There are some themes here. Several are sort algorithms (the horses and the balls) and a number are probability and distribution questions (e.g. the stairs and the stools). Several are clearly sales and customer service situations (e.g. the invisible pen).
And several are estimation problems (e.g. how many airplanes are in the air right now). The latter type question was very popular when I was at McKinsey & Co. Many interviews actually gave the victim interviewee some kind of business case. The point was to see how well the person broke down the problem, considered facts they would need to obtain, etc.
A subset of these was the ever-popular market estimation game, such as "how many home windows are bought each year in Mexico?" As an interviewer, one wants to see the person think "OK, there is new construction and replacement. For the new construction market, we need the size of the home construction market, number of windows per home...." That sort of thing.
We would also generally ask them to guess at numbers for all these and actually come up with a number. This is not some test of trivia -- being able to look at numbers and reality check them is an important skill, so having a reasonable intuition about the proper scale of business and economic statistics is useful. In fact, if there was one skill as a consulting manager I was constantly trying to hammer into younger consultants it was to look at the numbers coming out of their spreadsheets and ask them if they really make sense.