Three variable equations

by gpen1000, Mar 21, 2025, 1:55 PM

1. For integers $x$ , $y$ , and $z$ such that $\frac{\sqrt{x}}{\sqrt{y}} = z$ , find $\frac{\sqrt{z}}{\sqrt{x}}$ in terms of $x$ , $y$ , and $z$ .

2. For integers $x$ , $y$ , and $z$ such that $x = y - 1$ and $z = y + 1$ , prove that $y^3 = xyz + y$ .

three variables

variables

algebra

Basic Maths

by JetFire008, Mar 21, 2025, 1:19 PM

Find $x$ : $\sqrt{9}x=18$

This post has been edited 1 time. Last edited by JetFire008, 2 hours ago
Reason: LaTeX error

square roots

Basic maths

Mathcounts STRATEGIES

by Existing_Human1, Mar 20, 2025, 7:27 PM

Hello commuinty!

I am wondering what your strategies are for mathcounts. Please note I do not mean tips. These can be for all rounds, but please specify. BTW, this is for state, but it can apply to any competition.

Ex:
Team - sit in a specific order
Target - do the easiest first
Sprint - go as fast as possible

I just made up the examples, and you will probably have better strategies, so if you want to help out, please do

MATHCOUNTS

a problem

by Bummer12345, Mar 19, 2025, 8:00 PM

Alice and Bob play a game where Alice starts with $3$ MathJuice bottles and Bob starts with $2$ MathJuice bottles. An unfair coin is then flipped, with probability $\frac{2}{3}$ of landing heads. If the coin lands heads, Alice gives Bob a bottle; otherwise, Bob gives Alice a bottle. This process repeats until someone runs out of bottles.

(a): What is the probability that Bob will lose all of his bottles before Alice does?
(b): What is the expected number of times the coin has been flipped by the time the game ends?

Source: Own

This post has been edited 1 time. Last edited by Bummer12345, Yesterday at 1:49 AM

probability

expected value

How important is math "intuition"

by Dream9, Mar 19, 2025, 2:16 PM

When I see problems now, they usually fall under 3 categories: easy, annoying, and cannot solve. Over time, more problems become easy, but I don't think I'm learning anything "new" so is higher level math like AMC 10 more about practice, so you know what to do when you see a problem? Of course, there's formulas for some problems but when reading a lot of solutions I didn't see many weird formulas being used and it was just the way to solve the problem was "odd".

AMC 10

Why was this poll blocked

by jkim0656, Mar 18, 2025, 10:51 PM

Hey AoPS ppl!
I made a poll about Pi vs Tau over here:
https://artofproblemsolving.com/community/c3h3527460
But after a few days it got blocked but i don't get why?
how is this harmful or different from other polls?
It really wasn't that harmful or popular i got to say tho... :noo:

This post has been edited 1 time. Last edited by jkim0656, Mar 18, 2025, 10:51 PM

poll

state mathcounts colorado

by aoh11, Mar 15, 2025, 12:20 AM

I have state mathcounts tomorrow. What should I do to get prepared btw, and what are some tips for doing sprint and cdr?

MATHCOUNTS

MC nationals 2023 sprint Q28

by Soupboy0, Mar 12, 2025, 9:46 PM

What common fraction is equivalent to the expression shown?

$\frac{\frac{1}{2021 \cdot 2022} + \frac{2}{2019 \cdot 2021} + \frac{3}{2017 \cdot 2020} + ... + \frac{1010}{3 \cdot 1013} + \frac{1011}{1 \cdot 1012}}{\frac{2022}{1011}+\frac{2022}{1010}+\frac{2022}{1009}+...+\frac{2022}{2}+\frac{2022}{1}}$ ?

can someone please help me

This post has been edited 1 time. Last edited by Soupboy0, Mar 12, 2025, 9:47 PM

murder drones

is this a Maxwell reference

MATHCOUNTS on ESPN

by rrusczyk, May 27, 2003, 11:14 PM

ESPN noon EST - the Countdown round of Nationals.

(Disclaimer: yours truly is an 'analyst' for the broadcast.)

MATHCOUNTS

squares in dots - MATHCOUNTS challenge problem

by rrusczyk, May 27, 2003, 4:59 PM

. . . . .
. . . . .
. . . . .
. . . . .

(That should be a 4x5 grid of dots.) Assuming each point is exactly one unit from its nearest neighbors, how many squares can be formed by connecting groups of four points?

MATHCOUNTS

Submit

The blog is locked right?
by First, Apr 14, 2018, 6:00 PM
Great, amazing, inspiring blog. Good luck in life, and just know I aspire to succeed as you will in the future.
by mgrimalo, Apr 7, 2018, 6:19 PM
Yesyesyes
by shiningsunnyday, Mar 29, 2018, 5:30 PM
:O a new background picture
by MathAwesome123, Mar 29, 2018, 3:39 PM
did you get into MIT?
by 15Pandabears, Mar 15, 2018, 10:42 PM
wait what new site?
by yegkatie, Feb 11, 2018, 1:49 AM
Yea, doing a bit of cleaning before migrating to new site
by shiningsunnyday, Jan 21, 2018, 2:43 PM
Were there posts made in December 2017 for this blog and then deleted?

I ask because I was purging my thunderbird inbox and I found emails indicating new blog posts of yours.

email do not lie
by jonlin1000, Jan 21, 2018, 12:12 AM
@below sorry not accepting contribs
by shiningsunnyday, Dec 11, 2017, 11:15 AM
contrib plez?
also wow this blog is very popular
by DavidUsa, Dec 10, 2017, 7:53 PM
@First: lol same

first shout of december
by coolmath34, Dec 6, 2017, 2:32 PM
XD this blog is hilarious
by Mitsuku, Nov 21, 2017, 7:40 PM
@wu2481632: stop encouraging SSD to procrastinate(blog entries are fun but procrastination isn't).
by First, Aug 7, 2017, 5:02 PM
3.5 weeks without a post
by Flash12, Aug 4, 2017, 8:10 AM
First august shout!!
by adik7, Aug 1, 2017, 6:52 AM
"Also, I figured that whenever"

Darn, whenever what?

Belated (oops sorry) well-wishes on the 2016 AMC10A!
by DeathLlama9, Feb 3, 2016, 3:23 AM
what is a 8char?
lol 8char
by whiteawesomesun, Jan 30, 2016, 9:43 AM
lol 8char
by chocopuff, Jan 30, 2016, 3:38 AM
yadayadayadayadayadayada amc 10 is near... hope you get into JMO...
by whiteawesomesun, Jan 30, 2016, 2:45 AM
so much hype and stress!
by chocopuff, Jan 29, 2016, 2:14 PM
Lol lets reconcile man
by Konigsberg, Jan 20, 2016, 11:36 PM
DUDUUDDUDUUDE STAPHHHHH. war? war? TF boys
by whiteawesomesun, Jan 19, 2016, 8:50 AM
dude dude stop stop war war
by Konigsberg, Jan 18, 2016, 3:44 AM
I'm excited!
by paperplates, Jan 15, 2016, 6:55 AM
nice! \8char
by adihaya, Jan 14, 2016, 6:47 AM
yay, looks like this is going to be a cool blog!
by jh235, Jan 7, 2016, 8:15 PM
Post something!
by whiteawesomesun, Jan 4, 2016, 3:54 PM
at least I claim second shot
by Kline, Dec 29, 2015, 1:45 AM
first shout >
by oceanair, Dec 28, 2015, 6:00 AM

416 shouts

SSD's Musings and Dreams

by gpen1000, Mar 21, 2025, 1:55 PM

by JetFire008, Mar 21, 2025, 1:19 PM

by Existing_Human1, Mar 20, 2025, 7:27 PM

by Bummer12345, Mar 19, 2025, 8:00 PM

by Dream9, Mar 19, 2025, 2:16 PM

by jkim0656, Mar 18, 2025, 10:51 PM

by aoh11, Mar 15, 2025, 12:20 AM

by Soupboy0, Mar 12, 2025, 9:46 PM

by rrusczyk, May 27, 2003, 11:14 PM

by rrusczyk, May 27, 2003, 4:59 PM