A hobo who does like to smoke cigars but does not have any money, collects cigars stumps. From every six stumps he finds he can make a new cigar. One a particular day he finds 36 stumps. How many cigars can he smoke on that day?

Two men are sitting around a round table. They both have an infinite amount of cigarettes. The men are going to play a game. Each turn they have to lie down one cigarette on the table. The rules are simple: two cigarettes may never touch each other and the game will end when it is impossible to add another cigarette. The one who lies down the last cigarette has won. Who will win this game (suppose that both players play the best possibly move), the one who starts the game or the one who plays the second cigarette?

Move your head somewhat away from the monitor and answer the following question: what is the difference between the left and the right figure?