The Toilet Paper Problem
-- Donald E. Knuth, The American Mathematical Monthly, Vol. 91, No. 8. (Oct., 1984), pp. 465-470.

The toilet paper dispensers in a certain building are designed to hold two rolls of tissues, and a person can use either roll. There are two kinds of people who use the rest rooms in the building: big-choosers and little-choosers. A big-chooser always takes a piece of toilet paper from the roll that is currently larger; a little-chooser always does the opposite. However, when the two rolls are the same size, or when only one roll is nonempty, everybody chooses the nearest nonempty roll. When both rolls are empty, everybody has a problem.

and
Acknowledgements. I wish to thank the architect of the computer science building at Stanford University for
implicitly suggesting this problem...