MathDB

It is known that there are

3

buildings in the same shape which are located in an equilateral triangle. Each building has a

2015

floor with each floor having one window. In all three buildings, every

1

st floor is uninhabited, while each floor of others have exactly one occupant. All windows will be colored with one of red, green or blue. The residents of each floor of a building can see the color of the window in the other buildings of the the same floor and one floor just below it, but they cannot see the colors of the other windows of the two buildings. Besides that, sresidents cannot see the color of the window from any floor in the building itself. For example, resident of the

10

th floor can see the colors of the

9

th and

10

th floor windows for the other buildings (a total of

4

windows) and he can't see the color of the other window. We want to color the windows so that each resident can see at lest

1

window of each color. How many ways are there to color those windows?

Problem Statement