[/quote]
,
\end{table}
x 
unit squares. Strawberries lie on some of the unit squares so that each row or column contains exactly one strawberry; call this arrangement 
.
be another such arrangement. Suppose that every grid rectangle with one vertex at the top left corner of the cake contains no fewer strawberries of arrangement 
by performing a number of switches, defined as follows:
denote the number of prime factors of 
,![\[ \sum_{n=1}^{1989} (-1)^{\Omega(n)}\left\lfloor \frac{1989}{n} \right \rfloor. \]](http://latex.artofproblemsolving.com/2/0/4/2043dca9f2ff2adfd3c8d49fa4dd278871968db0.png)
denote the set of positive integers.
such that for all 
,![\[f(mn)^2 = f(m^2)f(f(n))f(mf(n))\]](http://latex.artofproblemsolving.com/5/b/c/5bcd0f162c76b4177801933623724e576476fa88.png)
if and only if 
grid which is made up of 
unit squares and 
edges. We colour each of these edges either 
or 
.
where 
.
is the circumcenter of triangle 
is the projection of point 
onto line 
.
,
are 
,
,
,
intersects 
and 
at points 
and 
,
.
be real numbers less than 2.Then prove that 
be an acute-angled triangle and let 
,
,
be the midpoints of 
,
,
respectively. Construct a circle, centered at the orthocenter of triangle 
to intersect the circle at 
,
to intersect the circle at 
and 
to intersect the circle at 
.
.
and 
be two sequences of integers such that 
and 
for all 
.
divides 
for an infinity of integers 
such that 
for all 
Prove that 
Where 
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 
