## Leap Years and Friday 13s

December 24, 2017With 2018 close to around the corner, there's a lot of the usual talk about the new year and its properties (it's nice how it starts on a Monday, for instance), and it reminded me of a little fact I once heard: *every year, there'll be at least one Friday 13*.

It kind of surprised me back then because that seems like a lot — I'm not superstitious, but those who are would never get a break. It also got me wondering how you could be sure of that fact, and how you would even begin to prove it. Turns out, though, that it's a simple proof by exhaustion — there's only so many "types" of year. In fact, a year has only two determining factors: