Linda Cobb, The Queen of Clean®, recommends flipping on a seasonal schedule - side-to-side in spring and fall, and end-over-end in summer and winter.
In other words, when you flip the mattress over, alternate between flipping from the side, and flipping from the foot. This will take you through the cycle of four configurations.
>The absence of a golden rule for mattress flipping is a disappointment, but it does not portend the demise of Western Civilization. We can adapt; we can learn to live with it.
This reduces the number of possibilities to 2. Not very interesting, group theory-wise.