Sunday's Exercises - Answers

Here are the answers to Sunday's exercises:-

July 19 2019 - Friday	January 2 2016 - Saturday	September 6 2017 - Wednesday
February 11 2015 - Wednesday	March 25 2016 - Friday	August 7 2018 - Tuesday
October 13 2019 - Sunday	May 29 2015 - Friday	December 14 2017 - Thursday
June 29 2015 - Monday	April 23 2018 - Monday	November 20 2017 - Monday

Just keep practising.

Month Numbers for the 2010s Part 2 - 2015 - 2019

The previous post covered the months of the years 2010 - 2014. This article looks at the second half of the teens, and the years 2015 through to 2019.

As before, we make use of the figures for the month tables and year tables, and the method is as described in the previous post.

The unadjusted month figures are:-

Month	Month Number
January	0
February	3
March	3
April	6
May	1
June	4
July	6
August	2
September	5
October	0
November	3
December	5

The year numbers for 2010 to 2014 are:-

Year	Year Number
2015	3
2016	5
2017	6
2018	0
2019	1

And the day numbers are:-

Day Number	Day of The Week
0	Sunday
1	Monday
2	Tuesday
3	Wednesday
4	Thursday
5	Friday
6	Saturday

2016 is the leap year in this group.

The adjusted month figures for 2015 through 2019 are:-

Month	Unadjusted	2015	2016	2017	2018	2019
January	0	3	4	6	0	1
February	3	6	0	2	3	4
March	3	6	1	2	3	4
April	6	2	4	5	6	0
May	1	4	6	0	1	2
June	4	0	2	3	4	5
July	6	2	4	5	6	0
August	2	5	0	1	2	3
September	5	1	3	4	5	6
October	0	3	5	6	0	1
November	3	6	1	2	3	4
December	5	1	3	4	5	6

Other than that, the game is the same.

Practice on the following dates:-

July 19 2019	January 2 2016	September 6 2017
February 11 2015	March 25 2016	August 7 2018
October 13 2019	May 29 2015	December 14 2017
June 29 2015	April 23 2018	November 20 2017

The answers to the previous exercise are:-

July 4 2014 - Friday	January 21 2012 - Saturday	September 16 2010 - Thursday
February 13 2012 - Monday	March 13 2012 - Tuesday	August 27 2011 - Saturday
October 3 2013 - Thursday	May 4 2010 - Tuesday	December 4 2010 - Saturday
June 19 2013 - Wednesday	April 26 2010 - Monday	November 1 2010 - Monday

Month Numbers for the 2010s Part 1 - 2010 - 2014

Following on from this previous post, here's a shortcut to help you to work out what day any particular date falls on in any year between January 1 2010 and December 31 2019: the 2010s. I will do something for the 2020s later; this is to help you to work out the days that dates in the Teens fall on.

This is the guide to the first five years of the Teens, between 2010 01 01 and 2014 12 31. The second part covers the five-year period between 2015 01 01 and 2019 12 31.

The Method

The method, as explained in the older article, is simple. First, reduce the date of the month to a number below seven by removing the highest multiple of 7 from it. Thus the 23rd of a month yields the date number (23 - 21) = 2.

Second, add to this the month number, followed by the year number, as determined in the tables in the previous post. The month numbers for all years are the same:-

Month	Month Number
January	0
February	3
March	3
April	6
May	1
June	4
July	6
August	2
September	5
October	0
November	3
December	5

So, for instance, for the 23rd of September, add the month number for September (5) to the reduced date number (2); that yields 7.

Now adding the year number for the given year results in a number which can be reduced by further multiples of 7. Let's take the example of 23rd September 2014, chosen because 2014's year number is 2.

The date number + month number are 7; 7 + 2 = 9. Reducing this number yields (9 - 7) = 2.

Lastly, this final figure yields the day of the week on this lookup table.

Day Number	Day of The Week
0	Sunday
1	Monday
2	Tuesday
3	Wednesday
4	Thursday
5	Friday
6	Saturday

In the above example, 23rd September 2014 falls on a Tuesday.

The year number for each year in this decade are worked out by adding the difference between the year and the last leap year, which in this case is 2008 (before the scope of this article) and 2012. The leap year in the second article falls in 2016.

The year numbers for 2010 to 2014 are:-

Year	Year Number
2010	4
2011	5
2012	0
2013	1
2014	2

2012, being a leap year, has its own special rule: when working out a date in January and February in a leap year, after adding the month number subtract 1 before reducing the number by casting out the 7s.

Let's take 17th February 2012 (leap year: year number 0) as an example. 17 - 14 = 3; 3 + 3 = 6; 6 - 1 (for the leap year) = 5; 5 + 0 = 5. 17th February 2012 falls on a Friday.

Let's take a shortcut, now, and put the month numbers and year numbers together, preloading them before using them to work out the days any date falls on. These numbers have been reduced, where the adjusted numbers come to 7, 8 or 9 (a number reduced to -1 is changed to 6, etc).

Month	Unadjusted	2010	2011	2012	2013	2014
January	0	4	5	6	1	2
February	3	0	1	2	4	5
March	3	0	1	3	4	5
April	6	3	4	6	0	1
May	1	5	6	1	2	3
June	4	1	2	4	5	6
July	6	3	4	6	0	1
August	2	6	0	2	3	4
September	5	2	3	5	6	0
October	0	4	5	0	1	2
November	3	0	1	3	4	5
December	5	2	3	5	6	0

Don't worry! You won't have to memorise the whole table above! Just the month and year tables. The big table just contains the month and year figures already worked out for you.

Some examples using the big table:-

June 30th, 2013

30 - 28 = 2. The figure for June 2013 is 5. 2 + 5 = 7; 7 - 7 = 0. June 30 2013 fell on Sunday.

April 26th, 2012

26 - 21 = 5. The figure for April 2012 is 6. 5 + 6 = 11; 11 - 7 = 4. April 26 2012 fell on Thursday.

August 8th, 2014

8 - 7 = 1. The figure for August 2014 is 4. 4 + 1 = 5. August 8 2014 will fall on a Friday.

Now try it out for yourselves. Work out your birthdays in 2011, 2013 and 2014. Now work out your friends' or relatives' or loved ones' birthdays in 2010 and 2012. Make a game of it.

Practice on the following dates:-

July 4 2014	January 21 2012	September 16 2010
February 13 2012	March 13 2012	August 27 2011
October 3 2013	May 4 2010	December 4 2010
June 19 2013	April 26 2010	November 1 2010

Part 2 tomorrow, covering the years 2015 to 2019.

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

2016-09-15 Edit: Here's a new month table, specifically to keep track of the months of leap years.

Leap Year Month Lookup Table

Jan	6
Feb	2
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.

2016-09-15 Addendum: 3g. If you like, if the year in question is a leap year, consult the Leap Year Month Lookup Table above instead of applying 3f.

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.

++++++++++++++++++++++++++++++++++++++++

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.