We have 2015 marbles in a box, where each marble has one color from red, green or blue.
At each step, we are allowed to take 2 different colored marbles, then replace it with 2 marbles with the third color. For example, we take one blue marble and one green marble, and we fill with 2 red marbles.
Prove that we can always do a series of steps so that all marbles in the box have the same color. ColoringColor problemcombinatorics