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
Let 
be the intersection point of the segments 
and 
, where the points 
and 
lie respectively on the sides 
and 
of the triangle 
so that the quadrilaterals 
and 
are cyclic. Find the angle 
if the radii of the circles circumscibed around those cyclic quadrilaterals are equal.
be the intersection point of the segments 
and 
, where the points 
and 
lie respectively on the sides 
and 
of the triangle 
so that the quadrilaterals 
and 
are cyclic. Find the angle 
if the radii of the circles circumscibed around those cyclic quadrilaterals are equal.
and so 
.
by ASP in 
about 
we see, that 
(from cyclic 
)
(like external in 
)
we have 
.
