Consider the set M={1,2,…,2008}. Paint every number in the set M with one of the three colors blue, yellow, red such that each color is utilized to paint at least one number. Define two sets:
S1={(x,y,z)∈M3∣x,y,z have the same color and 2008∣(x+y+z)};
S2={(x,y,z)∈M3∣x,y,z have three pairwisely different colors and 2008∣(x+y+z)}.
Prove that 2∣S1∣>∣S2∣ (where ∣X∣ denotes the number of elements in a set X).