Two people take turn removing stones from a pile of n stones. Each person may, on each of his turns, remove either one stone or two stones. The person who takes the last stone is the winner and gets $1 from the other person. Player 1 gets to move first. Find the subgame perfect equilibria (SPE) for n = 1 and n = 2, then use these results to find the SPE for n = 3 and n = 4. Who is the winner in the SPE for an arbitrary n?