When I read the OP, I immediately remembered back some 20 years ago, when I had to solve the same problem at $work.

As it hasn't been mentioned so far, and in case the random monk is wondering what the whole procedure is good for:

That reordering of 1..n; !(n%4) is needed, when you want to print a booklet from n pages, 2 pages on one, duplex.

By searching for "booklet page reorder" (or similar) with your www search engine of choice, you'll be able to find some descriptions and even illustrations on the topic.