The Eight Monarchs (Some Mathematical Magic)

The eight Monarchs are the four Kings and four Queens of an ordinary deck of cards. We can perform our magic without a deck by using the grid below with the K-Q token ( a coin can be used instead if one wishes).

The Effect: The magician's back will be turned while Mark, the subject, places the token on one of the suit nodes. Mark is to remember this starting position. Then Mark makes a sequence of moves; a move being one of four possibilities: a horizontal move, a vertical move, or a diagonal move to a new node or a flip of the token on the same node. Mark calls out his sequence of moves to the magician and when finished, tells the magician either his end node or his start node and the magician, even not knowing whether it was the start or the end, immediately names the other terminal.