Set ordering in Python: why I didn't sleep last night

In yesterday's class of the Python-infused Linear Algebra course I'm taking, a fellow student noted the strange ordering of items in a set when printed. It seemed that the printed order of the set items always swapped the first two items, but left the rest unchanged. I don't know what sets he tried, but I was interested in the general behavior, and so began my quest through the Python source code...