Ten prisoners are arrested for a crime, but the jail is full and the
jailer has nowhere to put them. He eventually comes up with the
solution of giving them a puzzle so if they succeed they can go free
but if they fail they are executed. Each prisoner is assigned a hat
with a random color out of N colors. The number of hats of a given
color hat is not known to the prisoners. The jailers sets the
prisoners into a line, where each can see the hats in front of him but
not the ones behind. Each prisoner is allowed to say only one word
which must be a color name. If the color corresponds to her hat she is
released, otherwise she is killed. The prisoners have one hour to
formulate a plan so as to save as many of them as possible. How many
prisoners can survive and what is the plan to do so? The plan must
work for any positive value of N.