Suppose you have an infinite number of bricks and no cement or another material to connect the bricks to each other. You would like to build a tower like the one in the figure. How many bricks do you need in order to build a tower in which the highest brick is shifted three bricks with respect to the lowest brick?

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?

A - B = B

B * C = A

D : B = E

C * C = E

C + E = A

For which numbers stand A, B, C, D and E?