March 3, 2013, the NPR Sunday Puzzle was math:
“Eight people are seated at a circular table. Each person gets up and sits down again — either in the same chair or in the chair immediately to the left or right of the one they were in. How many different ways can the eight people be reseated?”
The answer is 49. Here’s how I got it. The three simplest reseatings have everybody move left, move right, or stay put. The others have pairs of adjacent people switch places. There are 8 with a single switch, 20 = (8 choose 2) – 8 with two switches, 16 = 8×4/2 with three switches, and 2 with four switches, for a grand total of 49.
They received just about 170 correct answers.