Answer:
I run around the city but I never move.
I am whole but incomplete. I have no eyes yet I see. You can see and see right through me. My largest part is one fourth of what I once was.
One pace to the north. Two paces to the east. Two paces to the south. Two paces to the west. One pace to the north.
I cannot be bought, cannot be sold, even if I'm sometimes made of gold. What am I?
You write on me and secrets I can keep. In places never seen. I spin like a top. Though stiff as a board I'm often described like a mop.
Why was the cook arrested?