This problem is based on the Josephus problem. There are 1000 people on the circumference of a very large round pool. A lifeguard comes by and shakes hand with the person 1 and pushes person 2 into the pool. Then the lifeguard shakes hands with the person 3 and pushes the person 4 into the pool. The lifeguard keeps doing this, shaking hands with one and pushing the next one into the pool, around and around the circle until only one person remains on the edge of the pool. In what spot was the person who remains?
