MathDB

Let an integer

n > 1

be given. In the space with orthogonal coordinate system

Oxyz

we denote by

T

the set of all points

(x, y, z)

with

x, y, z

are integers, satisfying the condition:

1 \leq x, y, z \leq n

. We paint all the points of

T

in such a way that: if the point

A(x_0, y_0, z_0)

is painted then points

B(x_1, y_1, z_1)

for which

x_1 \leq x_0, y_1 \leq y_0

and

z_1 \leq z_0

could not be painted. Find the maximal number of points that we can paint in such a way the above mentioned condition is satisfied.

Problem Statement