Could anybody help me to solve the following problem?
There were 12 dwarves living in a florest and each of them lives in a house that is painted blue or red. At the month "i" the dwarf number "i" visits all his friends and if most of his friends have their houses painted with one color diferent from his one, he join them by changing the color of his own house. This process continues on the next months. Prove that someday the dwarves will not need to change the color of their houses. (The friendships are mutual and don't change over the time).