As director of prisons, you will be in charge of the following game. Before any group of n (three for example) inmates eager to recover their freedom, you will say : I want to free one of you. To decide which one of you will recover his liberty, you have to participate to a game. There are 2n-1 (five for example) badges here: n (three) white and n-1 (two) black. I will put one of them behind your backs, so that only your (two) fellow inmates can see the color I have chosen for each of you. You can look at each of you but you cannot communicate in between you. The first of you who can find the color of his own badge based on a logical reasoning will be free. The game start after you - the director - has finished fixing the n (three) white badges in the back of the (three) inmates.