Suppose that three workers are given the task of scanning through a shelf of books in search of a given piece of information. To get the job done fairly and efficiently, the books are to be partitioned among the three workers. To avoid the need to rearrange the books or separate them into piles, it would be simplest to divide the shelf into three regions and assign each region to one worker.
But what is the fairest way to divide the shelf up? If each book is the same length, say 100 pages, the job is pretty easy. Just partition the books into equal-sized regions,