-
through 
and 
,
. Let 
denote the expected value of this score. Compute the value of the greatest integer less than or equal to 
.
has side lengths 
and 
.
on 
.
is rotated about 
to 
so that 
,
lie on the same line and 
is perpendicular to 
.
,
and 
are relatively prime positive integers, find 
.
then prove 
and 
.
and 
Prove that
and 
Prove that
Let 
Prove that
.
-
,
be the midpoint of side 
and 
be the midpoint of segment 
.
and 
intersect at 
.
.
such that 
is a square perfect.
friends in this. However, if two people are not friends at least they have a friend in this party. What is the largest possible number of people in the party?
be real numbers such that 
Prove that
Let 
Prove that
Let 
Prove that
be the altitude and 
be the intersection point of the altitudes of triangle 
is symmetric to 
intersects 
.
.
![$f\in\mathbb{C}[X], \ f=aX^3+bX^2+cX+d, \ a,b,c,d\in\mathbb{R}^*$](http://latex.artofproblemsolving.com/8/b/d/8bdc04d75d0654da65463301f6fd0b0af4160b2b.png)
a polynomial whose roots 
are in geometric progression with ration 
.
.
Y by
When exporting a rich format document in the writing tab into the message board, bold formatting specifically is broken and results in broken BBCode.
Page URL: virtual.aopsacademy.org/class/<any writing class works here>/writing
TO REPRODUCE
1. enter "Lorem ipsum".
2. apply bold to "Lorem"
3. apply italic to "ip".
4. click the Post Draft on Message Board
5. read the contents of the message board post.
FOR EXAMPLE
When I format "Lorem ipsum" (in the writing tab of course), but when I export to post it, I get
Notice that the first bolding does not start, only ends.
Page URL: virtual.aopsacademy.org/class/<any writing class works here>/writing
TO REPRODUCE
1. enter "Lorem ipsum".
2. apply bold to "Lorem"
3. apply italic to "ip".
4. click the Post Draft on Message Board
5. read the contents of the message board post.
FOR EXAMPLE
When I format "Lorem ipsum" (in the writing tab of course), but when I export to post it, I get
Lorem[/b] [i]ip[/i]sumNotice that the first bolding does not start, only ends.
