MathDB

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.

Problem Statement