Doomsday: Other Years

How to apply the Doomsday Algorithm to other years in the 1900s and 2000s

Added 1994-02-22, Updated 2017-01-03

Okay, we can do 2017. What about other years? If Doomsday is Tuesday this year, what was it last year, in 2016?

Well, you could go look it up in a calendar, but let me tell you it was a Monday. Doomsday advances by one day each year because 365 divided by 7 leaves 1 remainder. Doomsday advances two days each leap year, and we'll come back to more on that in a moment.

Let's work a couple of examples for last year, 2016, when Doomsday was Monday.

Example: what day was New Year's Eve last year?
Answer: Start with Doomsday for last year -- Doomsday 2016 was Monday. December (even) 12th was Monday, and so was the 26th. Five days later, December 31st, was Saturday. Or, if you're starting to get the hang of this, instead of "Monday + 5 = Saturday," you'll think "Monday - 2 = Saturday," which seems just a wee bit easier. Remember, all we're looking for is the day of the week. So New Year's Eve last year, 2016, was Saturday.

Example: what day of the week was New Year's Eve, 2015?
Answer: Since we were just doing examples for last year, let's try New Year's Eve, 2015 by going backwards from January 1st, 2016. Now, Doomsday 2016 was Monday, and since 2016 was a leap year, that means that January 4th, 2016 was Monday. So then January 1st, 2016 was 3 days earlier, i.e. Friday. Finally, this means that the day before, New Year's Eve, December 31st, 2015, was Thursday.

The Doomsday Algorithm is often used with people's birthdays. In order to do the Doomsday algorithm for any year in the 1900's, when most of us were born, we need to memorize the fact that Doomsday for 1900 is Wednesday. Then we do a calculation based on the number of years since 1900.

First, look at the following chart of Doomsdays:

   Sun  Mon  Tue  Wed  Thu  Fri  Sat
                 1900 1901 1902 1903
  ---- 1904 1905 1906 1907 ---- 1908
  1909 1910 1911 ---- 1912 1913 1914
  1915 ---- 1916 1917 1918 1919 ----
  1920 1921 1922 1923 ---- 1924 1925
  1926 1927 ---- 1928 1929 1930 1931
  ---- 1932 1933 1934 1935 ---- 1936
  1937 1938 1939 ---- 1940 1941 1942
  1943 ---- 1944 1945 1946 1947 ----
  1948 1949 1950 1951 ---- 1952 1953
  1954 1955 ---- 1956 1957 1958 1959
  ---- 1960 1961 1962 1963 ---- 1964
  1965 1966 1967 ---- 1968 1969 1970
  1971 ---- 1972 1973 1974 1975 ----
  1976 1977 1978 1979 ---- 1980 1981
  1982 1983 ---- 1984 1985 1986 1987
  ---- 1988 1989 1990 1991 ---- 1992
  1993 1994 1995 ---- 1996 1997 1998
  1999 ---- 2000 ...

Notice that Doomsday 1900 is Wednesday. This is the anchor for all the years in the 1900's. (Notice also that 1900 is not a leap year, so Doomsday 1900 is February 28th.) How do we remember 1900=Wednesday? Dr. Conway suggests the mnemonic "We-in-dis-day", indicative of the fact that most of us were born in the 1900's.

Now every twelve years, Doomsday advances by one. Check for yourself. In the chart above, pick a year and look ahead twelve years—down two rows and over one day. This leads to the following rule...

For any year 19YY, using the YY part of the year, calculate:

  1. the number of 12's in the YY part of the year
  2. the remainder of step 1
  3. the number of 4's in the remainder of step 1

Feel free to throw out multiples of 7 along the way if you find this easy to do.

Now we need to add the result of our calculation to 1900=Wednesday to get the Doomsday for that year. We do by this treating Wednesday as day 4. Quite easy to remember, since that's Wednesday's day of the week in the normal Sunday-to-Saturday calendar.

Example: what is Doomsday 1929?
Answer:

  1. 29 divided by 12 is 2
  2. ... remainder 5
  3. 5 divided by 4 is 1

Adding these up, we get 5+2+1=8, and we can throw out a 7 to get 1. Finally, this 1 has to be added to 1900=Wednesday, so Doomsday for 1929 is Thursday.

Example: what is Doomsday 1999?
Answer:

  1. 99 divided by 12 is 8
  2. ... remainder 3
  3. and of course 3 divided by 4 is 0

Adding these up, we get 8+3+0=11 i.e. 4. This has to be added to 1900=Wednesday, so Doomsday for 1999 is Sunday.

We should now be able to do any day in the 1900's in our head. Let's do a couple more examples...

Example: what day of the week was November 27, 1982?
Answer: 82 / 12 = 6 ... remainder 10 ... 10 / 4 = 2 ... 6 + 10 + 2 = 18 which is 4 days to be added to Wednesday (for 1900) ... so Doomsday 1982 was Sunday ... November(11) 7th was Sunday, 28th was Sunday ... November 27th 1982 was Saturday; that was the day the Doomsday Algorithm was featured on Quirks and Quarks (see Origins).

Example: what day of the week was July 20, 1969? (the date of the first landing of humans on the Moon)
Answer: 69 / 12 = 5 ... remainder 9 ... 9 / 4 = 2 ... 5 + 9 + 2 = 16 which is 2 days to be added to Wednesday (for 1900) ... so Doomsday 1969 was Friday ... July(7) 11th is Friday, 18th is Friday ... July 20th 1969 was Sunday

Increased Speed

Dr. Sidney Graham sent me the following:

Do you know Conway's method for "increased speed"? Basically, the trick is to memorize the list:

6, 11.5, 17, 23, 28, 34, ...., 84, 90, 95.5

These are the years in a century that have the same doomsday as the century year, i.e. Doomsday1900 = Doomsday1906 = Doomsday1917 etc.

The "11.5" refers to the fact that Doomsday1911 = Doomsday1900 - 1 and Doomsday1912 = Doomsday1900 + 1.

This list of years can be seen in the above table in the column under 1900. Here's that column again, all by itself:

   Sun  Mon  Tue  Wed  Thu  Fri  Sat
                 1900
                   06
                11 -- 12
                   17
                   23
                   28
                   34
                39 -- 40
                   45
                   51
                   56
                   62
                67 -- 68
                   73
                   79
                   84
                   90
                95 -- 96

Obviously, if you can memorize this list, you can increase the speed of your calculations. For some of us, that's a big IF; it reminds me of a comment someone made when first shown the entire Doomsday Algorithm:

Find the day of the week for any year in history in your head? Maybe, but only if one of the steps included in my head is telling myself "Remember where you put the printout of that page."

In any case, let's have a couple of examples:

Example: what day of the week was August 13, 1971
Answer: "67.5" means 1968 = Doomsday + 1 ... thus 1971 is Doomsday + 4 = Sunday ... August(8) 8th is Doomsday ... August 13th 1971 was a Friday

Example: what day of the week was December 24, 1973?
Answer: 73 = Doomsday ... thus 1973 is Wednesday ... December(12) 12th is Doomsday ... December 24th 1973 was a Monday

Log in