HOW TO MENTALLY CALCULATE THE DAY OF THE WEEK FOR ANY DATE.

2009-12-23 02:10:06

The Basic Steps

The basic steps for a date in the years 2000-2099 are as follows:

Example date July 13th, 2004

1. Take the last 2 digits of the year and add a quarter onto itself. (04 + 1 = 5)

2. Get the corresponding code for the month. (January = 6, February = 2, March = 2, etc. See month codes for details). July = 5

3. Take the day. (=13)

4. Add the numbers together (5 + 5 + 13 = 23)

5. Take away 7 (or multiples of 7) until a number from 1-7 is left. (23 - 21 =2)

6. This number corresponds to the day of the week. (1 = Monday, 2 = Tuesday, etc.) In this case 2 = Tuesday

The basic steps | Other points | Month codes | Leap years | Gregorian calendar | Shortcuts | Examples | Other methods | Books | Links | Whose idea?

Other points to take into account

Apart from the basic steps, other elements have to be taken into account:

• When adding a quarter of the year onto itself, If the quarter of the year is not a whole number, simply ignore the decimals. Do not round up. Therefore 27/4 = 6.75 = 6, and 2/4 = 0.5 = 0.

• Leap years: subtract 1 from the total if the month is January or February.

• Negative numbers. During the calculation you get 0 or negative numbers, just add seven until you get a number from 1-7.

• Different "centuries" *.

o 1700s add 5

o 1800s add 3

o 1900s add 1

o 2100s subtract 2

o 2200s subtract 4

(* For this method we have to consider a '00' year as part of the new century)

The basic steps | Other points | Month codes | Leap years | Gregorian calendar | Shortcuts | Examples | Other methods | Books | Links | Whose idea?

The codes for the months

At first the hardest part is learning the codes for the months. They are as follows:

Jan Feb Mar Apr. May Jun Jul Ago Sept Oct Nov Dec

6 2 2 5 0 3 5 1 4 6 2 4

Try to use some memory system to remember the codes for the months. for example, February is the 2nd month, March 2 music, etc. Try to find associations that will remind you.

If need be, you can add 7 or multiples of 7 to any of these values to help you remember them. For example, August could be 1 or 8, and as it is the 8th month, it may be easier to remember with 8 than with 1. This may be useful if you can match it with a well-known date. You could remember that the code for December is 25 (4+21), or for someone's birthday. The negative aspect of this is that you'll be taking away the 7 (or multiples) towards the end of the calculations, and you'll be working with bigger numbers.

The basic steps | Other points | Month codes | Leap years | Gregorian calendar | Shortcuts | Examples | Other methods | Books | Links | Whose idea?

Leap Years

• Remember that leap years are not always every 4 years. There are exceptions. Years that end in 00 are not leap years unless it is a multiple of 400. Therefore 1700, 1800, 1900, and 2100 are not leap years, but 2000 is.

The basic steps | Other points | Month codes | Leap years | Gregorian calendar | Shortcuts | Examples | Other methods | Books | Links | Whose idea?

The Gregorian Calendar

• The calendar as we know it only came into effect (in England) in 1752, replacing the Julian calendar. Changes included cutting 11 or more days out of the calendar and changing the first day of the year from march 21st to January 1st, and so this calculation method should not be used for dates before this changeover.
• Unfortunately, not everyone agreed to the change at the same time. The change was in fact officially enacted in 1582, but only some catholic countries actually did change at this time. After this other countries took their time before accepting the change. Great Britain in 1752, Japan in 1873 and China (the last) in 1949. In several cases, such as Germany, only some regions changed at a time, and Sweden removed the days one by one over a long time.
• The overall result of this is that for centuries, each country had its own system, and dates did not fall on the same day. if you are looking at a date, you need to take into account if it was before the changeover in that country, and take into account the 10 (or more) days removed from the calendar, the the fact that the years used to start on a different day.

The basic steps | Other points | Month codes | Leap years | Gregorian calendar | Shortcuts | Examples | Other methods | Books | Links | Whose idea?

Shortcuts

There are several shortcuts that can be used to simplify and speed up the process so that you can calculate the result almost immediately.

• When working out the year, remember that as the calendar repeats itself every 28 years within each "century", we can subtract 28 or multiples of 28 (56 or 84) so it is easier to add a quarter on to the year if it is a smaller number. Therefore 1996 is the same as 1996-84 =1912. It is much easier to add a quarter of 12 onto itself, than a quarter of 96. In this way, the greatest number you will have to work with is 27.

• When the year is a multiple of 4, such as 16, it is very easy to add a quarter (16/4=4 16+4 =20.). Some people may have problems when the number is not a multiple of 4. (e.g. 27/4). Because we do not need the decimals in the result, the easiest and quickest way is to take the nearest multiple of 4 below the number, and calculate a quarter of that, adding it onto the year. (e.g. 1927: the nearest multiple of 4 below this is 24. 24/4=6. add 6 to 27 to get 33.) Many people may find this easier than working out the division and then eliminating the decimals (27/4=6.75. eliminate the decimals to get 6. add 6 to 27 to get 33)

• It is good practice to subtract 7 or multiples of 7 at this point rather than adding on the month and the day before doing it. The same is true for the day. This is because it is easier to recognize and subtract multiples of 7 from smaller numbers.

• Simply remembering the final year code for the current year and the coming year makes instant calculations possible, as calculating the year code is the time-consuming process. For the years 2000-2003, the numbers correspond to the last digit of the year. This is a very quick method.

The basic steps | Other points | Month codes | Leap years | Gregorian calendar | Shortcuts | Examples | Other methods | Books | Links | Whose idea?

Examples

The thought process for a date such as 20/12/1967 should be as follows: (explanations are in parentheses)

67- 56 = 11

(Take multiples of 28 from the year - 84, 56 or 28)

11 + 2 = 13

(Add a quarter of the nearest multiple of 4 below the number, in this case the nearest multiple is 8, so a quarter of that is 2)

13 - 7 = 6

(Take away 7 or multiples of 7. This leaves us the year code)

December = 4

(The code for the month from the table above)

20 - 14 = 6

(Take away 7 or multiples of 7 from the day.)

6 + 4 + 6 = 16

(Add the codes for the year, the month and the day)

16+1=17

(Add 1 if the date is in the 1900s)

17 - 14 = 3

(Take away 7 or multiples of 7)

3 = Wed

(The final number indicates day of the week)

For a date in 2000, 2001, 2002 or 2003, remember that the year code is simply the last digit, so for a date in any of these years, we already know the year code.

So, to work out a date in 2000, we forget the year code: for example 4th August 2000

August = 1

(The code for the month)

1+4=5

(Add the codes for the month and the day)

5 = Friday

(The final number indicates day of the week)

The basic steps | Other points | Month codes | Leap years | Gregorian calendar | Shortcuts | Examples | Other methods | Books | Links | Whose idea?

Other methods

Doomsday

Works on the principle that the the 4/4, the 5/9, the 9/5 the 7/11 the 11/7, the 6/6 the 8/8, the 10/10 and the 12/12 always fall on the same day of the week each year. If you can work out this special day of the week for any year, then you the date you want is always close to one of the dates mentioned above. The problem is working out the special day for each year (doomsday).

"Lewis Carroll"

From Martin Gardner's The Universe in a Handkerchief (see books below): You have to divide the year by twelve to start off with. O.K. if you remember your 12 times table.

Windows 98/2000/ME/XP

Double-click on the time at the bottom right of your screen. You can then change the year and month to see the corresponding calendar. It only works for years 1980-2099

The Calendar - David Ewing Duncan

The story of the creation of the Western calendar, which is related in this book, is a story of emperors and popes, mathematicians and monks, and the growth of scientific calculation to the point where, bizarrely, our measurement of time by atomic pulses is now more accurate than time itself

The Oxford Companion to the year

The Oxford Companion to the year - Various

How our own complex calendar evolved with its irregular month lengths and its rules for when leap years occur, plus details of the calendars of many other cultures--Chinese, Hindu, Muslim, and many more-

The Universe in a Handkerchief

The Universe in a Handkerchief - Martin Gardner

This work contains puzzles and paradoxes from Lewis Carroll, whose interests ranged from inventing new games like Arithmetical Croquet, to important problems in symbolic logic and propositional calculus. (see other methods)

Mapping Time

Mapping Time - E.G.Richards

An account for the general reader of the history and underlying basis of each of the most important calendars of the world, from antiquity to modern times. There are descriptions of prehistoric calendars, of those devised by the Egyptians, the Mayans, the Aztecs and other civilizations, of the short-lived French Republican calendar, which introduced a ten-day week, and of our present-day Gregorian calendar.

How did I think of this?

• The short answer is: I didn't. I read a book written in the 1950's by Fred Barlow about genius, with some examples. One of the examples was this one. However it was in a very basic form, and he had obviously got it from a 19th century source, as the default result was for 19th century, and needed you to subtract from the final result for 20th/21st century dates. All I have done is change the 12 month codes so they work for this century, and simplified it a bit. The big change was when I read somewhere else that calendar makers only have 28 templates as the calendar repeats itself every 28 years. This allowed me to think up the rule of taking away 28 or multiples, and makes things a lot easier, avoiding large numbers.

With a little practice you should be able to work out days of the week for any date, and more importantly, you will be able to instantly work out the day of the week for coming events without having to resort to your diary or your computer. Apart from that, it's an impressive party trick.

If you find any faults or have any comments, please contact me at e-mail

Guy Rimmer