A minor quibble: the rules imply that you have to flip a coin. If the layout happens to already have all the right parities with respect to the magic square then you're screwed.
[UPDATE: this it wrong, but since three people have already responded explaining why I thought I would try to head off additional replies at the pass.]
[UPDATE: this it wrong, but since three people have already responded explaining why I thought I would try to head off additional replies at the pass.]