Can someone explain this one

by hawa, Apr 29, 2025, 1:36 AM

Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.

Counting Problems

by mithu542, Apr 28, 2025, 9:02 PM

Hello!

Here are some challenging practice counting problems. Enjoy! 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 2 times. Last edited by mithu542, Yesterday at 9:10 PM

counting

MATHCOUNTS

complementary counting

problem

practice

Purple Comet Math Meet

by GallopingUnicorn45, Apr 28, 2025, 7:14 PM

Hi, so I've been seeing some threads about the Purple Comet Math Meet. I've got some questions regarding this topic:

1. Is there a grade restriction? I'm in 4th grade and I looked over the middle school questions from last year, and they didn't seem too hard and I wanted to have a go at it.

2. Do you have to take some kind of placement test to apply?

3. Where does this math meet take place?

Thanks!

Purple Comet

Kindle Scribe on Purple Comet?

by RabtejKalra, Apr 27, 2025, 5:08 PM

Can I bring a Kindle Scribe to the Purple Comet examination, because I've downloaded lot of formulas into it, but don't want to waste the paper to print all of it. PLEASE ANSWER SOON, THE COMPETITION IS IN 4 HOURS!

Purple Comet Math Meet Recources

by RabtejKalra, Apr 24, 2025, 1:05 AM

I heard that you can take a packet of information to the Purple Comet examination with some formulas, etc. Does anybody have a copy of a guidebook with all the important formulas? I'm just too lazy to write one myself.......

Purple Comet

What is the most important topic in maths competition?

by AVIKRIS, Apr 19, 2025, 5:29 PM

Loading poll details...

I think arithmetic is the most the most important topic in math competitions.

arithmetic

Pre Algebra

poll

Preparing for Higher AIME+

by PhoenixMathClub, Apr 19, 2025, 1:51 PM

Hello, I am going to be a 7th grader next year and I really want to qualify for USAJMO in 8th grade, so far I have these goals reached

1. AMC 10 Honor Roll A and B 2025
2. AMC 8 DHR and HR
3. AIME 3

This year on AIME something happened and I got a 3

on the AMC's I got a 105 on AMC 10 A and I got a 114 on AMC 10 B. I want to improve mostly on AIME but since the AMC 10 is coming up quicker what would you guys recommend for getting 110+ on both of the AMC 10's and getting a 6+ on AIME? So far I am only doing Alcumus and have no books so far.... Checking the table of contents on the books Alcumus provides the same topics. I was thinking to take WOOT 1 and AMC 10 Problem Series.

Website to learn math

by hawa, Apr 9, 2025, 2:52 AM

Hi, I'm kinda curious what website do yall use to learn math, like i dont find any website thats fun to learn math

random achievements

by Bummer12345, Mar 25, 2025, 1:27 PM

What are some random math achievements that you have accomplished but possess no real meaning?

For example, I solved #10 on the 2024 national mathcounts team round, though my team got a 5 Click to reveal hidden text and ended up getting 30-somethingth place

skibidi dom dom yes yes yes

300 MAP Goal??

by Antoinette14, Jan 30, 2025, 10:30 PM

Hey, so as a 6th grader, my big goal for MAP this spring is to get a 300 (ambitious, i know). I'm currently at a 285 (288 last year though). I'm already taking a intro to counting and probability course (One of my weak points), but is there anything else you recommend I focus on to get a 300?

MAP

#16) Easy Inversion!

by Drunken_Master, Mar 1, 2018, 9:56 AM

Let $\Gamma_1$ , $\Gamma_2$ , $\Gamma_3$ , $\Gamma_4$ be distinct circles such that $\Gamma_1$ , $\Gamma_3$ are externally tangent at $P$ , and $\Gamma_2$ , $\Gamma_4$ are externally tangent at the same point $P$ . Suppose that $\Gamma_1$ and $\Gamma_2$ ; $\Gamma_2$ and $\Gamma_3$ ; $\Gamma_3$ and $\Gamma_4$ ; $\Gamma_4$ and $\Gamma_1$ meet at $A$ , $B$ , $C$ , $D$ , respectively, and that all these points are different from $P$ . Prove that

$\frac{AB\cdot BC}{AD\cdot DC}=\frac{PB^2}{PD^2}.$ Source
Solution

This post has been edited 1 time. Last edited by pro_4_ever, Mar 1, 2018, 10:27 AM

geometry

Inversion

Submit

Hey, what a nice blog!!!!!
by Power_Set, Jun 24, 2018, 9:53 PM
Is your blog dead ? No new post in almost 2 months.

My blog has died due to malnutrition of problems.
by integrated_JRC, May 2, 2018, 5:52 AM
@ below, I will do it soon
by pro_4_ever, Mar 1, 2018, 10:37 AM
Hi, I think we should 'hide' our solutions, as it is difficult to go up and down the blog
by Drunken_Master, Mar 1, 2018, 10:36 AM
Yeah, I created a test blog, it seems to be an AoPS problem not CSS, can't do anything about it. I'll post it in site support forum later.
by Vrangr, Feb 20, 2018, 5:48 AM
The problem is not in the CSS, I believe, as the CSS only looks after the appearance of the blog, and not the $\text{\LaTeX}$ rendering.
by WizardMath, Feb 19, 2018, 11:34 PM
I'll fix the CSS after boards of need be (I'll probably be starting my own blog too then)
by Vrangr, Feb 19, 2018, 4:41 PM
@ below,
Pls ask WizardMath...
The CSS is taken from his amazing Blog, "An Olympiad Journey"...
I know nothing abt programming.
(BTW I got permission for taking the CSS. No Copyright Issues!)
by pro_4_ever, Feb 19, 2018, 4:16 PM
Huge flaw in website design: comment gets erased if while typing $\LaTeX$ has an error and needs to be fixed.
by Vrangr, Feb 19, 2018, 12:26 PM
Upon WizardMath's Request, let us all post synthetic solutions. Well, let's declare that this blog is intended to give the reader some good problems with simple synthetic solutions. All the best. Not trying to be rude,but I might delete upcoming Bashes
by pro_4_ever, Feb 13, 2018, 4:50 PM
Here's an idea. Ban all bashes on this blog from now on. Also try posting your own previous geo solutions as storage (I hope this is allowed). This would make the quality of the blog better. Bashes are basically write-once, read-never things. Why bother?
by WizardMath, Feb 13, 2018, 4:33 PM
Somebody type Egmo 2013 Problem 1.
No bash,purely troll problem.
by QWERTYphysics, Feb 13, 2018, 4:11 PM
I hate having to see a pure geometry blog being swamped to death with bashes.

Obviously a bash is a super terrible idea. Don't do one.
Unless you are bad at synthetic.
by WizardMath, Feb 13, 2018, 2:58 PM
@ayan Done:)
by pro_4_ever, Feb 13, 2018, 1:38 PM
9th shout
by MEGAKNIGHT, Feb 13, 2018, 11:23 AM
@below Pls don't post a bash if you are thinking about posting a new entry!
by pro_4_ever, Feb 13, 2018, 11:11 AM
Wait, I thought bash is frowned upon in this blog.
by WizardMath, Feb 12, 2018, 6:57 PM
Hmmm...
Combi Geometry is accepted...
by pro_4_ever, Feb 10, 2018, 7:32 AM
Can we post Combi here?
by ayan.nmath, Feb 10, 2018, 7:31 AM
Parag dey
by Paragdey12, Feb 6, 2018, 1:17 PM
More posts please
by AnArtist, Feb 6, 2018, 2:38 AM
Second Shout!
by ccx09, Feb 3, 2018, 9:20 PM
1st shout!
by AnArtist, Jan 31, 2018, 9:20 AM