Doomsdays and Pi Day 2021

Doomsday and Pi Day

Happy New Year!

In 2021, Pi day or March 14 will fall on a Sunday, that year’s doomsday. So will Valentine’s Day Feb 14 and the Fourth of July, the American Independence Day.

There are easy-to-remember dates each month that will fall on the same day as the year’s doomsday. The term came from the Doomsday Algorithm developed by British mathematician John Conway to determine the day of the week for any given date.

For even numbered months, double dates April 4 (4/4), June 6 (or 6/6), August 8 (or 8/8), Oct 10 (or 10/10) and December 12 (or 12/12) will also fall on a Sunday..

If we would think of “a friend working from 9 to 5 in 7-11”, we can also easily remember that May 9 (or 5/9), July 11 (or 7/11), Sept 5 (or 9/5) and Nov 7 (or 11/7) will also fall on a Sunday in 2021.

The last day of February 28, or Feb 29 during leap years are also doomsdays.

Once every 4 years, during leap years, doomsday will be on Jan 4, while for the remaining 3 ordinary years, it will be Jan 3.

Before we solve for the doomsday for a given year, we must remember the day number codes and the century codes.

Number          Day                        Mnenomic
       0             Sunday              Noneday or Nunday
       1             Monday             Oneday
       2             Tuesday            Twosday
       3             Wednesday       Treblesday
       4             Thursday           Foursday
       5             Friday                Fiveday
       6             Saturday            Six-a-day

Century codes
1500            1600         1700        1800
1900            2000         2100        2200
2300            2400         2500        2600
3 (Wed)     2 (Tues)     0(Sun)      5(Fri)

Here are the simple steps to follow to determine the doomsday for the year, 2021.

1. Divide the last two digits of this year, 21 by 4 to get 5 which is the number of leap years after the century year 2000.

2. To this, add the last two digits of the year (21) and the century code, 2 (remember Y2K) → 5 + 21 + 2 = 28

3. Get the remainder when this sum is divided by 7 (seven days in a week) → 28 mod 7 = 0

4. Get the day for day code 0 → NoneDay is Sunday

Note that we when solving for the year code, we can deduct multiples of 7 or cast out 7s from the addends: for  5 + 21 + 2, we can cast out 21 and 5 + 2 to get the day code 0.

Since Dec 12, 2021 (12/12) will fall on a Sunday, Christmas, Dec 25, which is 13 days after, will fall on a Saturday.  Also, Dec 30, Rizal Day, will fall on a Thursday, and we will have a 4-day holiday weekend.