There are n people standing in a circle. A counter goes clockwise around the circle and repeatedly eliminates every k-th person in the circle, until one person (the winner) remains. Where should you stand initially to become the winner?
There are people standing in a circle waiting to be executed. The counting out begins at some point in the circle and proceeds around the circle in a fixed direction. In each step, a certain number of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. The task is to choose the place in the initial circle so that you are the last one remaining and so survive.
The problem is named after Flavius Josephus, a Jewish historian living in the 1st century. According to his account of the siege of Yodfat, he and his 40 soldiers were trapped in a cave, the exit of which was blocked by Romans. They chose suicide over capture and decided that they would form a circle and start killing themselves using a step of three. Josephus states that by luck or possibly by the hand of God, he and another man remained the last and gave up to the Romans.
For more information, see the Wikipedia article on the Josephus problem.