As today is ‘Friday the 13th’ we thought we’d introduce a fun little exercise in calculating the day of the week - in your head. If you are superstitious and spending the day in bed to avoid any bad things happening, you can work out in your head when you will next need to spend a ‘horizontal’ day. (This definitely puts a new spin on mental health day…)
There are lots of ways to do this, but the one method I found (on the Internet) that tickled my fancy is the ‘Doomsday Algorithm’. Besides the formula, all you need to memorize is a single Doomsday date for each month and your year's anchor date. They're quite easy. In any given year, 4/4, 6/6, 8/8, 10/10, and 12/12 fall on the same day of the week -- the Doomsday. Conveniently, the last day of February (the 28th in a regular year or the 29th if it's a leap year) also falls on this day. 5/9, 9/5, 7/11, and 11/7 fall on the Doomsday as well.
Here’s a graphic for the Doomsday numbers.
You’ll also need to remember your year’s anchor day. Here’s a graph for that – Tuesday for the 2000’s.
This rule allows you to mentally calculate the day of the week for any date. Here's the simplified version:
Anchor Day: First, memorize the anchor days for centuries. For the 1900s, the anchor day is Tuesday. For the 2000s, it's Sunday.
Doomsday for the Century: Find the doomsday for the century of the given year. You can do this by taking the last two digits of the year, dividing by 4, and adding the result to the anchor day.
Doomsday for the Year: Find the doomsday for the specific year using a reference day. Conway suggests using dates that always fall on the same doomsday each year. One such date is March 0 (yes, March 0), which is always February 28 or 29. Find the weekday for March 0 in the same year and use that as a reference.
Count the Days: Count the number of days between the reference day and the target day. Adjust for any multiples of 7.
The remainder will give you the day of the week.
Now, let's work through an example for Friday the 13th of August 2021:
Century Anchor Day: For the 2000s, the anchor day is Sunday.
Doomsday for the Century (21): 21÷4=5.25. Add this to the anchor day (Sunday + 5.25 = Friday.25). Round down to get Friday.
Doomsday for the Year (21): Find the day for March 0, 2021. Let's say it's a Sunday.
Count the Days to August 13: March 0 to August 13 is 166 days.
166÷7=23R5. Add 5 to Sunday, and you get Friday.
Therefore, according to the Doomsday Rule, Friday the 13th of August 2021 falls on a Friday.
