[/quote]
,
.
and![\[ f(x+y)+f(x^2+f(y))=f(f(x))^2+f(x)+f(y)+y,\forall x,y\in\mathbb{R}\]](http://latex.artofproblemsolving.com/c/8/9/c895ae7fdf8d7f284ac9fc94cc077d6edad6cbf0.png)
be a convex hexagon with 
and 
.
which is equidistant from sides 
and 
.
and 
are the centers of mass of 
and 
,
.
be a point in the plane, distinct from the vertices of 
.
the reflections of 
and 
,
are collinear if and only if 
coincide, prove that 
given that there exist positive integers 
satisfying
and 
,
as follows:
where 
are all the positive divisors of 
.
Find all positive integers 
.
Find all positive integers 
.
be an odd prime number. How many 
of 
are there, the sum of whose elements is divisible by 
be real numbers satisfying
be a fixed square and 
a variable point on segment 
.
is constructed such that 
is on segment 
and 
is on segment 
.
be the intersection point of lines 
and 
.
board, two opposite sides have been joined, forming a cylinder. Determine whether it is possible to place 
.
.
Y by
I am practicing previous years' MathCount papers, but they seem to get progressively harder each year.
So, for those of you who scored well in Mathcounts, how many sprint questions are/were you able to do in State/Nationals?
I want to get a sense of where I stand.
Thanks in advance!
So, for those of you who scored well in Mathcounts, how many sprint questions are/were you able to do in State/Nationals?
I want to get a sense of where I stand.
Thanks in advance!
This post has been edited 1 time. Last edited by kp34912, Mar 27, 2025, 9:27 AM
Reason: edited
Reason: edited
i mock ~30 total on nats from after 2020 
