5 Things About the Doomsday Algorithm

I mentioned last week that I’m currently reading a biography of John Conway, and I came across something interesting during the discussion of his version of the Doomsday Algorithm. Otherwise known as the “perpetual calendar” problem, it’s a method for mentally calculating what day of the week any given date fell on. Conway was so obsessed with this problem and improving his time for the mental math that he had his computer set up to make him solve ten of these before he got in. Supposedly his record was 10 dates in 15 seconds. #lifegoals. Anyway, this whole discussion got me poking around about this mental math trick, and I wanted to share a few things that I found:

1. Lewis Carroll published on this problem Yeah, the guy who wrote Alice in Wonderland also came up with a perpetual calendar algorithm, and it was published in Nature in 1887.
2. By “Doomsday” we mean “anchor day” John Conway has an excellent flare for the dramatic, and the title of this algorithm proves it. However, it’s a misleading title for what’s really going on. Basically, Conway realized that a whole bunch of easy to remember days (4/4, 6/6, 8/8, 10/10 and 12/12) all fall on the same day of the week in any given year. If you can figure out what day that was, you get an “anchor day” in those months. From there, he realized that 5/9, 9/5, 7/11 and 11/7 all fall on the same day as well, so you now have one known date in each month. As you can see, this simplifies further calculations considerably.
3. Do you bite your thumb at us sir? Conway does. One of his tricks for remembering his full trick is to use his fingers as prompts and bite his thumb to remember the number he got there. This link also has some very helpful videos of Conway explaining his method.
4. Others have improved on the method The gamesmanship of this method has been inspiring to a lot of mathy folks, and some of them continue to try to find simpler/better/faster ways for people to calculate the day of the week. This method looks like the current favorite for simplicity, and is the one I think I’m going to start with.
5. Don’t try to calculate anything from 1752 At least if you’re in the US or England, this is a trap. September 2nd-Sept 14th of that year don’t exist. Now there’s a trivia question for you.