Use cases
Let’s start with a statement of the problem.
The problem – part 1
About once or twice a month, my four delightful, intelligent, and playful grandchildren come to visit my wife and me. Like most grandparents, we keep a box full of toys in our upstairs game room for them to play with during their visits. The first thing they do upon arrival – at least the bigger grandkids– is to take every single toy out of the toy box and start playing. This results in the the following photo – basically toys randomly and uniformly distributed throughout the playroom. Honestly, you could not get a better random distribution. They are really good at this. Since, as grandparents, our desire is to maximize the amount of time that our grandchildren have fun at our house and we want them to associate Granddad and Grandmother's house with having fun, we don’t make them pick up the toys when they go home. You can see where this is heading.
By the way, if you are a parent, let me apologize to you in advance...
