The Josephus problem

$n$ people stand in a circle, numbered $1$ to $n$ clockwise. Starting the count at person $1$, every second person is eliminated ($2$ goes first, then $4$, and so on), continuing around and around the shrinking circle until only one person remains.

For a given $n$, which position survives? Work it out for $n = 100$, and find the general rule.