Chapter 2.C, Problem 11E

Mixing Marbles. Consider the case in which each of two piles initially contains fifteen marbles (see Example 4). Suppose that on the first transfer, three black marbles are moved to the white pile. On the second transfer, any three marbles are taken from the white pile and put into the black pile. Demonstrate, with diagrams and words, that you will always end up with as many white marbles in the black pile as black marbles in the white pile.