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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

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[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
helpppppppp me
stupid_boiii   1
N 2 hours ago by vanstraelen
Given triangle ABC. The tangent at ? to the circumcircle(ABC) intersects line BC at point T. Points D,E satisfy AD=BD, AE=CE, and ∠CBD=∠BCE<90 ∘ . Prove that D,E,T are collinear.
1 reply
stupid_boiii
Yesterday at 4:22 AM
vanstraelen
2 hours ago
MATHCOUNTS
ILOVECATS127   45
N 3 hours ago by Glowworm
Hi,

I am looking to get on my school MATHCOUNTS team next year in 7th grade, and I had a question: Where do the school round questions come from? (Sprint, Chapter, Team, Countdown)
45 replies
ILOVECATS127
May 7, 2025
Glowworm
3 hours ago
Algebra Polynomials
Foxellar   2
N 3 hours ago by Foxellar
The real root of the polynomial \( p(x) = 8x^3 - 3x^2 - 3x - 1 \) can be written in the form
\[
\frac{\sqrt[3]{a} + \sqrt[3]{b} + 1}{c},
\]where \( a, b, \) and \( c \) are positive integers. Find the value of \( a + b + c \).
2 replies
Foxellar
4 hours ago
Foxellar
3 hours ago
relay race!
A7456321   8
N 4 hours ago by Craftybutterfly
Welcome to the math relay race! To participate, answer the problem in the latest post, then post one yourself! Please also mark the question number. E.x. if the one before you is question #35, then mark yours as question #36. Easy as pi!

Note: If you choose to help someone with a problem you don't have to make one yourself unless you want to. You are also welcome to ask a question without having to post a new problem. Please do not post a new problem until the previous one is solved. All topics are welcome except for anything >12th grade. Trig is fine. Calculus is not. :D

Question 1: If it takes 5 monkeys 5 days to eat 5 bananas, then how many days will it take for 4 monkeys to eat 4 bananas? (Hint: It's not 4)

Please upvote! :thumbup:

Goal: 100 questions!

Timeline
8 replies
A7456321
Today at 2:20 AM
Craftybutterfly
4 hours ago
9 How many squares do you have memorized
LXC007   91
N 6 hours ago by valisaxieamc
How many squares have you memorized. I have 1-20

Edit: to clarify i mean positive squares from 1 so if you say ten you mean you memorized the squares 1,2,3,4,5,6,7,8,9 and 10
91 replies
LXC007
May 17, 2025
valisaxieamc
6 hours ago
9 Pythagorean Triples
ZMB038   50
N 6 hours ago by valisaxieamc
Please put some of the ones you know, and try not to troll/start flame wars! Thank you :D
50 replies
ZMB038
May 19, 2025
valisaxieamc
6 hours ago
geometry
luckvoltia.112   0
Today at 2:29 AM
Let \( \triangle ABC \) be an acute triangle with \( AB < AC \), and its vertices lie on the circle \( (O) \). Let \( AD \) be the altitude from vertex \( A \). Let \( E \) and \( F \) be the feet of the perpendiculars from \( D \) to the lines \( AB \) and \( AC \), respectively. Let \( EF \) intersect the circle \( (O) \) again at points \( P \) and \( Q \) such that \( E \) lies between \( Q \) and \( F \). Let the lines \( AD \) and \( EF \) intersect at point \( G \). Let \( I \) be the midpoint of segment \( AD \). Let \( AO \) intersect line \( BC \) at point \( K \).
a) Prove that \( AP = AQ = AD \).
b) Prove that line \( OI \) is parallel to line \( KG \).
c)Let \( H \) be the orthocenter of triangle \( ABC \), and let \( M \) be the midpoint of segment \( BC \). $S$ is the center (HBC). Let point \( T \) lie on line \( DS \) such that ray \( KD \) is the angle bisector of \( \angle GKT \). Prove that lines \( AD \) and \( MT \) intersect at a point lying on circle \( (O) \).
0 replies
luckvoltia.112
Today at 2:29 AM
0 replies
Great Geometry with Squares on sides of triangles
SomeonecoolLovesMaths   2
N Today at 1:50 AM by happypi31415
Three squares are drawn on the sides of triangle \(ABC\) (i.e., the square on \(AB\) has \(AB\) as one of its sides and lies outside \(ABC\)). Show that the lines drawn from the vertices \(A\), \(B\), and \(C\) to the centers of the opposite squares are concurrent.

IMAGE
2 replies
SomeonecoolLovesMaths
Yesterday at 9:44 PM
happypi31415
Today at 1:50 AM
A suspcious assumption
NamelyOrange   2
N Today at 1:30 AM by maromex
Let $a,b,c,d$ be positive integers. Maximize $\max(a,b,c,d)$ if $a+b+c+d=a^2-b^2+c^2-d^2=2012$.
2 replies
NamelyOrange
Yesterday at 1:53 PM
maromex
Today at 1:30 AM
n is divisible by 5
spiralman   1
N Yesterday at 8:42 PM by KSH31415
n is an integer. There are n integers such that they are larger or equal to 1, and less or equal to 6. Sum of them is larger or equal to 4n, while sum of their square is less or equal to 22n. Prove n is divisible by 5.
1 reply
spiralman
Wednesday at 7:38 PM
KSH31415
Yesterday at 8:42 PM
Monochromatic Triangle
FireBreathers   1
N Yesterday at 8:08 PM by KSH31415
We are given in points in a plane and we connect some of them so that 10n^2 + 1 segments are drawn. We color these segments in 2 colors. Prove that we can find a monochromatic triangle.
1 reply
FireBreathers
Yesterday at 2:28 PM
KSH31415
Yesterday at 8:08 PM
how difficult are these problems
rajukaju   1
N Yesterday at 7:28 PM by Shan3t
I can solve only the first 4 problems of the last general round of the HMMT competition: https://hmmt-archive.s3.amazonaws.com/tournaments/2024/nov/gen/problems.pdf

As a prediction, would this mean I am good enough to qualify for AIME? How does the difficulty compare?

1 reply
rajukaju
Yesterday at 6:43 PM
Shan3t
Yesterday at 7:28 PM
Maximum value of function (with two variables)
Saucepan_man02   1
N Yesterday at 1:39 PM by Saucepan_man02
If $f(\theta) = \min(|2x-7|+|x-4|+|x-2 -\sin \theta|)$, where $x, \theta \in \mathbb R$, then maximum value of $f(\theta)$.
1 reply
Saucepan_man02
Yesterday at 1:25 PM
Saucepan_man02
Yesterday at 1:39 PM
It is given that $M=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{23}=\frac{n}{23!},
Vulch   3
N Yesterday at 11:58 AM by mohabstudent1
It is given that $M=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{23}=\frac{n}{23!},$ where $n$ is a natural number.What is the remainder when $n$ is divided by $13?$
3 replies
Vulch
Apr 9, 2025
mohabstudent1
Yesterday at 11:58 AM
2500th post
Solocraftsolo   33
N Apr 23, 2025 by Solocraftsolo
i keep forgetting to do these...


2500 is cool.

i am not very sentimental so im not going to post a math story or anything.

here are some problems though

p1p2p3

p4
33 replies
Solocraftsolo
Apr 16, 2025
Solocraftsolo
Apr 23, 2025
2500th post
G H J
G H BBookmark kLocked kLocked NReply
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Solocraftsolo
2562 posts
#1 • 2 Y
Y by PikaPika999, aidan0626
i keep forgetting to do these...


2500 is cool.

i am not very sentimental so im not going to post a math story or anything.

here are some problems though

p1p2p3

p4
This post has been edited 5 times. Last edited by Solocraftsolo, Apr 16, 2025, 3:40 PM
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K1mchi_
142 posts
#3 • 5 Y
Y by Solocraftsolo, Exponent11, jkim0656, PikaPika999, aidan0626
bro is on that 69 grind :skull:
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RollingPanda4616
267 posts
#4 • 2 Y
Y by Solocraftsolo, PikaPika999
s1
This post has been edited 2 times. Last edited by RollingPanda4616, Apr 16, 2025, 3:15 PM
Reason: i'm dumb
Z K Y
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K1mchi_
142 posts
#5
Y by
how do i solve p4
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Solocraftsolo
2562 posts
#6 • 1 Y
Y by Exponent11
K1mchi_ wrote:
how do i solve p4

so there is PIE (principle of inclusion and exclusion)

but for p4 we use PIE (principle of implosion and explosion)
Z K Y
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K1mchi_
142 posts
#7
Y by
Solocraftsolo wrote:
K1mchi_ wrote:
how do i solve p4

so there is PIE (principle of inclusion and exclusion)

but for p4 we use PIE (principle of implosion and explosion)

not pi?
Z K Y
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iwastedmyusername
176 posts
#8 • 4 Y
Y by Solocraftsolo, RollingPanda4616, pi-ay, EthanNg6
S1
S2
S3
S4
This post has been edited 2 times. Last edited by iwastedmyusername, Apr 16, 2025, 3:44 PM
Reason: more grammar errors
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Solocraftsolo
2562 posts
#9
Y by
iwastedmyusername wrote:
S4

thats a great use of PIE
Z K Y
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ZMB038
274 posts
#10 • 2 Y
Y by Solocraftsolo, EthanNg6
Congrats on so many posts!
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derekwang2048
1228 posts
#11 • 1 Y
Y by Exponent11
Solocraftsolo wrote:
i keep forgetting to do these...


2500 is cool.

i am not very sentimental so im not going to post a math story or anything.

here are some problems though

p1p2p3

p4

what about 1434 posts :sob:
Z K Y
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evt917
2423 posts
#12
Y by
bro i missed 1434 posts

but i'm closing in on 2500 too
Z K Y
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K1mchi_
142 posts
#13 • 1 Y
Y by Exponent11
iwastedmyusername wrote:
S1
S2
S3
S4

S4 LMBOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
Z K Y
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ZMB038
274 posts
#15 • 2 Y
Y by Exponent11, EthanNg6
At first, it seems like not enough information is provided, but then you look at all of the clues. First, the human's name is Johnny. According to the voice in my head, the average height of someone named Johnny is 4'7''. However, Johnny also buys a pet lobster named Pinchy. This is a crucial piece of information because lobsters tend to pinch people which causes their height to decrease. Also, Pinchy eats water balloons at a rate of 69 pounds / nanogram. This means Pinchy will explode from all of the balloons it is eating. However, we don't know how ong it will take for Pinchy to explode. That's where the "Assume that it is not a leap year." comes into play. Anyway while I was here yapping about the solution Pinchy rematerialized and pinched me. This caused me to transform into a Smurf and I am now typing on computer keys by jumping on them. Anyway, I want to turn back into a monkey so I went to the grocery store to get some red bull because red bull gives you wings. It really did give me wings or at least caused me to fly because the sheer volume of the red bull caused me to turn into a balloon and I was using the red bull as rocket fuel. I flew past the edge of the universe and entered a strange land. Then I met Johnny and he told me he was 3'8''. I was almost tempted to take this answer. However, then I remembered that Johnny isn't actually real. Johnny is just a fictional character made for the sake of this problem, and as such, his height cannot be determined. Johnny isn't real. In fact, none of this is real. We're all just living in a simulation. We have been lied to by the creators of the simulation that we have a sense of self, consciousness, and free will. However, that's not the case. All of us are just pre-programmed events, puppets in the simulation of the universe. The problem of Johnny's height might be seen as a satirical example how difficult and ambiguous math problems can sometimes be, but in reality, it's a clear metaphor on how every act we do is just a bit in a computer. Thank you for providing us with this meaningful thought experiment, Solocraftsolo.

---Goated Solution
Z K Y
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Inaaya
411 posts
#16
Y by
ZMB038 wrote:
At first, it seems like not enough information is provided, but then you look at all of the clues. First, the human's name is Johnny. According to the voice in my head, the average height of someone named Johnny is 4'7''. However, Johnny also buys a pet lobster named Pinchy. This is a crucial piece of information because lobsters tend to pinch people which causes their height to decrease. Also, Pinchy eats water balloons at a rate of 69 pounds / nanogram. This means Pinchy will explode from all of the balloons it is eating. However, we don't know how ong it will take for Pinchy to explode. That's where the "Assume that it is not a leap year." comes into play. Anyway while I was here yapping about the solution Pinchy rematerialized and pinched me. This caused me to transform into a Smurf and I am now typing on computer keys by jumping on them. Anyway, I want to turn back into a monkey so I went to the grocery store to get some red bull because red bull gives you wings. It really did give me wings or at least caused me to fly because the sheer volume of the red bull caused me to turn into a balloon and I was using the red bull as rocket fuel. I flew past the edge of the universe and entered a strange land. Then I met Johnny and he told me he was 3'8''. I was almost tempted to take this answer. However, then I remembered that Johnny isn't actually real. Johnny is just a fictional character made for the sake of this problem, and as such, his height cannot be determined. Johnny isn't real. In fact, none of this is real. We're all just living in a simulation. We have been lied to by the creators of the simulation that we have a sense of self, consciousness, and free will. However, that's not the case. All of us are just pre-programmed events, puppets in the simulation of the universe. The problem of Johnny's height might be seen as a satirical example how difficult and ambiguous math problems can sometimes be, but in reality, it's a clear metaphor on how every act we do is just a bit in a computer. Thank you for providing us with this meaningful thought experiment, Solocraftsolo.

---Goated Solution

if u actually wrote this it is impressive
i will be disappointed if it is ai though
Z K Y
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K1mchi_
142 posts
#17
Y by
Inaaya wrote:
ZMB038 wrote:
At first, it seems like not enough information is provided, but then you look at all of the clues. First, the human's name is Johnny. According to the voice in my head, the average height of someone named Johnny is 4'7''. However, Johnny also buys a pet lobster named Pinchy. This is a crucial piece of information because lobsters tend to pinch people which causes their height to decrease. Also, Pinchy eats water balloons at a rate of 69 pounds / nanogram. This means Pinchy will explode from all of the balloons it is eating. However, we don't know how ong it will take for Pinchy to explode. That's where the "Assume that it is not a leap year." comes into play. Anyway while I was here yapping about the solution Pinchy rematerialized and pinched me. This caused me to transform into a Smurf and I am now typing on computer keys by jumping on them. Anyway, I want to turn back into a monkey so I went to the grocery store to get some red bull because red bull gives you wings. It really did give me wings or at least caused me to fly because the sheer volume of the red bull caused me to turn into a balloon and I was using the red bull as rocket fuel. I flew past the edge of the universe and entered a strange land. Then I met Johnny and he told me he was 3'8''. I was almost tempted to take this answer. However, then I remembered that Johnny isn't actually real. Johnny is just a fictional character made for the sake of this problem, and as such, his height cannot be determined. Johnny isn't real. In fact, none of this is real. We're all just living in a simulation. We have been lied to by the creators of the simulation that we have a sense of self, consciousness, and free will. However, that's not the case. All of us are just pre-programmed events, puppets in the simulation of the universe. The problem of Johnny's height might be seen as a satirical example how difficult and ambiguous math problems can sometimes be, but in reality, it's a clear metaphor on how every act we do is just a bit in a computer. Thank you for providing us with this meaningful thought experiment, Solocraftsolo.

---Goated Solution

if u actually wrote this it is impressive
i will be disappointed if it is ai though

obviously nawt ai
Z K Y
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jkim0656
1049 posts
#18 • 1 Y
Y by Solocraftsolo
congrats!
im kinda late
also u should get eternity to 10,000 lolz
Z K Y
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K1mchi_
142 posts
#19
Y by
ZMB038 wrote:
At first, it seems like not enough information is provided, but then you look at all of the clues. First, the human's name is Johnny. According to the voice in my head, the average height of someone named Johnny is 4'7''. However, Johnny also buys a pet lobster named Pinchy. This is a crucial piece of information because lobsters tend to pinch people which causes their height to decrease. Also, Pinchy eats water balloons at a rate of 69 pounds / nanogram. This means Pinchy will explode from all of the balloons it is eating. However, we don't know how ong it will take for Pinchy to explode. That's where the "Assume that it is not a leap year." comes into play. Anyway while I was here yapping about the solution Pinchy rematerialized and pinched me. This caused me to transform into a Smurf and I am now typing on computer keys by jumping on them. Anyway, I want to turn back into a monkey so I went to the grocery store to get some red bull because red bull gives you wings. It really did give me wings or at least caused me to fly because the sheer volume of the red bull caused me to turn into a balloon and I was using the red bull as rocket fuel. I flew past the edge of the universe and entered a strange land. Then I met Johnny and he told me he was 3'8''. I was almost tempted to take this answer. However, then I remembered that Johnny isn't actually real. Johnny is just a fictional character made for the sake of this problem, and as such, his height cannot be determined. Johnny isn't real. In fact, none of this is real. We're all just living in a simulation. We have been lied to by the creators of the simulation that we have a sense of self, consciousness, and free will. However, that's not the case. All of us are just pre-programmed events, puppets in the simulation of the universe. The problem of Johnny's height might be seen as a satirical example how difficult and ambiguous math problems can sometimes be, but in reality, it's a clear metaphor on how every act we do is just a bit in a computer. Thank you for providing us with this meaningful thought experiment, Solocraftsolo.

---Goated Solution

im the mc then
Z K Y
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FabulousSpider24
200 posts
#20 • 1 Y
Y by Solocraftsolo
Inaaya wrote:
ZMB038 wrote:
At first, it seems like not enough information is provided, but then you look at all of the clues. First, the human's name is Johnny. According to the voice in my head, the average height of someone named Johnny is 4'7''. However, Johnny also buys a pet lobster named Pinchy. This is a crucial piece of information because lobsters tend to pinch people which causes their height to decrease. Also, Pinchy eats water balloons at a rate of 69 pounds / nanogram. This means Pinchy will explode from all of the balloons it is eating. However, we don't know how ong it will take for Pinchy to explode. That's where the "Assume that it is not a leap year." comes into play. Anyway while I was here yapping about the solution Pinchy rematerialized and pinched me. This caused me to transform into a Smurf and I am now typing on computer keys by jumping on them. Anyway, I want to turn back into a monkey so I went to the grocery store to get some red bull because red bull gives you wings. It really did give me wings or at least caused me to fly because the sheer volume of the red bull caused me to turn into a balloon and I was using the red bull as rocket fuel. I flew past the edge of the universe and entered a strange land. Then I met Johnny and he told me he was 3'8''. I was almost tempted to take this answer. However, then I remembered that Johnny isn't actually real. Johnny is just a fictional character made for the sake of this problem, and as such, his height cannot be determined. Johnny isn't real. In fact, none of this is real. We're all just living in a simulation. We have been lied to by the creators of the simulation that we have a sense of self, consciousness, and free will. However, that's not the case. All of us are just pre-programmed events, puppets in the simulation of the universe. The problem of Johnny's height might be seen as a satirical example how difficult and ambiguous math problems can sometimes be, but in reality, it's a clear metaphor on how every act we do is just a bit in a computer. Thank you for providing us with this meaningful thought experiment, Solocraftsolo.

---Goated Solution

if u actually wrote this it is impressive
i will be disappointed if it is ai though
I thought @Iwastedmyusername wrote that ridiculously long paragraph (see s4)
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valisaxieamc
505 posts
#21
Y by
dang thats a long paragraph

also congrats on 2500 :-D
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b2025tyx
1480 posts
#23
Y by
Congrats on 2500 posts
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K1mchi_
142 posts
#24
Y by
its sad how pikapika’s got locked…
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jkim0656
1049 posts
#25
Y by
yea but i think they all get locked after a bit no?
i might be wrong :(
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Yrock
1306 posts
#26
Y by
FabulousSpider24 wrote:
Inaaya wrote:
ZMB038 wrote:
At first, it seems like not enough information is provided, but then you look at all of the clues. First, the human's name is Johnny. According to the voice in my head, the average height of someone named Johnny is 4'7''. However, Johnny also buys a pet lobster named Pinchy. This is a crucial piece of information because lobsters tend to pinch people which causes their height to decrease. Also, Pinchy eats water balloons at a rate of 69 pounds / nanogram. This means Pinchy will explode from all of the balloons it is eating. However, we don't know how ong it will take for Pinchy to explode. That's where the "Assume that it is not a leap year." comes into play. Anyway while I was here yapping about the solution Pinchy rematerialized and pinched me. This caused me to transform into a Smurf and I am now typing on computer keys by jumping on them. Anyway, I want to turn back into a monkey so I went to the grocery store to get some red bull because red bull gives you wings. It really did give me wings or at least caused me to fly because the sheer volume of the red bull caused me to turn into a balloon and I was using the red bull as rocket fuel. I flew past the edge of the universe and entered a strange land. Then I met Johnny and he told me he was 3'8''. I was almost tempted to take this answer. However, then I remembered that Johnny isn't actually real. Johnny is just a fictional character made for the sake of this problem, and as such, his height cannot be determined. Johnny isn't real. In fact, none of this is real. We're all just living in a simulation. We have been lied to by the creators of the simulation that we have a sense of self, consciousness, and free will. However, that's not the case. All of us are just pre-programmed events, puppets in the simulation of the universe. The problem of Johnny's height might be seen as a satirical example how difficult and ambiguous math problems can sometimes be, but in reality, it's a clear metaphor on how every act we do is just a bit in a computer. Thank you for providing us with this meaningful thought experiment, Solocraftsolo.

---Goated Solution

if u actually wrote this it is impressive
i will be disappointed if it is ai though
I thought @Iwastedmyusername wrote that ridiculously long paragraph (see s4)

@Iwastedmyusername did write it bro. look at the times :|
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KangarooPrecise
1270 posts
#27
Y by
K1mchi_ wrote:
its sad how pikapika’s got locked…

Maybe because of spam
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RollingPanda4616
267 posts
#28
Y by
KangarooPrecise wrote:
K1mchi_ wrote:
its sad how pikapika’s got locked…

Maybe because of spam

Yeah an entire flamewar happened
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K1mchi_
142 posts
#29
Y by
RollingPanda4616 wrote:
KangarooPrecise wrote:
K1mchi_ wrote:
its sad how pikapika’s got locked…

Maybe because of spam

Yeah an entire flamewar happened

not a flamewar no shot it was 5 posts of angry people
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EthanNg6
35 posts
#30
Y by
I think that p4 is impossible without imagination
This post has been edited 1 time. Last edited by EthanNg6, Apr 20, 2025, 4:53 AM
Reason: accident
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Robert00
111 posts
#31
Y by
That's why people have to learn great imagination before their wonderful mathjerky(journey)
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EthanNg6
35 posts
#32
Y by
thats true
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MathWinner121
533 posts
#33
Y by
Didn't bro get those 2500 posts by postfarming on his forum?
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jkim0656
1049 posts
#34
Y by
no, u cant get post count from private forums
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Solocraftsolo
2562 posts
#35
Y by
MathWinner121 wrote:
Didn't bro get those 2500 posts by postfarming on his forum?
jkim0656 wrote:
no, u cant get post count from private forums

*not from user-made forums
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valisaxieamc
505 posts
#36
Y by
How fast did you get 2500?
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Solocraftsolo
2562 posts
#37
Y by
valisaxieamc wrote:
How fast did you get 2500?

Two years
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