AoPS Academy
squares, we cover the area with several S-Tetrominos (=Z-Tetrominos) along the square so that in every square, there are two or fewer tiles covering that (tiles can be overlap). Find the maximum possible number of squares covered by at least one tile.
satisfies
for any non-negative integers 
and 
. Determine the number of possible sets of integers 
.
be a function from the Euclidean plane to the real numbers such that 
for any acute triangle 
with circumcenter 
, centroid 
and orthocenter 
. Prove that 
is constant.
be the positive real number. Prove that
is inscribed in a trihedral angle 
. Prove that the planes 
and 
are perpendicular if 
.
is inscribed in a trihedral angle . Prove that the planes and are perpendicular if .
