.
amount of people stand on coordinates 
where 
.
.
got 
people's water cup is empty. Every minute, two neighbouring people are chosen that does not have the same amount of water in their water cups, and they equalize the amount of water in their water cups.
litres of water.
and 
Show that
Let 
Show that
Let 
Show that
be a function such that
whenever 
.
for all 
.
is prime.
rows and 
columns. Each point is coloured with one of the colours red, blue or green. Show that no matter whatever way the colouring is done, there always exist four points
,
,
are decimal digits. Find the necessary conditions in 
to 
in 
steps. (Note: Two paths where identical set of points is traversed are considered different if the order of traversal of each point is different in both paths.)
are on a circle of radius 
and with center 
.
and 
are the mid points of 
and 
respectively. Then;
is a square.
to 
. Prove that
Y by
a) A positive integer is written at each vertex of a triangle. Then on each side of the triangle the greatest common divisor of its ends is written. It is possible that the numbers written on the sides be three consecutive integers, in some order?
b) A positive integer is written at each vertex of a tetrahedron. Then, on each edge of the tetrahedron is written the greatest common divisor of its ends . It is possible that the numbers written in the edges are six consecutive integers, in some order?
b) A positive integer is written at each vertex of a tetrahedron. Then, on each edge of the tetrahedron is written the greatest common divisor of its ends . It is possible that the numbers written in the edges are six consecutive integers, in some order?
