*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

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.
Really i am impressed from this post....the person who create this post he is a great human..thanks for shared this with us.i found this informative

ReplyDeleteand interesting blog so i think its very useful and knowledge able.

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vedic maths

thank you so much ...any person can understand this information at first attempt...hats off to the creator and Shakuntala Devi!!!I 'd read her book 10 years ago..

ReplyDeletehow can i find day of any date & year within 30sec ...its take too much time and i have only 30 or 40sec for exam of banking.....help me

ReplyDeleteWhen you're starting, you really need to commit those tables to memory. It just takes a lot of practice.

DeleteLet's say you want to work out what day 17th September 2016 falls on. You have to remember that the month number for September is always 5, and that the year number for 2016 is also always going to be 5. So that's 5+5 = 10.

When you're working out the number for the current date, you can just literally go from looking up Table 1 and working out what multiple of 7 to subtract to just saying "Oh, that's the 17th. The number is 3," because you'll have long ago worked out that 17-14 = 3. So add 3 to the month and year number, and that is 13.

Now you can do that casting out the sevens to the 13 too, and that comes up with 6, and you should have worked out that 6 means it's a Saturday. And so it is.

But suppose they ask you for 17 September 2018? What day will that fall on? It's a Monday, by the way, but here's how you work it out.

You just worked out that 17 September 2016 was a Saturday. You know it for a fact. But 2018 - 2016 = 2. So just add 2 to the number you worked out before, which was 13, and you get 15 for the same date in 2018.

Now take 14 from that, and you get 1. Monday. September 17 2018 falls on a Monday.

But now, they want to know what date 19th September 2007 fell on!

Start with 17 September 2016, your first number. That was a 13. Add 2 to get the number 15 for 19 September 2016. Now take away 9, because that's how many years there are between 19 September 2016 and 19th September 2007. So you've got a 6. But wait - you've also got to take away 3, because 2016, 2012 and 2008 are leap years. Always remember those leap years, because they generally take away 2 instead of 1.

So you've now got a 3 for September 19 2007. It's a Wednesday. Check it out.

If you want to impress, commit these tables to memory. You'll be working it out in your head so quickly, with practice. But it does take practice. Lots of it. You literally have to be doing things like looking at a random date on a television programme or in a book ("Gertrude Norris was born in Lancashire on August 3rd, 1937") and trying to work out what day of the week, Tuesday, that fell on.