These are fascinating! (I'm sure it's totally unrelated that I have plenty of work to get done and an actual deadline.)
But I'm not on a deadline. I'm hanging out in our room in a Super 8 in truly isolated rural Kansas, while Ace naps.
When I was in truly isolated rural Nebraska, the Super 8 had no vacancies.
All filled Super 8s are similar, but all Super 8s with vacancies have vacancies for specific reasons. Or maybe it's the reverse.
Lee has promised to take Nia to Kansas, possibly even this summer, and Nia is so fucking excited. It's kind of adorable, and she loves everything and will presumably have a great time.
5: well, there is only one way for a Super 8 to be full, but there are (n/2)(n+1) ways for it to have vacancies where n is the number of rooms.
There are many ways to incorrectly compute the possible number of ways to have vacancies, but all correct computations are similar.
Ugh. God, yes, you're right, that is wrong, isn't it.
(n choose n)+(n choose n-1)+...+(n choose 1).
I guess that's assuming we're distinguishing all the ways to have 1 vacancy.
Well, are we counting room one being vacant and all others occupied as different from room two being vacant and all others occupied?
I have photos that my paternal grandmother sent my grandfather in the Phillipines during WW2, of her and my dad and his older brother. Nothing is quite so deprecating as those captions in the article, but the tone is the same for the ones she's in. Well, here I am. Guess that's what I look like.
The ones with just the boys aren't deprecating, but still have the same tone. Decent looking boy I'd say. Looks pretty tough don't you think.
11:
Does that simplify to 2^n - 1? Each room can be empty or full, and only one out of the 2^n possible combinations corresponds to all the rooms being full.
15: it has to, right? The room occupancies are just an n digit binary number.
Like an empty subWay car, there's a reason that last room is empty at the cruddy motel.