Three players A, B and C sit around a circle to play a game in the order A \rightarrow B \rightarrow C \rightarrow A \rightarrow \cdots. On their turn, if a player has an even number of coins, they pass half of them to the next player and keep the other half. If they have an odd number, they discard 1 and keep the rest. For example, if players A, B and C start with (\underline{2}, 3,1) coins, respectively, then they will have (1, \underline{4}, 1) after A moves, (1,2, \underline{3}) after B moves, and (\underline{1}, 2,2) after C moves, etc. (Here underline indicates the player whose turn is next to move.) We call a position (\underline{x}, y, z) stable if it returns to the same position after every 3 moves.
(a) Show that the game starting with (\underline{1}, 2,2) ( A is next to move) eventually reaches (\underline{0}, 0,0).
(b) Show that any stable position has a total of 4 n coins for some integer n.
(c) What is the minimum number of coins that is needed to form a position that is neither stable nor eventually leading to (\underline{0}, 0,0)?