grid consisting of 2025 unit squares. Within each unit square is a car, facing either up, down, left, or right. If the square in front of a car in the direction it is facing is empty, it can choose to move forward. Each car wishes to exit the 
cars from the 
be a convex hexagon, such that the triangles 
and 
are equilateral and the diagonals 
and 
are concurrent. Prove that 
or 
for which 
is prime.
Y by Adventure10
Given are two parallel lines 
and 
and a point 
, that lies outside of the corridor bounded by and . Construct three lines 
, 
and 
through the point . These lines intersect in 
and in 
respectively. Let 
be the intersection of the lines 
and 
, 
be the intersection of the lines 
and 
and let 
be the intersection of the lines 
and 
. Show that there exists exactly one line 
, that contains the points 
and that is parallel to and .
and 
and a point 
, that lies outside of the corridor bounded by and . Construct three lines 
, 
and 
through the point . These lines intersect in 
and in 
respectively. Let 
be the intersection of the lines 
and 
, 
be the intersection of the lines 
and 
and let 
be the intersection of the lines 
and 
. Show that there exists exactly one line 
, that contains the points 
and that is parallel to and .
