Futility Closet describes a result that is startling, amazing, and mysterious.
“This is pretty: If you choose n > 1 equally spaced points on a unit circle and connect one of them to each of the others, the product of the lengths of these chords equals n.”
The Futility Closet posting includes an interactive display using Wolfram Technology by Jay Warendorff that let’s you select different n and see the results. It also includes a reference to a paper that proves the result; only the paper uses residue theory from complex variables, which seems a bit over-kill, though slick, for such a problem. I found a simpler route.
Here is a simple problem from an old 
Here is a simple Futility Closet problem from 2014.
Here is a nice logic puzzle from 2014 Futility Closet.
This is a problem from a while back (2015) at Futility Closet.
This is another fairly simple puzzle from Futility Closet.
Here is another simple problem from Futility Closet.
This statement showed up recently at 
Futility Closet presented a nifty method of solving the “counterfeit coin in 12 coins” problem in a way I had not seen before by mapping the problem into numbers in base 3. It wasn’t immediately clear to me how their solution worked, so I decided to write up my own explanation.