Alice and Bob play a game, taking turns, playing on a row of n seats. On a player’s turn, he or she places a coin on any seat provided there is no coin on that seat or on an adjacent seat. Alice moves first. The player who does not have a valid move loses the game.
(a) Show that Alice has a winning strategy when n=5.
(b) Show that Alice has a winning strategy when n=6.
(c) Show that Bob has a winning strategy when n=8.