The mathematical content may be a bit elementary for some readers here, but this is an entertaining article from American Scientist nonetheless. It’s not every day that there’s an article about group theory in the newsstands, and it’s about a real world problem that I believe many people have pondered over.
The article missed out the obvious solution:
1) Stand North of the bed.
2) Flip the mattress by lifting its nearest edge.
3) Rotate the entire bed 1/4 turn clockwise.