A logic puzzle with no solution?

Remember those old logic puzzles? Where you're, like, given the characteristics of four people and left to determine which of them did what? Usually you have to use a logic grid to solve it? Well, courtesy of Brad Plumer at the Washington Post and Walter Russell Mead, we now have a logic puzzle that describes the mess in the Euro Zone:

I suppose the question is, does this logic puzzle even have a solution?