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

G
Topic
First Poster
Last Poster
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:
All classes start 7:30pm ET/4:30pm PT unless otherwise noted.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
Wednesday, Jul 16 - Oct 29
Sunday, Aug 17 - Dec 14
Tuesday, Aug 26 - Dec 16
Friday, Sep 5 - Jan 16
Monday, Sep 8 - Jan 12
Tuesday, Sep 16 - Jan 20 (4:30 - 5:45 pm ET/1:30 - 2:45 pm PT)
Sunday, Sep 21 - Jan 25
Thursday, Sep 25 - Jan 29
Wednesday, Oct 22 - Feb 25
Tuesday, Nov 4 - Mar 10
Friday, Dec 12 - Apr 10

Prealgebra 2 Self-Paced

Prealgebra 2
Friday, Jul 25 - Nov 21
Sunday, Aug 17 - Dec 14
Tuesday, Sep 9 - Jan 13
Thursday, Sep 25 - Jan 29
Sunday, Oct 19 - Feb 22
Monday, Oct 27 - Mar 2
Wednesday, Nov 12 - Mar 18

Introduction to Algebra A Self-Paced

Introduction to Algebra A
Tuesday, Jul 15 - Oct 28
Sunday, Aug 17 - Dec 14
Wednesday, Aug 27 - Dec 17
Friday, Sep 5 - Jan 16
Thursday, Sep 11 - Jan 15
Sunday, Sep 28 - Feb 1
Monday, Oct 6 - Feb 9
Tuesday, Oct 21 - Feb 24
Sunday, Nov 9 - Mar 15
Friday, Dec 5 - Apr 3

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Wednesday, Jul 2 - Sep 17
Sunday, Jul 27 - Oct 19
Monday, Aug 11 - Nov 3
Wednesday, Sep 3 - Nov 19
Sunday, Sep 21 - Dec 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Friday, Oct 3 - Jan 16
Sunday, Oct 19 - Jan 25
Tuesday, Nov 4 - Feb 10
Sunday, Dec 7 - Mar 8

Introduction to Number Theory
Tuesday, Jul 15 - Sep 30
Wednesday, Aug 13 - Oct 29
Friday, Sep 12 - Dec 12
Sunday, Oct 26 - Feb 1
Monday, Dec 1 - Mar 2

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Friday, Jul 18 - Nov 14
Thursday, Aug 7 - Nov 20
Monday, Aug 18 - Dec 15
Sunday, Sep 7 - Jan 11
Thursday, Sep 11 - Jan 15
Wednesday, Sep 24 - Jan 28
Sunday, Oct 26 - Mar 1
Tuesday, Nov 4 - Mar 10
Monday, Dec 1 - Mar 30

Introduction to Geometry
Monday, Jul 14 - Jan 19
Wednesday, Aug 13 - Feb 11
Tuesday, Aug 26 - Feb 24
Sunday, Sep 7 - Mar 8
Thursday, Sep 11 - Mar 12
Wednesday, Sep 24 - Mar 25
Sunday, Oct 26 - Apr 26
Monday, Nov 3 - May 4
Friday, Dec 5 - May 29

Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)
Sat & Sun, Sep 13 - Sep 14 (1:00 - 4:00 PM PT/4:00 - 7:00 PM ET)

Intermediate: Grades 8-12

Intermediate Algebra
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22
Friday, Aug 8 - Feb 20
Tuesday, Aug 26 - Feb 24
Sunday, Sep 28 - Mar 29
Wednesday, Oct 8 - Mar 8
Sunday, Nov 16 - May 17
Thursday, Dec 11 - Jun 4

Intermediate Counting & Probability
Sunday, Sep 28 - Feb 15
Tuesday, Nov 4 - Mar 24

Intermediate Number Theory
Wednesday, Sep 24 - Dec 17

Precalculus
Wednesday, Aug 6 - Jan 21
Tuesday, Sep 9 - Feb 24
Sunday, Sep 21 - Mar 8
Monday, Oct 20 - Apr 6
Sunday, Dec 14 - May 31

Advanced: Grades 9-12

Calculus
Sunday, Sep 7 - Mar 15
Wednesday, Sep 24 - Apr 1
Friday, Nov 14 - May 22

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
Sunday, Aug 17 - Nov 9
Wednesday, Sep 3 - Nov 19
Tuesday, Sep 16 - Dec 9
Sunday, Sep 21 - Dec 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Oct 6 - Jan 12
Thursday, Oct 16 - Jan 22
Tues, Thurs & Sun, Dec 9 - Jan 18 (meets three times a week!)

MATHCOUNTS/AMC 8 Advanced
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
Sunday, Aug 17 - Nov 9
Tuesday, Aug 26 - Nov 11
Thursday, Sep 4 - Nov 20
Friday, Sep 12 - Dec 12
Monday, Sep 15 - Dec 8
Sunday, Oct 5 - Jan 11
Tues, Thurs & Sun, Dec 2 - Jan 11 (meets three times a week!)
Mon, Wed & Fri, Dec 8 - Jan 16 (meets three times a week!)

AMC 10 Problem Series
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
Sunday, Aug 10 - Nov 2
Thursday, Aug 14 - Oct 30
Tuesday, Aug 19 - Nov 4
Mon & Wed, Sep 15 - Oct 22 (meets twice a week!)
Mon, Wed & Fri, Oct 6 - Nov 3 (meets three times a week!)
Tue, Thurs & Sun, Oct 7 - Nov 2 (meets three times a week!)

AMC 10 Final Fives
Friday, Aug 15 - Sep 12
Sunday, Sep 7 - Sep 28
Tuesday, Sep 9 - Sep 30
Monday, Sep 22 - Oct 13
Sunday, Sep 28 - Oct 19 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, Oct 8 - Oct 29
Thursday, Oct 9 - Oct 30

AMC 12 Problem Series
Wednesday, Aug 6 - Oct 22
Sunday, Aug 10 - Nov 2
Monday, Aug 18 - Nov 10
Mon & Wed, Sep 15 - Oct 22 (meets twice a week!)
Tues, Thurs & Sun, Oct 7 - Nov 2 (meets three times a week!)

AMC 12 Final Fives
Thursday, Sep 4 - Sep 25
Sunday, Sep 28 - Oct 19
Tuesday, Oct 7 - Oct 28

AIME Problem Series A
Thursday, Oct 23 - Jan 29

AIME Problem Series B
Tuesday, Sep 2 - Nov 18

F=ma Problem Series
Tuesday, Sep 16 - Dec 9
Friday, Oct 17 - Jan 30

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!


MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT


Programming

Introduction to Programming with Python
Thursday, Aug 14 - Oct 30
Sunday, Sep 7 - Nov 23
Tuesday, Dec 2 - Mar 3

Intermediate Programming with Python
Friday, Oct 3 - Jan 16

USACO Bronze Problem Series
Wednesday, Sep 3 - Dec 3
Thursday, Oct 30 - Feb 5
Tuesday, Dec 2 - Mar 3

Physics

Introduction to Physics
Tuesday, Sep 2 - Nov 18
Sunday, Oct 5 - Jan 11
Wednesday, Dec 10 - Mar 11

Physics 1: Mechanics
Sunday, Sep 21 - Mar 22
Sunday, Oct 26 - Apr 26
0 replies
jwelsh
Jul 1, 2025
0 replies
k i A Letter to MSM
Arr0w   23
N Sep 19, 2022 by scannose
Greetings.

I have seen many posts talking about commonly asked questions, such as finding the value of $0^0$, $\frac{1}{0}$,$\frac{0}{0}$, $\frac{\infty}{\infty}$, why $0.999...=1$ or even expressions of those terms combined as if that would make them defined. I have made this post to answer these questions once and for all, and I politely ask everyone to link this post to threads that are talking about this issue.
[list]
[*]Firstly, the case of $0^0$. It is usually regarded that $0^0=1$, not because this works numerically but because it is convenient to define it this way. You will see the convenience of defining other undefined things later on in this post.

[*]What about $\frac{\infty}{\infty}$? The issue here is that $\infty$ isn't even rigorously defined in this expression. What exactly do we mean by $\infty$? Unless the example in question is put in context in a formal manner, then we say that $\frac{\infty}{\infty}$ is meaningless.

[*]What about $\frac{1}{0}$? Suppose that $x=\frac{1}{0}$. Then we would have $x\cdot 0=0=1$, absurd. A more rigorous treatment of the idea is that $\lim_{x\to0}\frac{1}{x}$ does not exist in the first place, although you will see why in a calculus course. So the point is that $\frac{1}{0}$ is undefined.

[*]What about if $0.99999...=1$? An article from brilliant has a good explanation. Alternatively, you can just use a geometric series. Notice that
\begin{align*}
\sum_{n=1}^{\infty} \frac{9}{10^n}&=9\sum_{n=1}^{\infty}\frac{1}{10^n}=9\sum_{n=1}^{\infty}\biggr(\frac{1}{10}\biggr)^n=9\biggr(\frac{\frac{1}{10}}{1-\frac{1}{10}}\biggr)=9\biggr(\frac{\frac{1}{10}}{\frac{9}{10}}\biggr)=9\biggr(\frac{1}{9}\biggr)=\boxed{1}
\end{align*}
[*]What about $\frac{0}{0}$? Usually this is considered to be an indeterminate form, but I would also wager that this is also undefined.
[/list]
Hopefully all of these issues and their corollaries are finally put to rest. Cheers.

2nd EDIT (6/14/22): Since I originally posted this, it has since blown up so I will try to add additional information per the request of users in the thread below.

INDETERMINATE VS UNDEFINED

What makes something indeterminate? As you can see above, there are many things that are indeterminate. While definitions might vary slightly, it is the consensus that the following definition holds: A mathematical expression is be said to be indeterminate if it is not definitively or precisely determined. So how does this make, say, something like $0/0$ indeterminate? In analysis (the theory behind calculus and beyond), limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits. However, if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. For example, we could say that $0/0$ is an indeterminate form.

But we need to more specific, this is still ambiguous. An indeterminate form is a mathematical expression involving at most two of $0$, $1$ or $\infty$, obtained by applying the algebraic limit theorem (a theorem in analysis, look this up for details) in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being calculated. This is why it is called indeterminate. Some examples of indeterminate forms are
\[0/0, \infty/\infty, \infty-\infty, \infty \times 0\]etc etc. So what makes something undefined? In the broader scope, something being undefined refers to an expression which is not assigned an interpretation or a value. A function is said to be undefined for points outside its domain. For example, the function $f:\mathbb{R}^{+}\cup\{0\}\rightarrow\mathbb{R}$ given by the mapping $x\mapsto \sqrt{x}$ is undefined for $x<0$. On the other hand, $1/0$ is undefined because dividing by $0$ is not defined in arithmetic by definition. In other words, something is undefined when it is not defined in some mathematical context.

WHEN THE WATERS GET MUDDIED

So with this notion of indeterminate and undefined, things get convoluted. First of all, just because something is indeterminate does not mean it is not undefined. For example $0/0$ is considered both indeterminate and undefined (but in the context of a limit then it is considered in indeterminate form). Additionally, this notion of something being undefined also means that we can define it in some way. To rephrase, this means that technically, we can make something that is undefined to something that is defined as long as we define it. I'll show you what I mean.

One example of making something undefined into something defined is the extended real number line, which we define as
\[\overline{\mathbb{R}}=\mathbb{R}\cup \{-\infty,+\infty\}.\]So instead of treating infinity as an idea, we define infinity (positively and negatively, mind you) as actual numbers in the reals. The advantage of doing this is for two reasons. The first is because we can turn this thing into a totally ordered set. Specifically, we can let $-\infty\le a\le \infty$ for each $a\in\overline{\mathbb{R}}$ which means that via this order topology each subset has an infimum and supremum and $\overline{\mathbb{R}}$ is therefore compact. While this is nice from an analytic standpoint, extending the reals in this way can allow for interesting arithmetic! In $\overline{\mathbb{R}}$ it is perfectly OK to say that,
\begin{align*}
a + \infty = \infty + a & = \infty, & a & \neq -\infty \\
a - \infty = -\infty + a & = -\infty, & a & \neq \infty \\
a \cdot (\pm\infty) = \pm\infty \cdot a & = \pm\infty, & a & \in (0, +\infty] \\
a \cdot (\pm\infty) = \pm\infty \cdot a & = \mp\infty, & a & \in [-\infty, 0) \\
\frac{a}{\pm\infty} & = 0, & a & \in \mathbb{R} \\
\frac{\pm\infty}{a} & = \pm\infty, & a & \in (0, +\infty) \\
\frac{\pm\infty}{a} & = \mp\infty, & a & \in (-\infty, 0).
\end{align*}So addition, multiplication, and division are all defined nicely. However, notice that we have some indeterminate forms here which are also undefined,
\[\infty-\infty,\frac{\pm\infty}{\pm\infty},\frac{\pm\infty}{0},0\cdot \pm\infty.\]So while we define certain things, we also left others undefined/indeterminate in the process! However, in the context of measure theory it is common to define $\infty \times 0=0$ as greenturtle3141 noted below. I encourage to reread what he wrote, it's great stuff! As you may notice, though, dividing by $0$ is undefined still! Is there a place where it isn't? Kind of. To do this, we can extend the complex numbers! More formally, we can define this extension as
\[\mathbb{C}^*=\mathbb{C}\cup\{\tilde{\infty}\}\]which we call the Riemann Sphere (it actually forms a sphere, pretty cool right?). As a note, $\tilde{\infty}$ means complex infinity, since we are in the complex plane now. Here's the catch: division by $0$ is allowed here! In fact, we have
\[\frac{z}{0}=\tilde{\infty},\frac{z}{\tilde{\infty}}=0.\]where $\tilde{\infty}/\tilde{\infty}$ and $0/0$ are left undefined. We also have
\begin{align*}
z+\tilde{\infty}=\tilde{\infty}, \forall z\ne -\infty\\
z\times \tilde{\infty}=\tilde{\infty}, \forall z\ne 0
\end{align*}Furthermore, we actually have some nice properties with multiplication that we didn't have before. In $\mathbb{C}^*$ it holds that
\[\tilde{\infty}\times \tilde{\infty}=\tilde{\infty}\]but $\tilde{\infty}-\tilde{\infty}$ and $0\times \tilde{\infty}$ are left as undefined (unless there is an explicit need to change that somehow). One could define the projectively extended reals as we did with $\mathbb{C}^*$, by defining them as
\[{\widehat {\mathbb {R} }}=\mathbb {R} \cup \{\infty \}.\]They behave in a similar way to the Riemann Sphere, with division by $0$ also being allowed with the same indeterminate forms (in addition to some other ones).
23 replies
Arr0w
Feb 11, 2022
scannose
Sep 19, 2022
k i Marathon Threads
LauraZed   0
Jul 2, 2019
Due to excessive spam and inappropriate posts, we have locked the Prealgebra and Beginning Algebra threads.

We will either unlock these threads once we've cleaned them up or start new ones, but for now, do not start new marathon threads for these subjects. Any new marathon threads started while this announcement is up will be immediately deleted.
0 replies
LauraZed
Jul 2, 2019
0 replies
k i Basic Forum Rules and Info (Read before posting)
jellymoop   368
N May 16, 2018 by harry1234
f (Reminder: Do not post Alcumus or class homework questions on this forum. Instructions below.) f
Welcome to the Middle School Math Forum! Please take a moment to familiarize yourself with the rules.

Overview:
[list]
[*] When you're posting a new topic with a math problem, give the topic a detailed title that includes the subject of the problem (not just "easy problem" or "nice problem")
[*] Stay on topic and be courteous.
[*] Hide solutions!
[*] If you see an inappropriate post in this forum, simply report the post and a moderator will deal with it. Don't make your own post telling people they're not following the rules - that usually just makes the issue worse.
[*] When you post a question that you need help solving, post what you've attempted so far and not just the question. We are here to learn from each other, not to do your homework. :P
[*] Avoid making posts just to thank someone - you can use the upvote function instead
[*] Don't make a new reply just to repeat yourself or comment on the quality of others' posts; instead, post when you have a new insight or question. You can also edit your post if it's the most recent and you want to add more information.
[*] Avoid bumping old posts.
[*] Use GameBot to post alcumus questions.
[*] If you need general MATHCOUNTS/math competition advice, check out the threads below.
[*] Don't post other users' real names.
[*] Advertisements are not allowed. You can advertise your forum on your profile with a link, on your blog, and on user-created forums that permit forum advertisements.
[/list]

Here are links to more detailed versions of the rules. These are from the older forums, so you can overlook "Classroom math/Competition math only" instructions.
Posting Guidelines
Update on Basic Forum Rules
What belongs on this forum?
How do I write a thorough solution?
How do I get a problem on the contest page?
How do I study for mathcounts?
Mathcounts FAQ and resources
Mathcounts and how to learn

As always, if you have any questions, you can PM me or any of the other Middle School Moderators. Once again, if you see spam, it would help a lot if you filed a report instead of responding :)

Marathons!
Relays might be a better way to describe it, but these threads definitely go the distance! One person starts off by posting a problem, and the next person comes up with a solution and a new problem for another user to solve. Here's some of the frequently active marathons running in this forum:
[list][*]Algebra
[*]Prealgebra
[*]Proofs
[*]Factoring
[*]Geometry
[*]Counting & Probability
[*]Number Theory[/list]
Some of these haven't received attention in a while, but these are the main ones for their respective subjects. Rather than starting a new marathon, please give the existing ones a shot first.

You can also view marathons via the Marathon tag.

Think this list is incomplete or needs changes? Let the mods know and we'll take a look.
368 replies
jellymoop
May 8, 2015
harry1234
May 16, 2018
Grandi Series is weird??
sadas123   7
N 4 hours ago by Not__Infinity
I was just watching this video and I kinda understood what they were saying they said:

$1-1+1-1+1-1+1-1 .... = \frac{1}{2}$

so at first I thought that = 0

but then I realized that if you give an variable such that:

$x= 1-1+1-1+1-1 .....$
then you get
$x = 1-x$
isolating x you get that
$2x = 1$
so
$x= \frac{1}{2}$

is there a way to get the definite answer because I am still confused.
7 replies
sadas123
Today at 12:52 AM
Not__Infinity
4 hours ago
9 zeroes!.
ericheathclifffry   50
N 5 hours ago by tigresstc
Redacted
50 replies
ericheathclifffry
May 5, 2025
tigresstc
5 hours ago
Creative Geometry Problem
giratina3   4
N 6 hours ago by cheltstudent
Let there be a triangle ABC. Let BX bisect CBA, CY bisect ACB, and XY parallel to BC. If AB = 12, BC = 24, and AC = 18, then what is the perimeter of the triangle AXY?

The hint gives away most of the problem, so make sure you consider the problem for a long time before reading it :thumbup:

(The answer is an integer to you coordinate bashers :play_ball:)

Hint
4 replies
giratina3
Yesterday at 8:10 PM
cheltstudent
6 hours ago
Worst math problems
LXC007   94
N Today at 2:58 AM by cheltstudent
What is the most egregiously bad problem or solution you have encountered in school?
94 replies
LXC007
May 21, 2025
cheltstudent
Today at 2:58 AM
AIME p7???
Soupboy0   9
N Today at 2:33 AM by giratina3
how the heck is this p7


Let $x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}$. Find $(x+1)^{48}$.

source: 2005 AIME II p7
9 replies
Soupboy0
Yesterday at 3:40 AM
giratina3
Today at 2:33 AM
9 Favorite topic
A7456321   230
N Today at 2:28 AM by mpcnotnpc
What is your favorite math topic/subject?

If you don't know why you are here, go binge watch something!

If you forgot why you are here, go to a hospital! :)

If you know why you are here and have voted, maybe say why you picked the option that you picked in a response) :thumbup:

CLICK ON ME YOU KNOW YOU WANT TO

Timeline
230 replies
A7456321
May 23, 2025
mpcnotnpc
Today at 2:28 AM
Private Forum for Geometry Study
fossasor   234
N Today at 2:07 AM by Serenah329
Hi all,

I've recently been trying to improve my skill at competition math, but I consistently struggle with geometry. Since doing math is more fun and motivating with others, I've created the GeoPrepClub. This is a private forum to increase geometry skill and help others increase theirs: we'll have problems, marathons, and much more. This is similar to forums such as "AMC8 Prep Buddies" by PatTheKing, but is focused exclusively on this subject. We welcome all skill levels and hope those with greater mathematical knowledge can assist those lacking in it.

If this sounds interesting to you, sing up below and I'll let you know once I've added you. Although the forum may not have much now, that's because I've only just released it, and I hope once I build a community, It will be a very useful and motivating space for those interested in improving their geometry. The link is
here.

I look forward to seeing you all in the forum!
234 replies
fossasor
Jun 10, 2025
Serenah329
Today at 2:07 AM
Bogus Proof Marathon
pifinity   7732
N Today at 2:06 AM by melloncandy
Hi!
I'd like to introduce the Bogus Proof Marathon.

In this marathon, simply post a bogus proof that is middle-school level and the next person will find the error. You don't have to post the real solution :P

Use classic Marathon format:
[hide=P#]a1b2c3[/hide]
[hide=S#]a1b2c3[/hide]


Example posts:

P(x)
-----
S(x)
P(x+1)
-----
Let's go!! Just don't make it too hard!
7732 replies
pifinity
Mar 12, 2018
melloncandy
Today at 2:06 AM
Puzzles for Fun!!!
Yoonyoung11   21
N Today at 2:04 AM by DynamicFox52
IF YOU SOLVE ONE, ADD ANOTHER ONE PLS:
1)There are three colored boxes: Yellow, Black, and Orange. Each box contains 2 envelopes. Each envelope contains cash - two of them contain Rs. 250000 each, two of them contain Rs. 150000 each, and the remaining two contain Rs. 100000 each.
There is one statement written on the cover of each box.
* Yellow Box: Both a yellow box and an orange box contain Rs. 100000 each.
* Black Box: Both a black box and a yellow box contain Rs. 250000 each.
* Orange Box: Both an orange box and a black box contain Rs. 150000 each.
Only one of the above 3 statements is true, and the corresponding box contains the maximum amount.
Can you tell which box contains the maximum amount and how much?
2)Stranded on a deserted island, Harry Puttar is left with only a 40 litres container of milk. To conserve his milk he decides that on the first day he will drink one litre of milk and then refill the container back up with water. On the 2nd day he will drink 2 litres and refill the container. On the 3rd day he will drink 3 litres and so on... By the time all the milk is gone, how much water has he drunk?
21 replies
Yoonyoung11
Jun 29, 2025
DynamicFox52
Today at 2:04 AM
Foil
Silverfalcon   29
N Today at 1:54 AM by booking
$(1+x^2)(1-x^3)$ equals

$ \text{(A)}\ 1 - x^5\qquad\text{(B)}\ 1 - x^6\qquad\text{(C)}\ 1+ x^2 -x^3\qquad \\ \text{(D)}\ 1+x^2-x^3-x^5\qquad \text{(E)}\ 1+x^2-x^3-x^6 $
29 replies
Silverfalcon
Oct 21, 2005
booking
Today at 1:54 AM
Exponent of 1 and -1
Silverfalcon   31
N Today at 12:13 AM by melloncandy
$(-1)^{5^2} + 1^{2^5} =$

$\textbf{(A)}\ -7 \qquad
\textbf{(B)}\ -2 \qquad
\textbf{(C)}\ 0 \qquad
\textbf{(D)}\ 1 \qquad
\textbf{(E)}\ 57$
31 replies
Silverfalcon
Oct 22, 2005
melloncandy
Today at 12:13 AM
9 Square roots
A7456321   34
N Yesterday at 10:27 PM by A7456321
Me personally I only have $\sqrt2=1.414$ memorized but I'm sure there are people out there with more!
update: i recently learned $\sqrt3=1.732$

CLICK ON ME YOU KNOW YOU WANT TO
34 replies
A7456321
May 29, 2025
A7456321
Yesterday at 10:27 PM
Troll Problem
giratina3   12
N Yesterday at 10:06 PM by ManolidisS
If $\frac{a}{a - 1} = \frac{b^2 + 2b - 1}{b^2 + 2b - 2}$, then what does $a$ equal in terms of $b$?

Hint 1
Hint 2
Hint 3
12 replies
giratina3
Friday at 8:28 PM
ManolidisS
Yesterday at 10:06 PM
The 24 Game, but with a twist!
PikaPika999   280
N Yesterday at 7:34 PM by PreciseScorpion58
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!
280 replies
PikaPika999
Jul 1, 2025
PreciseScorpion58
Yesterday at 7:34 PM
Last challenge problems in the books
ysn613   20
N Jul 7, 2025 by Quadratic_rush
Algebra
It is known that $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}\dots=\frac{\pi^2}{6}$ Given this fact, determine the exact value of $$\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}\dots.$$(Source: Mandelbrot)
Counting and Probability
A $3\times3\times3$ wooden cube is painted on all six faces, then cut into 27 unit cubes. One unit cube is randomly selected and rolled. After it is rolled, $5$ out of the $6$ faces are visible. What is the probability that exactly one of the five visible faces is painted? (Source: MATHCOUNTS)
Number Theory(This technically isn't the last problem but the last chapter doesn't have challenge problems)
The integer p is a 50-digit prime number. When its square is divided by 120, the remainder is not 1. What is the remainder?
I didn't include geometry because I haven't taken it yet, feel free to post it
Answer these problems and post what you think is the order of difficulty
20 replies
ysn613
May 26, 2025
Quadratic_rush
Jul 7, 2025
Last challenge problems in the books
G H J
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ysn613
119 posts
#1 • 1 Y
Y by PikaPika999
Algebra
It is known that $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}\dots=\frac{\pi^2}{6}$ Given this fact, determine the exact value of $$\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}\dots.$$(Source: Mandelbrot)
Counting and Probability
A $3\times3\times3$ wooden cube is painted on all six faces, then cut into 27 unit cubes. One unit cube is randomly selected and rolled. After it is rolled, $5$ out of the $6$ faces are visible. What is the probability that exactly one of the five visible faces is painted? (Source: MATHCOUNTS)
Number Theory(This technically isn't the last problem but the last chapter doesn't have challenge problems)
The integer p is a 50-digit prime number. When its square is divided by 120, the remainder is not 1. What is the remainder?
I didn't include geometry because I haven't taken it yet, feel free to post it
Answer these problems and post what you think is the order of difficulty
This post has been edited 1 time. Last edited by ysn613, May 26, 2025, 7:06 PM
Reason: h
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
CuriousMathBoy72
887 posts
#2 • 1 Y
Y by PikaPika999
for algebra that was really easy, pretty obv pattern anyway
c&p also easy just casework bash works
NT i sold that class i dont know how to solve it
easiest to hardest
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Math-lover1
441 posts
#3 • 1 Y
Y by PikaPika999
algebra sol
This post has been edited 1 time. Last edited by Math-lover1, May 26, 2025, 8:19 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Andyluo
1058 posts
#4 • 3 Y
Y by aidan0626, jkim0656, PikaPika999
My 1000th Post!

p1

p2

p3

Question 3 is easily the hardest, question 1 is more "difficult" theory wise, but faster if you know the idea. Question 2 is very standard casework. Me personally, 3>2>1.

I find it funny that I used to find these questions hard...
This post has been edited 2 times. Last edited by Andyluo, May 26, 2025, 8:23 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Bummer12345
188 posts
#5 • 1 Y
Y by PikaPika999
nt sol
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ysn613
119 posts
#6 • 1 Y
Y by PikaPika999
I also think number theory was by far the hardest, but I think algebra actually is harder than counting and probability(less standard method, takes special manipulation to avoid infinite series)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Math-lover1
441 posts
#7 • 1 Y
Y by PikaPika999
Andyluo wrote:
I find it funny that I used to find these questions hard...

admits
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
lavender_cloud
24 posts
#8 • 1 Y
Y by PikaPika999
Math-lover1 wrote:
Andyluo wrote:
I find it funny that I used to find these questions hard...

admits

imao. lol. (caught in 4k)
This post has been edited 1 time. Last edited by lavender_cloud, May 26, 2025, 9:29 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
elizhang101412
1371 posts
#9 • 1 Y
Y by PikaPika999
ysn613 wrote:
I also think number theory was by far the hardest, but I think algebra actually is harder than counting and probability(less standard method, takes special manipulation to avoid infinite series)

bruh what
alg is literally just divide by 4 and subtract from original sum
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Li0nking
7 posts
#10 • 1 Y
Y by PikaPika999
This is not middle school problem!
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
mdk2013
666 posts
#11 • 1 Y
Y by PikaPika999
i genuinely cannot believe that i was once struggling to solve p1, ah ive grown in my math so much
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
lavender_cloud
24 posts
#12 • 1 Y
Y by PikaPika999
Li0nking wrote:
This is not middle school problem!

fr
elizhang101412 wrote:
ysn613 wrote:
I also think number theory was by far the hardest, but I think algebra actually is harder than counting and probability(less standard method, takes special manipulation to avoid infinite series)

bruh what
alg is literally just divide by 4 and subtract from original sum

truuu
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ZMB038
444 posts
#13 • 1 Y
Y by PikaPika999
P1 is so easy it's funny
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
valenbb
806 posts
#14 • 1 Y
Y by PikaPika999
Here are some more:
Precalc: Triangle ABC is isosceles with $AB=AC$ and $BC=1$. $D$ is on $\overline{AB}$ such that $AD=1$ and $\angle DAC=\frac\pi 7.$ Find $CD.$



Intro to Geo: Diagonals $\overline{AC}$ and $\overline{BD}$ of regular heptagon $ABCDEFG$ meet at $X$. Prove that $AB+AX=AD.$
That is a problem from the proofs section so i'll post a non proof one:
Four balls of radius $1$ are all tangent to each other. What is the radius of the smallest sphere that can enclose all of the balls?


Prealgebra: Five married couples get together at a party. At the start of the party, each person shakes hands with everyone they didn't know at the beginning of the party. After all of the handshakes, Kyle, one of the husband, asks everyone else how many hands they shook. He received each number from $0$ to $8$ as an answer once. How many hands did Kyle shake?


Inter Alg: (Source: AIME) Determine $x^2+y^2+z^2+w^2$ given $$\frac{x^2}{2^2-1^2}+\frac{y^2}{2^2-3^2}+\frac{z^2}{2^2-5^2}+\frac{w^2}{2^2-7^2}=1,$$$$\frac{x^2}{4^2-1^2}+\frac{y^2}{4^2-3^2}+\frac{z^2}{4^2-5^2}+\frac{w^2}{4^2-7^2}=1,$$$$\frac{x^2}{6^2-1^2}+\frac{y^2}{6^2-3^2}+\frac{z^2}{6^2-5^2}+\frac{w^2}{6^2-7^2}=1,$$$$\frac{x^2}{8^2-1^2}+\frac{y^2}{8^2-3^2}+\frac{z^2}{8^2-5^2}+\frac{w^2}{8^2-7^2}=1.$$

My 7th grade math textbook :rotfl:: A spinner has 5 equals sections. 2 are colored red, 2 are colored blue, and the other is colored yellow. What is the probability of spinning and landing on a blue section, then spinning again and landing on a yellow section?
This post has been edited 1 time. Last edited by valenbb, May 30, 2025, 12:24 AM
Reason: bug
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
jb2015007
2035 posts
#15
Y by
valenbb wrote:
Here are some more:
Precalc: Triangle ABC is isosceles with $AB=AC$ and $BC=1$. $D$ is on $\overline{AB}$ such that $AD=1$ and $\angle DAC=\frac\pi 7.$ Find $CD.$



Intro to Geo: Diagonals $\overline{AC}$ and $\overline{BD}$ of regular heptagon $ABCDEFG$ meet at $X$. Prove that $AB+AX=AD.$
That is a problem from the proofs section so i'll post a non proof one:
Four balls of radius $1$ are all tangent to each other. What is the radius of the smallest sphere that can enclose all of the balls?


Prealgebra: Five married couples get together at a party. At the start of the party, each person shakes hands with everyone they didn't know at the beginning of the party. After all of the handshakes, Kyle, one of the husband, asks everyone else how many hands they shook. He received each number from $0$ to $8$ as an answer once. How many hands did Kyle shake?


Inter Alg: (Source: AIME) Determine $x^2+y^2+z^2+w^2$ given $$\frac{x^2}{2^2-1^2}+\frac{y^2}{2^2-3^2}+\frac{z^2}{2^2-5^2}+\frac{w^2}{2^2-7^2}=1,$$$$\frac{x^2}{4^2-1^2}+\frac{y^2}{4^2-3^2}+\frac{z^2}{4^2-5^2}+\frac{w^2}{4^2-7^2}=1,$$$$\frac{x^2}{6^2-1^2}+\frac{y^2}{6^2-3^2}+\frac{z^2}{6^2-5^2}+\frac{w^2}{6^2-7^2}=1,$$$$\frac{x^2}{8^2-1^2}+\frac{y^2}{8^2-3^2}+\frac{z^2}{8^2-5^2}+\frac{w^2}{8^2-7^2}=1.$$

My 7th grade math textbook :rotfl:: A spinner has 5 equals sections. 2 are colored red, 2 are colored blue, and the other is colored yellow. What is the probability of spinning and landing on a blue section, then spinning again and landing on a yellow section?

My 8th grade textbook: Triangle $ABC$ has side lengths of $x,12,$ and $15.$ Find the perimeter of the triangle (pretty easy lol)

Bruh u js took the last problem from int alg bruh lol def not hardest imo
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
iwastedmyusername
223 posts
#16
Y by
how is the 8th grade textbook one easy, there are infinite different answers
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
valenbb
806 posts
#17
Y by
iwastedmyusername wrote:
how is the 8th grade textbook one easy, there are infinite different answers

oh my fault, i forgot to say. It states that $x$ is the shortest side length
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
elizhang101412
1371 posts
#18
Y by
valenbb wrote:
iwastedmyusername wrote:
how is the 8th grade textbook one easy, there are infinite different answers

oh my fault, i forgot to say. It states that $x$ is the shortest side length

still infinite answers
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
valenbb
806 posts
#19
Y by
wait i'm stupid. it's a right triangle
sorry, i'm bugging js forget the problem
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
CJB19
178 posts
#20
Y by
Oh so it's just 9 right
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Quadratic_rush
7 posts
#21
Y by
answer:pi/8
Z K Y
N Quick Reply
G
H
=
a