E 25. Dividing cards

Here is a problem from Math Charmers, a delightful book by Alfred S. Posamentier.

You are in a completely dark room, seated at a table. There are twelve playing cards laid out in front of you. You know that five of them are face up and the remaining seven are face down, but you have no way of determining whether a card is face up or not. Your task, should you decide to accept it, is to divide the cards into two piles so that each pile has the same number of cards face up as the other. You may, of course, turn cards over.

While at first this sounds impossible, there is a simple solution.