In this previous post, I recalled a discussion I once had with John Conway about the pros and cons of different systems for mentally calculating the day of the week for any given date. In this post, I’ll present two of the most popular systems for doing this, the “Apocryphal Method” [Note added 5/3/20: In a previous version of this post I called this the Gauss-Zeller algorithm, but its roots go back even further than Gauss] and Conway’s Doomsday Method. I personally use a modified verison of the apocryphal method. I’ll present both systems in a way which allows for a direct comparison of their relative merits and let you, dear reader, decide for yourself which one to learn.