Days and Calendar Dates - Vedic Maths and Timekeeping

A good few years back, I bought a book, Figuring: The Joy of Numbers, written by Shakuntala Devi - an Indian woman whom I much admire.

One whole chapter of this book concerned itself with the Gregorian Calendar, and with a series of tables by which one could work out exactly what day a given date in the calendar would fall on, no matter what the date.

You have to memorise the contents of the following tables ...:-

Casting Out Sevens

00

07

14

21

28

Month Lookup Table

Jan	0
Feb	3
Mar	3
Apr	6
May	1
Jun	4
Jul	6
Aug	2
Sep	5
Oct	0
Nov	3
Dec	5

Here comes the fun bit ...

Year Lookup Table

a		b		c		d
00	6	00	4	00	2	00	0
04	4	04	2	04	0	04	5
08	2	08	0	08	5	08	3
12	0	12	5	12	3	12	1
16	5	16	3	16	1	16	6
20	3	20	1	20	6	20	4
24	1	24	6	24	4	24	2
28	6	28	4	28	2	28	0
32	4	32	2	32	0	32	5
36	2	36	0	36	5	36	3
40	0	40	5	40	3	40	1
44	5	44	3	44	1	44	6
48	3	48	1	48	6	48	4
52	1	52	6	52	4	52	2
56	6	56	4	56	2	56	0
60	4	60	2	60	0	60	5
64	2	64	0	64	5	64	3
68	0	68	5	68	3	68	1
72	5	72	3	72	1	72	6
76	3	76	1	76	6	76	4
80	1	80	6	80	4	80	2
84	6	84	4	84	2	84	0
88	4	88	2	88	0	88	5
92	2	92	0	92	5	92	3
96	0	96	5	96	3	96	1

Century	Table
1600, 2000, 2400, 2800, 3200, 3600, 4000 ...	a
1700, 2100, 2500, 2900, 3300, 3700, 4100 ...	b
1800, 2200, 2600, 3000, 3400, 3800, 4200 ...	c
1900, 2300, 2700, 3100, 3500, 3900, 4300 ...	d

And finally, the lookup table for the days of the week:-

Day Lookup Table

Sun	0
Mon	1
Tue	2
Wed	3
Thu	4
Fri	5
Sat	6

Using The Tables

The example we will be using throughout is 23rd March 1973.

1. Subtract the largest multiple of seven from the first table from the date.

Example: 23 - 21 = 2

2. Add the figure from the month lookup table appropriate for the month.

Example: March's number is 3:

2+3 = 5

2a. If the sum so far is 7+, cast out the sevens until you get a number less than 7.

Example: 5 is less than 7, so no sevens to be cast out.

3. Determine the year number.

3a. Look up the closest leap year that is earlier than the target year.

Example: The nearest number is 72. Since 1972 is in the 1900 century, the column is a, yielding the number 6.

3b. Add that figure to the sum calculated so far.

Example: 5 + 6 = 11.

3c. Cast out sevens again until you end up with a figure less than 7.

Example: 11 - 7 = 4.

3d. Add the difference between the target year and the nearest lowest leap year to the sum so far.

Example: 4 + 1 = 5.

3e. Cast out the sevens.

Example: 5 is less than 7, so nothing is to be subtracted here.

3f. If the date falls in January or February of an actual leap year, subtract 1 from the sum so far. NOTE: Only century years where the year is divisible by 400 are leap years. 2000 and 2400 (column a) are leap years: 2100, 2200 and 2300, not being divisible by 400, are not.

Example: 1973 is not a leap year, so nothing further is to be subtracted.

4. Look up the value in the Day Lookup Table to determine the day the target date falls on.

Example: March 23, 1973 has the final value of 5. On the day lookup table, this works out as Friday. March 23 1973 fell on a Friday.

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Where my work expands upon Shakuntala Devi's in her book is the Year Lookup Table. I have managed to expand the original year lookup table which, in Figuring: The Joy of Numbers, only covered the period 1900 - 1972. My table not only covers leap years in the period 1900 - 1996; it covers the period from the start of the 1600s and on to any arbitrary date in the future, assuming the Gregorian Calendar will still be in use, say, in the Year 3785.

This has been a lot of work for me, but the tables above should prove highly useful to anyone with an interest in the calendar, and in developing the talent for working out what day any arbitrary date falls on.

Originally posted on The Vedic Maths India Blog and The Plainclothes Clown. Based on Shakuntala Devi's Figuring: The Joy of Numbers. The Year Lookup Table above is Copyright © Alex Greene, 2011.