Three friends sit around a table, each with a large plate of cheese. Instead of eating it, every minute each of them simultaneously pass half of their cheese to the neighbor on the left and the other half to the neighbor on the right.

a) Is it true that the amount of cheese on the first person's plate will converge to some limit as time goes to infinity? Explain.

b) The next week they meet again, adding a fourth friend and follow the same procedure. What can you say about the eventual distribution of the cheese?