[/quote]
,
,
be the circumcenter and 
the orthocenter of an acute triangle 
Prove that the area of one of the triangles 
and 
is equal to the sum of the areas of the other two.
with any line through the centroid 
and I have no clue as to why that is true. Plz help
be positive integers, and define![\[ n = a + b + c + d + e + f. \]](http://latex.artofproblemsolving.com/9/d/d/9ddfecfa5800050bc15dcaa48d17d12e431fc358.png)
Suppose that 
divides both of the following expressions:![\[
abc + def \quad \text{and} \quad ab + bc + ca - de - ef - fd.
\]](http://latex.artofproblemsolving.com/c/5/8/c5817937f736a7b00c85e1f92b8e561ba26cf8b0.png)
Prove that 
be a triangle with orthocentre 
be the foot of altitudes of 
onto the opposite sides, respectively. Consider 
,
about line 
.
cut 
,
be the orthocenter of 
.
are concyclic.
is called 
if there exists a permutation 
of the numbers 
,
and 
have different parities for every 
;
the sum 
is a quadratic residue modulo 
for every 
.
compute the smallest possible value of ![\[\sum_{k=1}^{n}\left\lfloor\frac{a_k}{k}\right\rfloor\]](http://latex.artofproblemsolving.com/5/6/2/562c27c7779285b6439c4087f52933a41f29ee2e.png)
over all permutations 
of 
such that 
is chosen on the side 
of a triangle 
in such a way that 
.
and 
and 
,
be the incenter of triangle 
.
intersects the line segment 
at its midpoint.
be an integer. We call a pair of integers 
g![\[0\leqslant a<k,\hspace{0.2cm} 0<b \hspace{1cm} \text{and} \hspace{1cm} (a+b)^2=ka+b\]](http://latex.artofproblemsolving.com/e/8/d/e8df562e024b8476d69fdaea15338c27bb6c4eb8.png)
Prove that the number of 
.
be an equilateral triangle with incircle 
.
.
Y by Iamawesome1, dragon78, Math-Ninja, legolover2018, foxtrot3, wlm7, juked, YJG, sudzoof, asterix_1, mathisgreat247, j3370, lakeway224, green517, Mathnerd1223334444, RishabP, Krypton36, Devastator, avaaops, jlordhe, pianoman24, mathlogician, problemwizard123, OlympusHero, Adventure10, Mango247
Recently, over the past couple of weeks, I've seen a bunch of math marathons, and other silly math games being posted. These spammy actions are clogging up the forum. Posting in a copy marathon: "Ughh another marathon" actually spams it more! I'm going to dive deeper in reasons why people do things like this, and how to remove them. I have some experience, as I used to do this.
Before you read on, this is where all of the marathons went.
1. They need more attention.
This one is not very common, so I'm going to get it out of the way first. If a user is new, and doesn't get what the community is for, he/she will start posting polls and marathons to catch attention, or to get upvotes...
2. Upvotes.
Upon seeing successful marathons like the 24 math game, people will want to get upvotes. (By the way, the 24 game is >50 upvotes, so it will be natural to do this)
3. Ignorance.
I'm hoping this is the most common. Some people might not even know that they shouldn't post them! In this case, a nice PM or post should be fine.
4. Pure trolls.
Now these are the types of people that post to
i. Get attention
ii. Be mean
iii. Clog up the forum
We need to report these types of posts.
How to fix these problems:
If you know a user that is nice, never trolls, and starts posting these polls on MSM, then PM them, and ask them why they did this. If you don't know them, and it is one of their first posts, then they either will be new/ignorant, or they are multis/trolls. If you realize the person knows an awful amount of AoPS forums, he/she might be a multi account, but don't conclude yet. We want to give new users a chance! If a new user makes a silly poll, PM the user first. If they are a troll, report the topic.
Now you might say, "What if the marathon is good?"
Well yes, I have seen a couple of good ones. If you have a solid idea, keep it in your head, then ask around the community if it is a good idea. This will help you to not spam. Please do not spam by asking people.
Another thing that is clogging MSM is the absurd amount of Alcumus problems. What's the point of asking alcumus in MSM? To get the answer right? Go to the Alcumus forum! There's already one there! Make sure you use Gamebot though!
If you don't have time to read through this whole post, read this summary:
AND...
Please no advertising in Middle school math, high school math, high school olympiads, and I could go on and on
Thanks for helping to "un-clog" the forum on the very best website in the world!
~lakecomo224
I'm not clogging don't worry. Please don't spam in this thread. Thank you.
Before you read on, this is where all of the marathons went.
1. They need more attention.
This one is not very common, so I'm going to get it out of the way first. If a user is new, and doesn't get what the community is for, he/she will start posting polls and marathons to catch attention, or to get upvotes...
2. Upvotes.
Upon seeing successful marathons like the 24 math game, people will want to get upvotes. (By the way, the 24 game is >50 upvotes, so it will be natural to do this)
3. Ignorance.
I'm hoping this is the most common. Some people might not even know that they shouldn't post them! In this case, a nice PM or post should be fine.
4. Pure trolls.
Now these are the types of people that post to
i. Get attention
ii. Be mean
iii. Clog up the forum
We need to report these types of posts.
How to fix these problems:
If you know a user that is nice, never trolls, and starts posting these polls on MSM, then PM them, and ask them why they did this. If you don't know them, and it is one of their first posts, then they either will be new/ignorant, or they are multis/trolls. If you realize the person knows an awful amount of AoPS forums, he/she might be a multi account, but don't conclude yet. We want to give new users a chance! If a new user makes a silly poll, PM the user first. If they are a troll, report the topic.
Now you might say, "What if the marathon is good?"
Well yes, I have seen a couple of good ones. If you have a solid idea, keep it in your head, then ask around the community if it is a good idea. This will help you to not spam. Please do not spam by asking people.
Another thing that is clogging MSM is the absurd amount of Alcumus problems. What's the point of asking alcumus in MSM? To get the answer right? Go to the Alcumus forum! There's already one there! Make sure you use Gamebot though!
If you don't have time to read through this whole post, read this summary:
AND...
Please no advertising in Middle school math, high school math, high school olympiads, and I could go on and on
Thanks for helping to "un-clog" the forum on the very best website in the world!
~lakecomo224
I'm not clogging don't worry. Please don't spam in this thread. Thank you.
This post has been edited 2 times. Last edited by lakecomo224, May 8, 2018, 5:46 PM
math game failed there since it was just way too math related.
