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 99×2007 with one side of each color. And 100×2008? And 99×2008?
combinatoricsColoringcombinatorial geometry