Plan ahead for the next school year. Schedule your class today!

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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Jul 1, 2025
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
and train with the best! Please note that early bird pricing ends August 19th!
Are you tired of the heat and thinking about Fall? You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US.

Our full course list for upcoming classes is below:
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0 replies
jwelsh
Jul 1, 2025
0 replies
The 24 Game, but with a twist!
PikaPika999   442
N 3 minutes ago by vmene
So many people know the 24 game, where you try to create the number 24 from using other numbers, but here's a twist:

You can only use the number 24 (up to 5 times) to try to make other numbers :)

the limit is 5 times because then people could just do $\frac{24}{24}+\frac{24}{24}+\frac{24}{24}+...$ and so on to create any number!

honestly, I feel like with only addition, subtraction, multiplication, and division, you can't get pretty far with this, so you can use any mathematical operations!

Banned functions
442 replies
PikaPika999
Jul 1, 2025
vmene
3 minutes ago
Math Counts
sudarya   0
8 minutes ago
Hello guys!



My account name is sudarya and I am working hard to go to Math Counts Nationals with my state (Wisconsin). I am having some trouble lately at some state problems, and I kind of need some encouragement from you guys. This is my only hope of making it to Nationals, and I really trust you guys to make this dream a reality for me. Thank you so much!


0 replies
sudarya
8 minutes ago
0 replies
2500 VIMC mathematics competition
OWOW   57
N 42 minutes ago by OWOW
Hello! This is my second math competition I made up, this time, set in the year 2500 on a Venus base in the upper atmosphere.
This is basically AMC8 for Venusians.

2500 VIMC

What is the sum of all perfect squares less than 2500 in the form $9p^2$ where $p$ is prime?

Equilateral triangle $ABC$ has Area of $6$. If point $D$ is the midpoint of $AB$, then line $L$ is $CD$, which cuts the equilateral triangle in half. What is the sum of the perimeters of $ACD$ and $BCD$?

A Quadnumber is a number whose digits sum to $4$. How many positive 3-digit quadnumbers are there? (ex. $310$ is a quadnumber because it is positive, 3-digit, and the digits sum to $4$)

A wheel has $100$ equal sections with the numbers from $1$ to $100$ written on them. If you spin the wheel $N$ times, what is the probability that you will land on a prime number on any of the $N$ spins? (Clarification: Probability of Landing on a prime AT LEAST ONCE in the N spins)

Car A travels at a constant $10$ mph. Car B is a probabilistic car, and at the start of every hour, it gets the option for a $10\%$ chance of traveling at $5$ mph, an $80\%$ chance of traveling at $10$ mph, and a $10\%$ chance of traveling at $15$ mph. Once Car B decides on a speed, it acts like a normal car for the rest of the hour with a constant speed at which it picked at the start of the hour, and then the same options happen at the start of the next hour, and so on. Car A and Car B leave at the same time, and they both go in the same direction. What is the probability that Car B is right next to Car A (same speed, same position) for only $3$ hours in the next 6 hours?

If $x \equiv 2\pmod{3}$, and $x \equiv 3\pmod{4}$, and $x \equiv 4\pmod{5}$, what is the least positive value of $x$.

If $f(x)=3x-1$ and $g(x)$ is $x^2-3x+3$, what is $f(g(5)-f(4))+g(f(3)-g(2))+1$?



This competition is shorter than the Mars version (MIMC 2200) which was 10 questions. But this one I believe is harder than the MIMC. (designed to be, anyway) Btw here is the entire MIMC competition in case you missed it a couple weeks ago.



$25^2-10^2=$?

If ball A costs $\$1.50$, and ball B costs $\$1.75$, what is the average cost per ball if you buy $10$ of ball A and $4$ of ball B? Please write as an improper fraction

How many divisors does $2200^3$ have?

If $f(2200-k)=10(k-2)$, then what is $f(f(2^{11}))$?

If three distinct positive primes, $(p,q,r)$, sum to 50, what is the greatest possible value of $(r^p)-(q^p)$ such that $p<q<r$?

What positive integer $x$ satisfies: $x^5-(x+4)^3+10^{(5-3)}=0$?

If a circle with radius $1$ is inscribed in a square, which is inscribed in another circle, what is the area of the outer circle minus the area of the inner circle?

What is the sum of $b$ and $c$ such that the roots of $x^2+bx+c=0$ sum to $11c$ and multiply to $12b-7$?

If the operation $a\#b = \dfrac{(a-b+1)^2}{(b-a+1)^2}$, what is the largest possible value of $(3\#x)$ given that $x$ is a positive integer?

How many 4-digit numbers have the property that the sum of the thousands and tens digits combined is the square of the sum of the hundreds and ones digits combined?

Pls write all solutions like this:
ex. S1 (Contest: either VIMC or MIMC)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Completed problems (I'm not going to show solutions here so other people can solve it)
MIMC: 1,2,3,4,5,6,7,8,9 (9/10 done)
VIMC: 1,2,3,4,6,7 (6/7 done)
57 replies
OWOW
Jul 16, 2025
OWOW
42 minutes ago
gcd of n(n+1)(n+2)(n+3)(n+4)
Marius_Avion_De_Vanatoare   14
N an hour ago by PikaPika999
Find the greatest common divisor of the numbers: $1\cdot 2\cdot 3 \cdot 4 \cdot 5$ and $2\cdot 3 \cdot 4 \cdot 5 \cdot 6 \dots 2025 \cdot 2026 \cdot 2027 \cdot 2028 \cdot 2029$.
14 replies
Marius_Avion_De_Vanatoare
Jun 14, 2025
PikaPika999
an hour ago
No more topics!
Probability problem
CJB19   10
N May 20, 2025 by CJB19
Me and my math teacher got different answers for this so I'm asking you all:

Clare has a spinner split into fourths and labeled A, B, C, and D so that there is a $\frac{1}{4}$ chance of it landing on each section. She plays a game where if you spin it and it lands on A, you win. However, if you don't land on A the first time, you can try again. What are the odds of winning? (You don't spin again if you land on A the first time)
10 replies
CJB19
May 19, 2025
CJB19
May 20, 2025
Probability problem
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CJB19
178 posts
#1
Y by
Me and my math teacher got different answers for this so I'm asking you all:

Clare has a spinner split into fourths and labeled A, B, C, and D so that there is a $\frac{1}{4}$ chance of it landing on each section. She plays a game where if you spin it and it lands on A, you win. However, if you don't land on A the first time, you can try again. What are the odds of winning? (You don't spin again if you land on A the first time)
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pingpongmerrily
4055 posts
#2 • 1 Y
Y by OTA1
do you get 2 max tries?
the odds would be 7/16 i think
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Yiyj
434 posts
#3 • 1 Y
Y by OTA1
If you only get two tries…
This post has been edited 1 time. Last edited by Yiyj, May 19, 2025, 6:55 PM
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Soupboy0
635 posts
#4
Y by
literally $1$ if forever though :skull:
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Capybara7017
682 posts
#5
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Soupboy0 wrote:
literally $1$ if forever though :skull:

duh
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red_raven_9
6 posts
#6
Y by
x/y

but I don't know what x or y is...

:cool: :wow:
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Inaaya
506 posts
#7 • 1 Y
Y by booking
1- (3/4)^n for n spins?
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valisaxieamc
606 posts
#8
Y by
What did u get cause I got Click to reveal hidden text
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CJB19
178 posts
#9
Y by
7/16 is correct
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ScrappyBoss0825
5 posts
#10
Y by
It's 7/16. What did your math teacher get?
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CJB19
178 posts
#11
Y by
Idk she just said she got something different than I did (This was a brief interaction during a lesson) but I wasn't sure what it was so I asked AoPS (I was wrong because I suck at probability)
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