MathDB

The pieces in a game are squares of side

1

with their sides colored with

4

colors: blue, red, yellow and green, so that each piece has one side of each color. There are pieces in every possible color arrangement, and the game has a million pieces of each kind. With the pieces, rectangular puzzles are assembled, without gaps or overlaps, so that two pieces that share a side have that side of the same color. Determine if with this procedure you can make a rectangle of

99\times 2007

with one side of each color. And

100\times 2008

? And

99\times 2008

Problem Statement