Question 112
In the remote region of Torturia, the vizier arranges $n$ condemned prisoners in a circle, numbered in order from 1 to $n$. Relentlessly, he sends every second prisoner to the executioner: prisoners $2,4, \ldots$ and so on, going around the circle and skipping one person between two executions, until only one remains. Compute, in terms of $n$, the number of the last remaining prisoner.