Ooh, a tricky one last time, eh? props to jedifreeman, kidmissile, divinemissb, and woap for almost getting it right. They were all correct in HOW the links may be traded, but NO ONE got the number of cuts right.
Farah will only need to cut one link: the third one. This allows her to remove the first two links as a single chain of two, and the last four links, as a single chain of four, leaving her the cut third link separate. By trading back and forth, each day, she will be able to increase her payment to the clerk by one link each day (day 1: the single link, day 2: the chain of two, day three: the chain of two and the single, day 4: the chain of four, etc...).
Sneaky, sneaky, eh? Well, wrap your mind around this one, specially selected for dravengodvamp's release:
Sid Shady is in prison and is planning an escape. The cell he is in measures three meters by three meters by three meters. The walls are made of reinforced concrete and they extend two meters below the dirt floor. The only openings are the locked door and a skylight one meter in diameter. Sid thinks he has found a way to escape, so he begins by digging a tunnel. He knows that he cannot tunnel himself out, but digging the tunnel is a crucial part of his plan. How does he plan to escape?