How to compute the day of the week for any modern date
quickly in your head by the "Fourth of July" method
------------------------------------------------------

News flash: I have come up with another method for computing
the day of the week.  See my web site for details.

Some basic facts:

April, June, September, and December each have 30 days.
February usually has 28, but has a 29th in leap years.
All the other months have 31 days.

Every fourth year is a leap year.  Century years are
usually not (1800 and 1900 weren't), but 2000 was.


Since there are seven days of the week, anybody can easily
visualize the full calendar for any given year by just knowing
the calendars for seven of the months: May through August
and October through December.

There is an easy way to do this, and that is to memorize one date in
each of these months, selecting those dates so that all of them will
be on the same day of the week.  The particular day of the week will
change from year to year, but in any given year the chosen dates will
fall on the same day of the week.  Use the birthdays of family and friends
where possible -- you don't have to use the same dates as I do.  (But
if your key date in July is not the 4th, 11th, 18th, or 25th, you'll
have to adjust the rest of this technique to match your choice.)

The dates that I keep memorized are these:

	May 16th (my brother's birthday)
	June 6th (D-Day)
	July 4th (Independence Day in the U.S.)
	August 1st
	October 10th (10/10)
	November 7th (birthday of two significant people in my life)
	December 26th (Boxing Day)

All of these are Thursdays in 2002 and Fridays in 2003.

For January, February, March, April, and September, I remember that
they always have the same calendars as later months, apart from the
number of days in the month.

			non-leap year	leap year
			-------------	---------
	January		October		July
	February	November	August
	March			November
	April			July
	September		December


Figuring out the day of the week for any other date is pretty
straightforward.  You just add or subtract multiples of 7 from
the key date in the month to get within 7 days of the date in
question, and then work forward or backwards on the weekdays.

For example, August 16th, 2003:

	The key date in August is the first of the month, which
	has to be a Friday.  Two weeks later, the 15th is also
	a Friday.  So I will turn forty on a Saturday.


The second part of the technique is knowing how to figure the key
day of the week for a given year.  This is also easy, and all you
really have to memorize is the key day of the week for these centuries:

	1700's	Sunday
	1800's	Friday
	1900's	Wednesday
	2000's	Tuesday
	2100's	Sunday again (and the cycle repeats forever)

And since 2000 was a leap year, you can treat dates in 2000-2099
as if they were years 100-199 in the 1900's.  So the one thing
you really have to know is that July 4th, 1900, was a Wednesday.

(This scheme works for dates in the Gregorian calendar, which was
 adopted in the English-speaking world in September 1752.  Calculations
 before that date in the old Julian calendar are too tricky to do in
 your head.)

To calculate the key day of the week within a century, take the
last two digits of the year in question, and compute

	the quotient of division by 12
	the remainder of division by 12
	the quotient of that remainder, divided by 4

Add these three up, and then add that sum to the century's day of
the week.  This yields the key day of the week for that year.

Example:  What day of the week was 10/29/1929?

	1929 = 1900 + 29
	29 = 2 * 12 + 5, and 5 / 4 = 1
	2 + 5 + 1 = 8
	Wednesday + 8 = Wednesday + 1 = Thursday
	October's key date is 10/10; 10/29 is 19 days later.
	Thursday + 19 = Thursday + 5 = Tuesday

	(10/29/1929 was "Black Tuesday" on Wall Street).


Example:  What day of the week was the first moon landing (7/20/1969?)

	1969 = 1900 + 69
	69 = 5 * 12 + 9, and 9 / 4 = 2
	5 + 9 + 2 = 16
	Wednesday + 16 = Wednesday + 2 = Friday
	July's key date is the 4th; 7/20 is 16 days later
	Friday + 16 = Friday + 2 = Sunday


Example:  What day of the week was the Declaration of Independence signed?

	1776 = 1700 + 76
	76 = 6 * 12 + 4, and 4 / 4 = 1
	6 + 4 + 1 = 11
	Sunday + 11 = Sunday + 4 = Thursday
	The fourth of July is the key date, so it was a Thursday.


Note that this calculation has a cycle of 84 years, so
1784, 1884, and 1984 can be also be used as base years.
(Just remember Orwell's "1984".) For dates in the early 2000's,
one can subtract 2000, add 16, and treat it as a date in the
early 1900's.

Example:  What day of the week was Clinton's first inauguration (1/20/1992)?

	1992 = 1984 + 8
	8 = 0 * 12 + 8, and 8 / 4 = 2
	0 + 8 + 2 = 10
	Wednesday + 10 = Wednesday + 3 = Saturday
	1992 was a leap year, so January matched July, so 1/4 is the key date
	Two weeks later, the 18th was also a Saturday.
	So the 20th was a Monday.


Of course, for recent and upcoming years, I just remember these
Fourths of July:

	2000	Tuesday
	2001	Wednesday
	2002	Thursday
	2003	Friday
	2004	Sunday
	2005	Monday