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.
In 2015, this special day of the week, which Conway calls "Doomsday,"
was a Saturday.
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 9/5, 7/11, 5/9 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.
Alternatively, you can use the Doomsday for the previous year
to handle January and February, without worrying about leap years.
Simply note that 1/2 and 2/6 fall on the Doomsday for the previous
In 2015, which is a not leap year, therefore, the following dates fall
on Doomsday (Saturday): 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.
When was Valentine's day? Since this is a not leap year, 2/0, 2/7 and
2/14 are Saturdays. So, Valentine's day (2/14) also fell on a Saturday.
On what date did Labor Day fall in 2015? Labor Day is the first Monday
in September. If 9/5 was a Saturday, then 9/7 was a Monday, and this
must have been Labor Day.
Practice: On what date did Thanksgiving fall in 2015? Thanksgiving is
the fourth Thursday of November. You figure it out, then check
with a calendar to see if you were 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. (This is a new method, devised by Mike
Walters, that is easier than the method that John Conway originally
If the year is 20xx, is xx even? If if is, set A=xx; if it is odd, set
Set B=A/2 (A is always even so you can do this exactly).
If B is even set C=B; if it is odd, set C=B+11 (this is the same thing
you did in the first step). C will be an even number.
Divide C by 7 and compute the remainder. Call this remainder R.
Count R days backwards starting from Tuesday (which
is the special Doomsday that applies to this century). This gives you
the Doomsday for the year 20xx. From this point on, just use Part 1.
Example: What was Doomsday in 2015? Well, xx=15, which is odd, so
A=15+11=26. B=A/2=13. B is odd so C=B+11=24. If we divide C=24 by 7, we
get 21 with remainder R=3. Count 3 days backwards from Tuesday
to get Saturday. Doomsday in 2015 was a Saturday (a fact we used in Part
Example: The World Trade Center and Pentagon suffered terrorist attacks
on September 11, 2001. xx=1, which is odd, so A=12. B=A/2=6, which is
even, so C=6. The remainder when dividing 6 by 7 is 6, so counting 6
days backwards from Tuesday (or equivalently, counting 1 day forwards)
tells us that doomsday in 2001 was a Wednesday. Therefore, 9/5 was a
Wednesday, 9/12 was a Wednesday, and 9/11 was a Tuesday.
In the 20th century, use the same rule, except count backwards from Wednesday
instead of Tuesday. Wednesday is the special doomsday day for
the 20th century.
Example: On what day of the week did D-Day, June 6, 1944, fall? Well,
44 is even so A=44, B= 22 and since B is even, C= 22. The remainder when
dividing C by 7 is 1 so R=1. In the 20th century count 1 day backwards
from Wednesday 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. Hint: This is also a 20th century date.
Practice: On what day of the week were you born? Calculate it using the
Doomsday rule and check it on a calendar or (if you already know it)
with your memory.
The Gregorian calendar, which is our civil calendar, was introduced in
1582 (1752 in English-speaking countries, and not until 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
The only thing that changes in other centuries is that instead of using
Tuesday for the century doomsday as in Part 2 (for the 21st century), 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.
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: xx=76, which is even, so A=xx and B=A/2=38, which is also
even. So C=38, and C/7=35 Remainder 3 and R=3. The century doomsday for
17xx is Sunday, so counting backwards 3 days we find that doomsday for
1776 was a Thursday. 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
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 the Julian Doomsday as follows: xx= 82
which is even, so A=82 and B=41. B is odd, so C=B+11=52. C/7=7 Remainder
3 so R=3. cc=15 which is 2 weeks and 1 day, so we count 1 day backwards
from Sunday to find that the (Julian) century doomsday for 15xx is
Saturday, and since R=3 count another 3 days backwards from Saturday to
find that the (Julian) doomsday for 15xx is Wednesday.
The last day of the old Julian calendar was October 4, 1582. Since
10/10/1582 (Julian) was a Wednesday, 10/3/1582 was also 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 R=3 that we just calculated
and count 3 days backwards from Wednesday (the Gregorian century
doomsday for the 15xx dates) 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 (Gregorian), five days later, was a
Friday, which is 1 day later than Thursday, 10/4/1582 (Julian).
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.)
Note: I wrote above, "if there were such a date as
10/10/1582." Actually, we can calculate backwards from the actual date
of introduction of the Gregorian calendar using the Gregorian rules if
we wish, and we designate such dates as being on the Gregorian Proleptic
Calendar. "Proleptic" just means "before this calendar was officially
introduced, but using the same calculation rules".
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
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
Conway's original method, and not the method described here. However,
they give identical results.