What is the day of the week, given any date?

This is really a nice trick. You can easily calculate the day of the
week, given any date in history, and with a little practice you can even
do it in your head. The method is based on one developed by John Horton
Conway, and is described in *Winning Ways,* a book that he wrote with
Berlekamp and Guy. It is described in Volume 2.

The secret of the method is to have a way of knowing the day of the week
for one day in each month of the year. Conway's method uses the fact that
the following dates *always* fall on the same day of the week in any
given year. They are easy to memorize, and once one has this down pat, some
simple calculations allow you to do this for any year. These are the dates
that always fall on the same day of the week.

This year, this special day of the week, which Conway calls *"Doomsday,"*
is a Friday.

4/4, 6/6, 8/8, 10/10 and 12/12 always fall on the same day of the week (Doomsday)
in any year.

If you memorize the phrase "I went to my nine-to-five job at the seven-eleven,"
you can also remember easily that 5/9, 9/5, 7/11 and 11/7 also fall on Doomsday.

Also, 3/0 (the zeroth day of March, i.e, the last day of February) falls
on Doomsday.

January and February are complicated by the existence of Leap Years. In
ordinary years, 2/0 (the last day of January) also falls on Doomsday, as
does 1/3; in Leap Years, 2/1 and 1/4 fall on Doomsday.

In 1997, which is not a leap year, therefore, the following dates fall on
Doomsday (Friday): 1/3, 2/0 (1/31), 3/0 (2/28), 4/4, 5/9, 6/6, 7/11, 8/8,
9/5, 10/10, 11/7 and 12/12.

So, when is Christmas this year? If 12/12 is a Friday, then so are 12/19
and 12/26, so 12/25 has to be a Thursday.

When is Valentine's day? Since this is a not leap year, 2/0, 2/7 and 2/14
are Fridays. So, Valentine's day (2/14) also falls on a Friday.

On what date does Labor Day fall this year? Labor Day is the first Monday
in September. If 9/5 is a Friday, then 9/1 is a Monday, and this must be
Labor Day.

Practice: On what date does Thanksgiving fall this year? Thanksgiving is
the *fourth* Thursday of November. You figure it out, then check with
a calendar to see if you were right.

Practice: On what day of the week were you born? Calculate it, and check
with a calendar (or with your parents). Did you get it right?

The next and hardest part of the trick (because it requires a small amount
of calculation) is to determine Doomsday for the year in question. Here's
how to do it.

If the year is 19xx, divide xx by 12 to get a quotient Q and a remainder
R;

Divide the remainder R by 4 to get another quotient S (forget the new remainder,
it is not used).

Add Q, R and S together, and count that many days starting from *Wednesday*
(which is the special Doomsday that applies to this century). This gives
you the Doomsday for the year 19xx. From this point on, just use Part 1.

Example: This year is 1997. 97/12 = 8 remainder 1 so Q=8, R=1 and S=0. Nine
days from Wednesday is a Friday, so in 1997, Doomsday is Friday (which we
already said).

Example: On what day of the week did D-Day, June 6, 1944, fall? Well, 44/12
= 3 remainder 8, and 8/4 = 2 with remainder 0 which we forget. 3+8+2=13,
and counting 13 days from Wednesday is the same as counting -1 day, so Doomsday
for 1944 is a Tuesday. Since 6/6 (June 6) is June's magic day, we now know
that June 6, 1944 was a Tuesday.

Practice: On what day of the week was Pearl Harbor bombed? It was December
7, 1941.

The Gregorian calendar, which is our civil calendar, was introduced in 1582
(1752 in English-speaking countries, and only in 1919 in Russia). So one
has to know whether the Gregorian or the old Julian calendar is being used.
The rule in this section applies only to the Gregorian Calendar.

The only thing that changes in other centuries is that instead of using
Wednesday as in Part 2, we use another day that depends on the century.
This *century day *cycles over 4 centuries, so that it is the same
in 16xx, 20xx, 24xx etc. Specifically,

In years 15xx, 19xx, 23xx, etc., use Wednesday

In years 16xx, 20xx, 24xx, etc., use Tuesday

In years 17xx, 21xx, 25xx, etc., use Sunday

In years 18xx, 22xx, 26xx, etc., use Friday

Example: On what day of the week did July 4, 1776 fall? First, calculate
Doomsday: 76/12 = 6 remainder 4; 4/4 = 1 remainder 0 (forget the 0). 6+4+1=11
and counting 11 days from Sunday, which is the Doomsday for years 17xx,
we get Thursday, which is Doomsday for 1776. Now July 11 is 7/11, which
is a Thursday, so July 4, which is 1 week earlier, is also a Thursday. The
Declaration of Independence was signed on a Thursday.

Practice: The Civil War of the United States opened with the firing on Fort
Sumter, which took place on April 12, 1861. What day of the week was that?

Finally, the same principles can be used if the date is on the old Julian
Calendar, which was introduced by Julius Caesar some 2000+ years ago. The
only difference is that the different leap year rule of the Julian calendar
means that the rule given in Part 3 has to be modified. In years ccxx on
the Julian calendar, we get the century Doomsday by *subtracting* cc
from Sunday (i.e., counting back one day for each century).

Example: In 1582 we find that the *Julian* Doomsday is as follows:
82/12 = 6 remainder 10; 10/4 = 2 forget the remainder. 6+10+2 = 18. Sunday
+ 18 - cc = Sunday+18-15 = Sunday+3 so count 3 days forward from Sunday
to find Wednesday.

The last day of the old Julian calendar was October 4. Since 10/10/1582
(Julian) is a Wednesday, so is 10/3/1582 is a Wednesday, and the next day,
October 4, 1582, was a Thursday.

The next day, October 15, 1582 (Gregorian), was the first day of the new
Gregorian calendar. Take the number 18 that we just calculated and count
18 days from Wednesday to get Gregorian Doomsday: That gives us a Sunday.
Now 10/10/1582 (Gregorian) would have been a Sunday if there were such a
date...So 10/15/1582, five days later, was a Friday.

**Note that** this is the day after Thursday. This is important. So far
as we know, the weekly cycle of the days of the week has not been broken
for thousands of years.

We have found that Thursday, October 4, 1582 (Julian) was followed by Friday,
October 15, 1582 (Gregorian).

People complained that 10 days were missing from their lives!

Practice: September 2, 1752 (Julian) was followed in the English-speaking
world by September 14, 1752 (Gregorian). On what day of the week did each
fall? (Do the calculations separately and verify that the weekly cycle was
not broken when the calendars changed.)

A related page can be found at How
to determine the day of the week, given the date.

This JavaScript example calculates the day of the week on the Gregorian
calendar for any date in the twentieth century. For date mm/dd/yy in this
century, enter mm, dd, yy below and click "compute." To use it,
you have to be using a JavaScript-aware browser such as Netscape v. 2.0
or later, or Microsoft Explorer. You may use it for practice.

Month mm |
Day dd |
Year 19yy |
Doomsday |
For Month |
DayOfWeek | |

You can use the **Document Source** function in the **View** menu
to look at the source of this HTML document (if you wish). In the source,
you'll see various math and formatting functions using the JavaScript language.

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