# Perpetual Calendar

Masaganang Bagong Taon sa Inyong Lahat!

Beginning this year MATH-Inic Philippines in partnership with Palawan Pawnshop-Express Pera Padala will post a “Math Tip for the Week” in our websites and Facebook pages.

We will start with techniques which can be used in everyday life: in sari-sari stores, in the market, in public transport, in the kitchen and even in school. We will try to show that most computations can be performed easily without the use of calculators or pencil and paper.

Hopefully we can demonstrate that MATH can be fun, fast and easy so that students will not avoid their MATH classes and STEM courses.

Given the decreasing number of traditional printed calendars given by business establishments these past years, our New year’s gift to our readers is a perpetual calendar based on the **Doomsday Algorithm** developed by British Mathematician John Conway. It can be used to determine the day of the week for any given date using easy to remember dates each month.

For me this calendar is very important because I always want to know on what days of the week my birthday, All Saint’s day and Christmas Day will fall.

The **Doomsday** for 2022 is **Monday**.

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 Monday.

If we would think of “**a friend working from 9AM to 5PM 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 Monday in 2022.

The last day of February, the 28th in ordinary years, or the 29th during leap years are also **Doomsdays.** So March 14, 2022 which to Math enthusiasts is **Pi-Day**, will also fall on a Monday like this year’s Valentine’s Day, Feb 14 because 2022 is not a leap year.

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**.

Now I know that since Sept 5 (9/5) this year will be a Monday, my birthday Sept, 26 (5 + 21) will also be a Monday. With Nov 7(11/7) being a Monday, Nov 1 will be a Tuesday. Also, since Dec 12(12/12) is a Monday, Dec 25 (12 + 13), 2022 will be a Sunday.

Before we solve for the 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, 2022.

1. Divide the last two digits of this year, 22 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 (22) and the century code, 2 (remember Y**2**K) → 5 + 22 + 2 = 29

3. Get the remainder when this sum is divided by 7 (seven days in a week) → 29 mod 7 = 1

4. Get the day for day code 1 → OneDay is Monday

Note that we when solving for the year code, we can deduct multiples of 7 or cast out 7s from the addends: for 5 + 22 + 2, we can cast out 5 + 2 and to deduct 21 from 22 to get the day code 1.