I always enjoy hearing about the Physics of everyday objects, and there were several such presentations at the Michigan AAPT meeting. One of these, by David A. Van Baak, was about refrigerator magnets.
It turns out that refrigerator magnets, because of the way they are made, have a striped pattern of magnetization (N-S-N-S-N-S, though the magnetization actually varies continously). You can see this easily yourself if you hold one behind one of those magnetic films (pictured above), or if you just take two magnets, hold them back to back, and then try to slide one along the other. Every couple of millimeters or so is a “happy spot” where north on one magnet meets south on the other, and the magnets will try to freeze in position there.
One consequence of this striped magnetization is that a magnetic field only exists on one side of the magnet. (I’m still trying to wrap my mind around exactly why.) Try putting the magnet onto your refrigerator backwards – won’t work. And not because of the thin sheet of paper in the way.