[/left]
Relay Section Point Values
[left]A team's score is computed by adding the points the team won in the team and relay sections, as well as the points each member won in the speed and accuracy sections. Prizes will be awarded to teams and individuals with the most points.[/left]
formed from the digits 
,
,
,
,
,
of the digits are less than 
satisfies the condition because it contains at least 
does not satisfy the condition because it does not contain at least 
.
of size 
with 
such that![\[A^2+B^2=AB+BA=2I\]](http://latex.artofproblemsolving.com/c/3/4/c34e5f7ff2e0a180d2553fec45f278370ac9f8e6.png)
![$f : [0,1] \longrightarrow \mathbb{R}$](http://latex.artofproblemsolving.com/9/a/4/9a4b7997c35990f839742d29866122791ade8b7c.png)
is differentiable with 
.
for all ![$x \in [0,1]$](http://latex.artofproblemsolving.com/d/3/4/d3423a3200d0ad7660fc4265d59d5598a53d551d.png)
,
for all 
.
is differentiable and 
for all 
.
,
.
for which there exists positive integers 
,
,
satisfying![\[
2a^n+3b^n=4c^n.
\]](http://latex.artofproblemsolving.com/0/2/9/0295405b01494edc05ce9867b2ec48a4e069bf26.png)
matrices 
and 
with integer entries, that satisfy the following conditions:
;
;
.
denotes the 
points are chosen at random, independently, and distributed uniformly in the unit disc 
.
be the convex hull of the chosen points. Which probability is larger: that 
be the 
be the set of 
.
is constitued of 2 elements to be determined.
for which there exist a differentiable function 
and exist a sequence 
of real positive numbers, convergent to 
such that![\[
g'(x) = \lim_{n \to \infty} \frac{f(x + a_n) - f(x)}{a_n}, \forall x \in \mathbb{R}.
\]](http://latex.artofproblemsolving.com/5/c/1/5c1966d819f6562ec5b2e6e9979729cd944ab781.png)
is continuous on 
,
with 
![$f : [a, b] \to \mathbb{R}$](http://latex.artofproblemsolving.com/4/b/a/4baf2d51eb4d8376d7a95126b727c893b588c70d.png)
satisfies the condition of the mean value theorem and function ![$g : [p, q] \to \mathbb{R}$](http://latex.artofproblemsolving.com/6/2/c/62c861380387bf2de75bd22027dfb1e7ba486736.png)
has the property 
on the interval ![$[a, b],$](http://latex.artofproblemsolving.com/2/5/5/255c58a4522df6b7519d2ccd3abac472060b117a.png)
but 
does not satisfy the condition of the mean value theorem on the interval ![$[p, q].$](http://latex.artofproblemsolving.com/e/b/d/ebd6eb93b7a86b867e34fae52d2fb3e22a962036.png)
Investigate whether there is a value of 
such that 
Prove your answe
Y by
Hi,
I just received my USAJMO score distribution: 000 701 (very cursed I know)
The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
I just received my USAJMO score distribution: 000 701 (very cursed I know)
The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
and BC has slope 
,
?
