Doomsdays and Pi Day

Happy New Year!

In 2020, which is a leap year, Pi day or March 14 will fall on a Saturday. So will Sept 12, the date of the 1st International Vedic Mathematics Olympiad (IVMO 2020), which will be held in regional centers around the world.

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 Saturday.

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 Saturday in 2020.

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

Once every four years, during leap year, 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, 2020.

1. Divide the last two digits of this year, 20 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 (20) and the century code(2) → 5 + 20 + 2 = 27

3. Get the remainder when this sum is divided by 7 (seven days in a week) → 27 mod 7 = 6

4. Get the day for day code 6 → Six-a-Day is Saturday

Since Dec 12, (12/12) will fall on a Saturday, Christmas, Dec 25  which is 13 days after, will fall on a Friday. Also, Dec 30, Rizal Day, will fall on a Wednesday, and we will have a 5-day holiday weekend.

Philippine Independence was declared on June 12, 1898. What day was it? 98 div 4 is 24 so we add 24 + 98 + 5 (the century code for 1800) to get 127. And 127 divided by 7 will have a remainder of 1. Therefore, the doomsday for 1898 is “Oneday” or Monday. And June 6 was a Monday. June 12, which is six days later was a Sunday.

Note that we when solving for the year code, we can deduct multiples of 7 from every addend 24 -21 = 3;
98 – 98 = 0 and 5 -7 = -2. Thus 3 + 0 -2 = 1.