What Day of the Week Was a Given Date?

Date: 01/05/2006 at 15:27:30
From: Karen
Subject: (no subject)

Is there a simple way to figure out what day of the week any date in
history fell on?

Date: 01/06/2006 at 03:41:32
From: Doctor Minter
Subject: Re: 

Hi Karen,

What a great question!  There certainly is!  Let's do a step by step 
example for the date of July 27, 1915.

Start by assigning the months these (seemingly random) values:

  January    0
  February   3
  March      3
  April      6
  May        1
  June       4
  July       6
  August     2
  September  5
  October    0
  November   3
  December   5

If you want to impress people by being able to use this formula in 
your head, memorize these values.  Other than that, it's quite 
straightforward.

Now, label the days of the week sequentially starting with Sunday:

  Sunday     0 
  Monday     1
  Tuesday    2
  Wednesday  3
  Thursday   4
  Friday     5
  Saturday   6

Divide the last two digits of the year (i.e. 15 for 1915) by four.  
Ignore any remainder, and do not round up.  Simply drop any decimal 
places.

   15/4 = 3.75 -> 3

Add this number to the dividend (the year without the "19").  
1915 -> 15

   15 + 3 = 18

Add this to the target day (date) of the month.

   18 + 27 = 45

Now add the month value from the above list.  July's value is 6.

   45 + 6 = 51

Divide this number by 7, and note the remainder.

   51/7 = 49 r 2

The quotient is inconsequential, but the remainder value corresponds 
to the value from the list of the days of the week.  The day of the 
week that corresponds to 2 is Tuesday.

So July 27, 1915 was a Tuesday!

A short way to write out this formula is

   (year / 4) + year + day + MV
   ----------------------------
                7

where MV is the month value from the above list, year is the last two
digits only, and you remember to take only the quotient in the year/4
calculation and only the remainder in the final calculation.

There are some important notes for using this formula:

The month values (MV's) listed at the beginning correspond ONLY to 
years in the 20th century.  Thus, using these MV's will only give 
correct answers to years beginning with 19.

To find days of the week in other centuries, simply add or subtract 
from the MV list above.  For the 1800's, add 1 to each MV.  For the 
1700's, add 2 to each, for the 1600's, add 3 to each, and for the
1500's, add 4 to each.

This trend does NOT continue to the 1400's, or even to any years 
before 1582, when the calendar that we use today was originally 
adopted.  Before 1582, a different calendar was used, and this 
formula breaks down.  (You could find what day of the week a date 
prior to then WOULD HAVE been if we had always used our current 
calendar with this trend, but don't expect historical accuracy if you 
do so.)

To obtain a current or future date, subtract 1 from each MV for the 
2000's, subtract 2 from each MV for the 2100's, etc.  Since the 21st
century is relatively young, I decided to give the starting MV's for
the 20th century (the 1900's).

For any year divisible by four (i.e. Leap Year), subtract 1 (in 
addition to any other necessary additions or subtractions implemented 
by the two previous notes) from the MV's of January or February.  If 
the month of the desired date is not Jan or Feb, ignore this note.

I hope that this has been helpful.  Please feel free to write again 
if you need further assistance, or if you have any other questions.  
Thanks for using Dr. Math!

- Doctor Minter, The Math Forum
  http://mathforum.org/dr.math/