Doomsday algorithm is a strangely termed method of determining the day of the week using some clever quick calculations. The doomsday value is some weekday. It turns out that regardless of the year the following dates fall on the same weekday for a given year:
- January 3rd or 4th when it is in a leap year.
- the last day of February
- March 7th
- April 4th
- May 9th
- June 6th
- July 11th
- August 8th
- September 5th
- October 10th
- November 7th
- December 12th
Note that the numeric representation of these dates are: 3/7 4/4, 5/9, 6/6, 7/11, 8/8, 9/5, 11/7, and 12/12. One of the doomsdays for January falls either on the 3rd for a common year, or the 4th for a leap year. The days in the even numbered months are particularly easy to remember.
Each century has an anchor day:
| Century | anchor day |
|---|---|
| 1800-1899 | Friday |
| 1900-1999 | Wednesday |
| 2000-2099 | Tuesday |
To calculate the doomsday for the year: Divide the year's last two digits by 12 using whole number math. So you have some whole number and a remainder. Add those numbers together. Now add one quarter of the remainder (without the fraction part) to that sum. Now, you this is how many days ahead the doomsday is from the anchor day.
So for 2023, we have 1 + 11 + 2. That is 14. So fourteen days ahead of Tuesday is another Tuesday. So the doomsday for 2023 is Tuesday. If the current date isn't in the list you find one that is close and you advance the days until you get to the date you want to know the day of week for.
Now all of these days of the year 2023 above fall on a Tuesday. And in particular today, September 5th, 2023 is Tuesday. Welcome to doomsday.
Posted with proof of brain