[/quote]
,
,
,
be real numbers, such that 
and 
.
.
,
,
around a circle so that the sum of every 
.
Let 
.
amount of people stand on coordinates 
where 
.
.
got 
people's water cup is empty. Every minute, two neighbouring people are chosen that does not have the same amount of water in their water cups, and they equalize the amount of water in their water cups.
litres of water.
,
,
.![\[\sum_{i=1}^{n}\frac{1}{1+x_{i}}\cdot \sum_{i=1}^{n}x_{i}\leq \sum_{i=1}^{n}\frac{x_{i}^{k+1}}{1+x_{i}}\cdot \sum_{i=1}^{n}\frac{1}{x_{i}^{k}}\]](http://latex.artofproblemsolving.com/2/6/4/264d110e2a40c7f787c650aa8b8dc30af5d28263.png)
be an integer. You have two 
boards. Each board contains the numbers 
and 
,
row and 
column of the first board is different from the number that is in the 
be a convex pentagon such that![\[ \angle BAC = \angle CAD = \angle DAE\qquad \text{and}\qquad \angle ABC = \angle ACD = \angle ADE.
\]](http://latex.artofproblemsolving.com/d/3/d/d3d9a82f4318190298a8f008d417a364e03f1fca.png)
The diagonals 
and 
meet at 
.
bisects the side 
.
,
,
is the incenter, 
is the intersection of 
-
.
lies on the external angle bisector of 
such that 
and 
.
lies on 
.
is tangent to 
and 
at 
,
is tangent to 
at 
and both circles pass through the inside of triangle 
is the Midpoint od the arc 
be a sequence of positive real numbers, and 
be a positive integer, such that![\[a_n = \max \{ a_k + a_{n-k} \mid 1 \leq k \leq n-1 \} \ \textrm{ for all } \ n > s.\]](http://latex.artofproblemsolving.com/f/1/2/f12c9c5e0f154549118a33a2f359329333f432a7.png)
and 
,![\[a_n = a_{\ell} + a_{n - \ell} \ \textrm{ for all } \ n \geq N.\]](http://latex.artofproblemsolving.com/b/0/b/b0b2bd4507621302eeee27ae50ed9c0afd72c6ef.png)
meet the circle again at 
parallel to 
.
is parallel to 
.
Y by Cattus1221, lpieleanu, jkim0656, Alex-131, justJen, EpicBird08, littlefox_amc, blueprimes, deduck, Exponent11, alan9535, aidan0626
Hey! I got accepted into Ross Indiana, and I think I'll probably also get accepted into HCSSiM. I've been looking between the two camps, and I'm trying to decide which one to go to -- both seem like really fun options.
Instead of trying to explain my personal preferences and thought processes, I thought it might be a good idea to ask the community for their personal opinions on these camps. What are some things that you like or dislike about both camps? (Whether it be through personal experience or by word-of-mouth, but please specify if it's just something you've heard)
This will probably help me be more informed on making a final decision, so I'd appreciate any advice. Thanks in advance!
Instead of trying to explain my personal preferences and thought processes, I thought it might be a good idea to ask the community for their personal opinions on these camps. What are some things that you like or dislike about both camps? (Whether it be through personal experience or by word-of-mouth, but please specify if it's just something you've heard)
This will probably help me be more informed on making a final decision, so I'd appreciate any advice. Thanks in advance!
This post has been edited 1 time. Last edited by akliu, Apr 18, 2025, 6:20 PM
Reason: probably definitely
Reason: probably definitely
.
