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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
Yesterday at 11:16 PM
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)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]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
Yesterday at 11:16 PM
0 replies
k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
3 variables NT
NicoN9   0
19 minutes ago
Source: Japan Junior MO Preliminary 2020 P8
Find all triples $(l, m, n)$ such that \[
l^2+mn=m^2+ln,\quad  n^2+lm=2020,\quad  l\le m\le n.
\]
0 replies
NicoN9
19 minutes ago
0 replies
Filling with tiles
NicoN9   0
21 minutes ago
Source: Japan Junior MO Preliminary 2020 P7
Consider the following tiles, created by using three and five unitsquare, respectively.
IMAGE
There are twelve of L, and four of X. We fill the following gray region created by $56$ unitsquare, using L and X.

IMAGE
Find the number of ways to do so.
0 replies
NicoN9
21 minutes ago
0 replies
3D combo puzzle
NicoN9   0
23 minutes ago
Source: Japan Junior MO Preliminary 2020 P6
As shown below, there is a figure $Q$ created by removing the unitcube at the cornor of the cube with side length $5$. Also, there are infinitely many figure $L$ created with four unitcube, and infinitely many unitcubes.

IMAGE
We paste together $L$ and unitcubes to create $Q$.
What is the maximum possible number of $L$ that we can use?
0 replies
NicoN9
23 minutes ago
0 replies
quadrilateral ABCD and mid of AC, BD
NicoN9   0
25 minutes ago
Source: Japan Junior MO Preliminary 2020 P5
Suppose $ABCD$ is a convex quadrilateral such that $AB=CD=7$, $DA=6$, $\angle B=72^\circ$, and $\angle C=48^\circ$. Let $P$, and $Q$ be the midpoint of segment $AC$, and $BD$, respectively. Find the value of $PQ$.
0 replies
NicoN9
25 minutes ago
0 replies
isosceles right triangle with four squares inscribed
NicoN9   0
27 minutes ago
Source: Japan Junior MO Preliminary 2020 P4
Four squares with side length $1$ are inscribed in isosceles right triangle, as shown below. Find the area of the isosceles right triangle.
IMAGE
0 replies
NicoN9
27 minutes ago
0 replies
number of palindromes divisible by 11
NicoN9   0
29 minutes ago
Source: Japan Junior MO Preliminary 2020 P3
We call an integer palindrome if it's the same value when read it backwards, and the unit digit is nonzero. Find the number of positive integers less than or equal to $10000$ such that it is a palindrome, and divisible by $11$.
0 replies
NicoN9
29 minutes ago
0 replies
Consecutive sum of integers sum up to 2020
NicoN9   0
31 minutes ago
Source: Japan Junior MO Preliminary 2020 P2
Let $a$ and $b$ be positive integers. Suppose that the sum of integers between $a$ and $b$, including $a$ and $b$, are equal to $2020$.
All among those pairs $(a, b)$, find the pair such that $a$ achieves the minimum.
0 replies
NicoN9
31 minutes ago
0 replies
3 right-angled triangle area
NicoN9   0
32 minutes ago
Source: Japan Junior MO Preliminary 2020 P1
Right angled triangle $ABC$, and a square are drawn as shown below. Three numbers written below implies each of the area of shaded small right angled triangle. Find the value of $AB/AC$.

IMAGE
0 replies
NicoN9
32 minutes ago
0 replies
Function equation
LeDuonggg   3
N 35 minutes ago by luutrongphuc
Find all functions $f: \mathbb{R^+} \rightarrow \mathbb{R^+}$ , such that for all $x,y>0$:
\[ f(x+f(y))=\dfrac{f(x)}{1+f(xy)}\]
3 replies
LeDuonggg
Yesterday at 2:59 PM
luutrongphuc
35 minutes ago
A sequence containing every natural number exactly once
Pomegranat   4
N 44 minutes ago by Pomegranat
Source: Own
Does there exist a sequence \( \{a_n\}_{n=1}^{\infty} \), which is a permutation of the natural numbers (that is, each natural number appears exactly once), such that for every \( n \in \mathbb{N} \), the sum of the first \( n \) terms is divisible by \( n \)?
4 replies
Pomegranat
3 hours ago
Pomegranat
44 minutes ago
9 What is the most important topic in maths competition?
AVIKRIS   65
N an hour ago by Craftybutterfly
I think arithmetic is the most the most important topic in math competitions.
65 replies
AVIKRIS
Apr 19, 2025
Craftybutterfly
an hour ago
9 AMC 8 Scores
ChromeRaptor777   124
N an hour ago by AVY2024
As far as I'm certain, I think all AMC8 scores are already out. Vote above.
124 replies
ChromeRaptor777
Apr 1, 2022
AVY2024
an hour ago
9 What competitions do you do
VivaanKam   5
N 2 hours ago by valisaxieamc

I know I missed a lot of other competitions so if you didi one of the just choose "Other".
5 replies
VivaanKam
Wednesday at 6:43 PM
valisaxieamc
2 hours ago
1234th Post!
PikaPika999   258
N 2 hours ago by valisaxieamc
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: $(4-3)\cdot(2-1)$
258 replies
PikaPika999
Apr 21, 2025
valisaxieamc
2 hours ago
Counting Problems
mithu542   2
N Wednesday at 7:28 PM by Inaaya
Hello!

Here are some challenging practice counting problems. Enjoy! (You're allowed to use a calculator) hint


1.
Yan rolls 9 standard six-sided dice.
What is the probability that at least one pair of dice has a sum of 8?
Round your answer to 3 decimal places.

2.
Each face of a cube is painted one of 5 colors: red, blue, green, yellow, or white.
What is the probability that no two adjacent faces are painted the same color?
Round your answer to 3 decimal places.

3.
You roll 8 standard six-sided dice in a row.
What is the probability that at least one pair of adjacent dice differ by exactly 2?
Round your answer to 3 decimal places.

4.
A 4×4×4 cube (made of 64 mini-cubes) is randomly painted, each mini-cube colored independently either black or white.
What is the probability that at least one mini-cube adjacent to the center mini-cube is black?
Round your answer to 3 decimal places.

5.
Yan rolls 7 dice, each numbered 11 to 88.
What is the probability that at least two dice show the same number?
Round your answer to 3 decimal places.

6.
Each vertex of a cube is randomly colored either red, blue, or green.
What is the probability that there exists at least one face whose four vertices are all the same color?
Round your answer to 3 decimal places.

7.
You roll 6 standard six-sided dice.
What is the probability that the sum of all six dice is divisible by 4?
Round your answer to 3 decimal places.

8.
Each face of a cube is randomly colored red, blue, green, or yellow.
What is the probability that no two opposite faces are painted the same color?
Round your answer to 3 decimal places.

9.
Yan flips a fair coin 12 times.
What is the probability that there is at least one sequence of 4 consecutive heads?
Round your answer to 3 decimal places.

10.
Each edge of a cube is randomly colored either red, blue, or green.
What is the probability that no face of the cube has all three edges the same color?
Round your answer to 3 decimal places.
2 replies
mithu542
Apr 28, 2025
Inaaya
Wednesday at 7:28 PM
Counting Problems
G H J
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mithu542
1573 posts
#1
Y by
Hello!

Here are some challenging practice counting problems. Enjoy! (You're allowed to use a calculator) hint


1.
Yan rolls 9 standard six-sided dice.
What is the probability that at least one pair of dice has a sum of 8?
Round your answer to 3 decimal places.

2.
Each face of a cube is painted one of 5 colors: red, blue, green, yellow, or white.
What is the probability that no two adjacent faces are painted the same color?
Round your answer to 3 decimal places.

3.
You roll 8 standard six-sided dice in a row.
What is the probability that at least one pair of adjacent dice differ by exactly 2?
Round your answer to 3 decimal places.

4.
A 4×4×4 cube (made of 64 mini-cubes) is randomly painted, each mini-cube colored independently either black or white.
What is the probability that at least one mini-cube adjacent to the center mini-cube is black?
Round your answer to 3 decimal places.

5.
Yan rolls 7 dice, each numbered 11 to 88.
What is the probability that at least two dice show the same number?
Round your answer to 3 decimal places.

6.
Each vertex of a cube is randomly colored either red, blue, or green.
What is the probability that there exists at least one face whose four vertices are all the same color?
Round your answer to 3 decimal places.

7.
You roll 6 standard six-sided dice.
What is the probability that the sum of all six dice is divisible by 4?
Round your answer to 3 decimal places.

8.
Each face of a cube is randomly colored red, blue, green, or yellow.
What is the probability that no two opposite faces are painted the same color?
Round your answer to 3 decimal places.

9.
Yan flips a fair coin 12 times.
What is the probability that there is at least one sequence of 4 consecutive heads?
Round your answer to 3 decimal places.

10.
Each edge of a cube is randomly colored either red, blue, or green.
What is the probability that no face of the cube has all three edges the same color?
Round your answer to 3 decimal places.
This post has been edited 3 times. Last edited by mithu542, Apr 29, 2025, 9:30 PM
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Bummer12345
138 posts
#2
Y by
number 1 has to be inspired by that one target p8 question with 6 dice and sum to 7
Z K Y
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Inaaya
304 posts
#3
Y by
ill solve some of these when i get some of my math and ai4girls done trust
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