1. The problem statement, all variables and given/known data Two glasses. First glass has 1 L of water. Second glass has 1 L of alcohol. Step (1) Pour 1/2 of liquids from glass 1 to glass 2. Step (2) Pour 1/2 of liquids from glass 2 to glass 1. What is the limiting situation after 1 billion steps. 2. Relevant equations N/A 3. The attempt at a solution I tried solving the question with a series. if Q = the size of the transfer each time. Glass 1: Xn+1 = (1-q)Xn + q (1+(q-1)Xn)/(1+q) Glass 2: 1-Xn+1 = (1-(1-q)Xn)/(1+q) And by proving that 1/2 0 xn will converge to 0, I reach a conclusion. However, I was told my by instructor that I actually need to use transitional matrixes and the solution should indicate that the content of alcohol / water in both glasses will fluctuation between 1/2 and 1/3. Thanks for anyone's help!