Fermi was famous for asking difficult general questions of interest that could be approximated through a series of good guesses, such as: “How many molecules of rubber are rubbed off of car tires in the country each year?” “How many stars are visible at night to the naked eye?” Order-of-magnitude approximations are generally appropriate answers.
This is equally interesting outside of physics, though it relies on knowing different trivia and rules of thumb. “How many schools are there in the country?” “How many people climb these mountains each year?”
I was up early this morning for a walk, and at work at 6. It was gray out, yet across the river bright lights were on in a cube of windows in the middle of the John Hancock building. It has large glass windows, so its lights make an impression; there were lights in dozens of rooms in one corner of the building, looking out of the river, covering many floors. One light every 4 windows, perhaps a cube 8 offices on a side extending up 8 floors. 100 offices if just by the building’s edge, 500 if the pattern continued inside. Part of a large company, surely. The lights were bright enough to be construction, which would explain them being on round the clock [as much as anything would; I’ve never understood that practice].
So who was the company? There were about 60 floors in all, and the lights were between 35 and 45. Searching for new companies moving into the Tower turned up Bain Consulting…
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