygy will be counted multiple times as rotations
This post has been edited 1 time. Last edited by DDCN_2011, Yesterday at 2:35 AM
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That_One_Genius.
12 posts
That_One_Genius.
#6 h  Yesterday at 3:35 AM
Y by
I might be wrong, but isn't it 6(not counting symmetries)?
Solution
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maxamc
560 posts
maxamc
#7 h  Yesterday at 12:47 PM
Y by
That_One_Genius. wrote:
I might be wrong, but isn't it 6(not counting symmetries)?
Solution

how about 5y, 5g
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H1u2g4o4
1 post
H1u2g4o4
#8 h  Yesterday at 4:06 PM
Y by
Yellow Green Circular arrangement Number of types
Yellow Green
5 0 1
4 1 1
3 2 2
2 3 2
1 4 1
0 5 1

all:8
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