KöMaL 2008 K160

Jack loves playing the following memory game: There are 18 kinds of picture cards, two copies of each. The 36 cards are shuffled and all layed on the table face down. The game consists of turns. In each turn, two cards are turned face up. If they are a pair of identical cards, they are removed from the table. If not, they are turned face down again. The game continues until he has removed all cards from the table. Since Jack has excellent memory, he can always remember the position of any card that he has seen. With this condition, is it possible for a game to consist of 17 turns? Of 18 turns? Of 35 turns? If so, give an example for a possible game. If not, explain why. (Assume that Jack is always trying to finish the game in the lowest number of turns, that is, he will not turn up cards again that he has already seen.)