My exam included this fill-in-the-blank question:
Please write __ this address. (on/at/to)
I filled the blank with on.
Is that correct?
You can write on paper or any surface, such as a hand or on a wall.
So "Please write on this address" I would interpret to mean the inscriber has to write over a pre-typed address. "On" in this case indicates place. The request sounds odd to me but from a grammatical point of view it is arguably correct.
As for using the preposition "at" I would consider the sentence to be incomplete. A direct object is needed.
"Please write to me/him/her/us/them at this address"
My preferred answer would be: "Please write to this address" You are asked to communicate and transfer your message from one place (presumably your home) to another ("this address"). http://dictionary.reference.com/browse/to?s=t
If a preposition is required, "to" would be the preferred. "At" would also be acceptable, although possibly formal/archaic.