There are two main competing principles at work while washing the dishes: most annoying first and dirtiest last. Luckily these two principles are less contradictory than they might seem at first glance. Utensils, with all of their finicky little nooks and crannies, tend to be fairly clean. The same applies to those annoying glasses, that have to go early. The dirtier, yet also infinitely more relaxing plates come next, and at the end follow the dirty pots and pans.
Jotted down on 2016-08-06.
One-word sonnet added on 2017-01-25.