Doomsday Algorithm
The Doomsday Algorithm gives the day of the week for any date (and you can do it in your head).
Revised 2009-02-28, with examples for 2009.
Contents
To learn the Doomsday Algorithm, read the following sections, in the order indicated.
Use the handy navigation links at the right to jump around.
February 28/29, the last day of the February, is known as "Doomsday"
Even months are April, June, August, October, and December (months 4, 6, 8, 10, and 12)
Odd months are March, May, July, September, and November (months 3, 5, 7, 9, and 11)
2008 calendar shows the current year in calendar form, highlighting the Doomsday in each month
Other years explains how to apply the Doomsday Algorithm to other years
Other centuries extends the Doomsday Algorithm to other centuries
The Hand is Dr. Conway's shortcut method
Origins describes the creation of the Doomsday Algorithm by Dr. John Horton Conway
Links are provided to other resources on the Web for additional information
Have fun!
February 28/29
To use the Doomsday Algorithm in any year, we first need to know the Doomsday for that year.
Doomsday is February 28 or 29. In other words, Doomsday is always the last day of February. In normal years, Doomsday is February 28, and in leap years, Doomsday is February 29.
In 2009, which is not a leap year, the last day of February is Saturday the 28th.
Once we know Doomsday, it's pretty easy to get the day of the week for any day in February. This is done by adding and subtracting, using multiples of 7, and you should be comfortable doing this in your head, otherwise the rest of the algorithm will give you trouble! Luckily, most people, through practice or whatever, are good at mentally picturing a month if they have something to anchor it on, and Doomsday is this anchor. For February, it's always the 28th in normal years, and the 29th in leap years.
Example: what was this year's Valentine's Day, February 14th?
Answer: Doomsday 2009 is
Saturday the 28th of February. So one week earlier, the 21st is also
Saturday. Another week earlier is
Saturday the 14th. So Valentine's Day 2009 is a
Saturday.
Example: what was this year's Groundhog day, February 2nd?
Answer: Doomsday 2009 is
Saturday the 28th...
Saturday the 21st...
Saturday the 14th...
Saturday the 7th... and then we have to go five days back, to get from
the 7th to the 2nd. So Groundhog Day, February 2nd, is
Monday this year.
If going back five days is hard (and it often is, especially looking back over a weekend), there's a little trick we can use here. Going two days forward gives the same day of the week as five days back. So if February 7th is Saturday, then two days forward is Monday the 9th, which is the same day of the week as seven days earlier, Monday the 2nd. Remember, all we're after is the day of the week, so "-5" is the same as "+2" but "+2" is usually easier to do.
Even Months
Okay, the last day of February is Doomsday. Once we know what day of the week Doomsday is, we immediately know the day of the week of certain other days in the year. There are actually 52 (or 53) other Doomsdays each year, all on the same day of the week as "the" Doomsday at the end of February.
So each month has a special day which we remember, because it is on the same day of the week as the Doomsday at the end of February. Just keep in mind that the entire year is determined by the Doomsday at the end of February, and that all the other Doomsdays within the year are on the same day of the week.
Let's begin with the even months. These are months 2, 4, 6, 8, 10, and 12, i.e. February, April, June, August, October, and December. Actually, we never do February this way, because it's special, and we've already covered it.
For even months (not including February), the Nth of that month is a Doomsday (i.e. the same day of the week as the last day in February). This is a delightful coincidence, and it's so easy to remember:
- April 4th is a Doomsday
- June 6th is a Doomsday
- August 8th is a Doomsday
- October 10th is a Doomsday
- December 12th is a Doomsday
Neat, eh? Now we can simply work our way around any even month based on its Doomsday.
Example: what is this year's Christmas Day, December 25th?
Answer: Doomsday 2009 is
Saturday. So December (even month) 12th is the Doomsday for December, so it's also
Saturday. Two weeks later, December 26th is also
Saturday, so Christmas this year is
Friday December 25th. Easy!
In fact, after you do the Doomsday algorithm often enough, you just
start remembering things like
Christmas is always the day before Doomsday.
Example: what is this year's Canadian Thanksgiving Day,
the second Monday in October?
Answer: Doomsday 2009 is
Saturday. So October (even) 10th is
Saturday, and so
two days later, October
12th is
Monday. This has to be the
second Monday of October, since a week earlier is October
5th, but a week earlier than that is in September.
So the Canadian Thanksgiving, the second Monday
in October, is Monday,
October 12th.
Odd Months
Now let's do the odd months—months 1, 3, 5, 7, 9, and 11, i.e. January, March, May, July, September, and November.
Skip January and March for a moment.
Consider the following mnemonic phrase:
I work 9-5 at the 7-11
"Nine to five" is a common working day, and 7-Eleven is a chain of convenience stores. The phrase means:
- for the 9th month, Doomsday is the 5th
- for the 5th month, Doomsday is the 9th
- for the 7th month, Doomsday is the 11th
- for the 11th month, Doomsday is the 7th
This gives us Doomsday for May, July, September, and November. Now we just work our way around again within each month, using Doomsday for that month.
Example: what day is this year's July 4th?
Answer: Doomsday 2009 is
Saturday. The Doomsday for July (7th month) 11th is
Saturday. So one week earlier, July 4th is also
Saturday.
In fact, after you do the Doomsday algorithm often enough, you just
start remembering things like
July 4th is always Doomsday.
Example: what is this year's Labour Day,
the first Monday of September?
Answer: Doomsday 2009 is
Saturday. September (9th month) 5th is
Saturday. Going backwards from Saturday the 5th, we reach September
1st on Tuesday. The day before, Monday, is actually August 31st.
So to get to the first Monday in September, we have to go forward from Saturday the 5th to Monday the 7th.
Labour Day this year, the first Monday of September, is September
7th.
Now March.
Doomsday, the last day of February, is often also called the "0th" of March. You might have to think about that for a moment, until you realize that the next day is the 1st of March. So if the "0th" of March is Doomsday, then the 7th of March, exactly one week after the last day of February, no matter whether it's the 28th or 29th, is also Doomsday.
Example: what day is this year's St. Patrick's Day, March 17th?
Answer: Doomsday 2009 is
Saturday. March "0th" is
Saturday. March 7th is
Saturday. March 14th is
Saturday. Go three days forward, to get to
Tuesday, March 17th.
Finally, we have to be able to do January.
The easiest way to calculate January's Doomsday was described to me by reader Bob Goddard:
It's January 3rd three years out of four, the non-leap years. It's January 4th only in the fourth year, the years divisible by 4.
This is so much simpler than what I had before (which involved January 31st and "January 32nd"). Why couldn't I have seen the simple way?!
Example: what was this year's New Year's Day (January 1st)?
Answer: Doomsday 2009 is
Saturday, and since this year
is not a leap year, January
3rd is
Saturday. Go back two days, and January 1st is
Thursday. Simple, eh? Thanks, Bob.
2008 calendar
If you've worked your way through the rules but have trouble remembering them, it may help to see them in calendar form. Here are links to single-page versions of the Doomsday Calendar (the first two are actually GIFs; sorry 'bout that) suitable for printing:
Here's the Doomsday Calendar for 2009 with all the Doomsdays highlighted:
Doomsday Calendar for 2009
1.Jan(3rd/non-leap) 2.Feb(29th/leap)
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 3 1 2 3 4 5 6 7
4 5 6 7 8 9 10 8 9 10 11 12 13 14
11 12 13 14 15 16 17 15 16 17 18 19 20 21
18 19 20 21 22 23 24 22 23 24 25 26 27 28
25 26 27 28 29 30 31
3.Mar(7th) 4.Apr(4th)
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 3 4 5 6 7 1 2 3 4
8 9 10 11 12 13 14 5 6 7 8 9 10 11
15 16 17 18 19 20 21 12 13 14 15 16 17 18
22 23 24 25 26 27 28 19 20 21 22 23 24 25
29 30 31 26 27 28 29 30
5.May(9th) 6.Jun(6th)
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 1 2 3 4 5 6
3 4 5 6 7 8 9 7 8 9 10 11 12 13
10 11 12 13 14 15 16 14 15 16 17 18 19 20
17 18 19 20 21 22 23 21 22 23 24 25 26 27
24 25 26 27 28 29 30 28 29 30
31
7.Jul(11th) 8.Aug(8th)
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 3 4 1
5 6 7 8 9 10 11 2 3 4 5 6 7 8
12 13 14 15 16 17 18 9 10 11 12 13 14 15
19 20 21 22 23 24 25 16 17 18 19 20 21 22
26 27 28 29 30 31 23 24 25 26 27 28 29
30 31
9.Sep(5th) 10.Oct(10th)
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 3 4 5 1 2 3
6 7 8 9 10 11 12 4 5 6 7 8 9 10
13 14 15 16 17 18 19 11 12 13 14 15 16 17
20 21 22 23 24 25 26 18 19 20 21 22 23 24
27 28 29 30 25 26 27 28 29 30 31
11.Nov(7th) 12.Dec(12th)
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 3 4 5 6 7 1 2 3 4 5
8 9 10 11 12 13 14 6 7 8 9 10 11 12
15 16 17 18 19 20 21 13 14 15 16 17 18 19
22 23 24 25 26 27 28 20 21 22 23 24 25 26
29 30 27 28 29 30 31
Other Years
Okay, we can do 2009. What about other years? If Doomsday is Saturday this year, what was it last year, in 2008?
Well, you could go look it up in a calendar, but let me tell you it was a Friday. 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, 2008, when Doomsday was Friday.
Example: what day was New Year's Eve last year?
Answer: Start with Doomsday for last year -- Doomsday
2008 was
Friday. December (even) 12th was
Friday, and so was the 26th.
Five days later, December 31st, was
Wednesday. Or, if you're starting to get the hang of this,
instead of
"Friday + 5 =
Wednesday," you'll think
"Friday - 2 =
Wednesday," 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,
2008, was
Wednesday.
Example: what day of the week was New Year's Eve,
2007?
Answer: Since we were just doing examples for last year,
and since we know that last year's Doomsday was
Friday, let's try New Year's Eve,
2007 by going backwards from January 1,
2008. Now, Doomsday
2008 was
Friday, and since
2008 was a leap year, that means that January 4th,
2008 was
Friday. So then January 1st,
2008 is three days earlier, i.e.
Tuesday. Finally, this means that the day before, New Year's Eve, December 31st,
2007, has to be
Monday.
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:
- the number of 12's in the YY part of the year
- the remainder of step 1
- 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:
- 29 divided by 12 is 2
- ... remainder 5
- 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:
- 99 divided by 12 is 8
- ... remainder 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?
(see Origins below)
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 is Sunday, 28th is Sunday
... November 27th 1982 was Saturday (as all regular listeners of Q&Q know).
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 (see Links below) 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
Other Centuries
In Other years, we learned that Doomsday for 1900 was Wednesday. What is Doomsday for other centuries?
Let's start with the 21st century, i.e. the 2000's.
The 2000's
Well, it turns out the 2000's are real easy. Recall the chart we were looking at earlier. Here it is again, extended into the 2000's a few years...
Sun Mon Tue Wed Thu Fri Sat 1999 ---- 2000 2001 2002 2003 ---- 2004 2005 2006 2007 ---- 2008 2009 2010 2011 ---- 2012 2013 2014 2015 ---- 2016 2017 2018 2019 ...
Notice that Doomsday for 2000 is Tuesday, i.e. "2000=Tue". This is the mnemonic that helps us anchor the other years in this century.
Remember the formula we learned for the 1900's, where we got the multiples of 12, kept the remainder, and added the number of 4's in the remainder? That still works, we just apply it to this century with Tuesday as the Doomsday for the 2000's.
Let's work through a couple of examples.
Example: what day of the week is May 29, 2017?
(That would have been
John F. Kennedy's 100th birthday, had he lived.)
Answer: 17 / 12 = 1
... remainder 5
... 5 / 4 is 1
... 1 + 5 + 1 = 7 which is 7=0 days to be added to Tuesday (for the 2000's)
... Doomsday 2017 is Tuesday (which the chart above confirms)
... May(5) 9th is Tuesday, 23rd is Tuesday
... May 29, 2017 is a Monday
Example: what day of the week is October 14, 2066?
(That will be the 1000th anniversary of the Battle of Hastings.)
Answer: 66 / 12 = 5
... remainder 6
... 6 / 4 is 1
... 5 + 6 + 1 = 12 which is 5 days to be added to Tuesday (for the 2000's)
... Doomsday 2066 is Sunday
... October(10) 10th is Sunday
... October 14, 2066 is a Thursday
Other Centuries
Let's construct another chart of years, extending backwards and forwards from the previous chart, except we want it to cover a bigger range of years. Let's show only those rows with a century year:
Sun Mon Tue Wed Thu Fri Sat
1599 1600 1601 1602 1603
1700 1701 1702 1703 1704 1705
1796 1797 1798 1799 1800 1801
1897 1898 1899 1900 1901 1902 1903
1999 2000 2001 2002 2003
2100 2101 2102 2103 2104 2105
2196 2197 2198 2199 2200 2201
2297 2298 2299 2300 2301 2302 2303
2399 2400 2401 2402 2403
2500 2501 2502 2503 2504 2505
Examine this chart carefully, until you convince yourself that it is behaving exactly as you would expect for leap century years and non-leap century years. Remember the rule for determining a leap year:
- if it's divisible by 4, it is a leap year,
- unless it's divisible by 100, then it's not a leap year,
- unless it's divisible by 400, then it is a leap year
- unless it's divisible by 100, then it's not a leap year,
Each normal year advances Doomsday by one day. Each leap year advances Doomsday by two days. Now look at the century years again:
Sun Mon Tue Wed Thu Fri Sat 1700 1600 2100 2000 1900 1800 2500 2400 2300 2200
What's the best way to memorize century Doomsdays? I'm not sure. Here's what I use. Notice that century Doomsdays fall only on "Sun-Tue-Wed-Fri". I say "Son to wed Friday", thinking of my own (second) son and how pleased I would be if he were indeed getting married this Friday (my first son got married on a Saturday in 2003).
Combine "Sun-Tue-Wed-Fri" with Dr. Conway's "We-in-dis-day" for 1900=Wednesday and "2000=Tuesday", and I can reconstruct the chart mentally. The tricky part is that the years go right to left in each row, but 2000=Tue and 1900=Wed help with this. The easy part is that if you can get just that one row, with 2000=Tue and 1900=Wed in it, then the other years have the same Doomsday, plus or minus 400 years.
Example: what day of the week is
Canada's 300th birthday, July 1, 2167?
Answer: 67 / 12 = 5
... remainder 7
... 7 / 4 = 1
... 5 + 7 + 1 = 13 i.e. 6
... 6 + 2100=Sunday = Saturday
... July(7) 11th is a Saturday, so July 1, 2167, is Wednesday.
Example: what day of the week is
the 1000th anniversay of the Magna Carta, June 15, 2215?
Answer: 15 / 12 = 1
... remainder 3
... 3 / 4 = 0
... 1 + 3 + 0 = 4
... 4 + 2200=Friday = Tuesday
... June(6) 6th is Tuesday, so June 15, 2215, is Thursday.
(Thanks to Deven Corzine for spotting the
error and contacting me; it has been corrected.)
Somewhat tedious, isn't it? You are ready for "The Hand."
The Hand
Dr. Conway now teaches the Doomsday algorithm, complete with Century adjustment, using a very simple visual aid—your hand.
_____
____/ ___)____ <-- 1
_______) <-- 2
________) <-- 3
____ _______) <-- 4
\________) <-- 5
1 -- Doomsday Difference
2 -- Century Day
3 -- number of DOZENS
4 -- remainder
5 -- number of 4s in remainder
The Doomsday Difference is the difference between the required date and a nearby Doomsday, recorded as so many days "on" (i.e. to be added) or "off" (subtracted) from that Doomsday.
Recall a couple of the examples we've covered:
July 4th is always Doomsday, i.e. the Doomsday Difference is 0
Christmas, December 25th, is always "1 off" Doomsday
Be careful with the Doomsday Difference for dates in January and February. (Thanks to Bob Goddard for pointing this out.) In a leap year, we must subtract 1 from the Doomsday Difference for January and February dates:
Valentine's Day, February 14, is always "1 off" Doomsday in leap years, when Doomsday is February 29th; in ordinary years, the Doomsday Difference for Valentine's Day is 0
Groundhog Day, February 2, is only "1 on" Doomsday in leap years, when Doomsday is February 29th; in ordinary years, the Doomsday Difference for Groundhog Day is "2 on"
New Year's Day, January 1, is always "3 off" Doomsday in leap years, when Doomsday is the 4th of January; in ordinary years, the Doomsday Difference for New Year's Day is "2 off"
Examples using the hand
Here, in his own description, is how Dr. Conway would calculate the day of the week for Pearl Harbor Day, December 7th, 1941.
The various numbers to be attached to the hand are (reading from the thumb):
- "2 on" (for Dec 7)
- "Wednesday" (for 1900)
- "3 dozen" (getting us to 1936)
- "5 remainder" (number of years after 1936)
- "and 1" (since one of those 5 years was a leap year).
Don't start adding these up until you've formed them all, and then proceed as far as possible by cancelling first 14s, then 7s. To make sure we haven't forgotten them, let's say:
" 2, Wed, 3, 5, 1 "
(touching the appropriate digits as we do so), and then cancel that 2+5=7 (and folding down the thumb and ring finger) to get
"Wed, 3 and 1 " = Wed + 4 = Sun
I also advise use of my mnemonic names for weekdays, namely
NUNday, ONEday, TWOSday, tWEBLESday, FOURSday, FIVEday, SIXurday, SE'ENday
which can be pronounced so that they both sound like numbers and weekdays, and so help you do the addition, for example
" TREBLES, 3 and 1 = SEVENday " (Sunday)
in the above case.
The nice part about Dr. Conway's Hand is that we do the calculations in the same order we usually say the date -- month/day, then century/year. For example, for August 4, 1997, we do August 4, then 19, then 97.
Example: what day is August 4, 1997? Answer:
_____
____/ ___)____ <-- 4 off (Aug 4)
_______) <-- Wed (for 1900)
________) <-- 8 DOZENS
____ _______) <-- remainder 1
\________) <-- and 0
which is "4 off, tWEBLESday, 8, 1" or -4+3+8+1 which is 1, so August 4, 1997 is a Monday.
Finally, one last warning: Watch out for Gregorian versus Julian dates. The Doomsday algorithm described up to this point covers only Gregorian dates.
Example: what day was September 14, 1752?
Answer:
_____
____/ ___)____ <-- 2 on (Sep 14)
_______) <-- Sun (for 1700)
________) <-- 4 DOZENS
____ _______) <-- remainder 4
\________) <-- and 1
which is "2, Sun, 4, 4, 1" and we can throw out the 2, a 4 and the 1 to get 4 on Sunday, so September 14, 1752 was a Thursday.
That was a trick question, sort of. September 14, 1752 was the first day of the Gregorian calendar in England and its colonies. (The Gregorian calendar was originally adopted in parts of Europe in 1583). So September 1752 actually looked like this:
Sun Mon Tue Wed Thu Fri Sat
1 2 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
Neat, eh?
Origins
The Doomsday algorithm was created by John Horton Conway, an eminent mathematician, perhaps best known as the inventor of the Game of Life (see Link below).
I first heard about the Doomsday algorithm on November 27, 1982, on a CBC Radio program called Quirks and Quarks. Dr. Conway was interviewed by Jay Ingram, who's now Co-host and Producer of @discovery.ca. In those days Quirks and Quarks occasionally made typed transcripts available, and I sent away for one.
Dr. Conway had just published a book that year (co-authored by Elwyn R. Berlekamp and Richard K. Guy) called Winning Ways For Your Mathematical Plays, Volume 2: Games in Particular, Academic Press, London, 1982, ISBN 01-12-091102-7. The Doomsday algorithm is on pages 795-797, and the rest of the book is mainly about games, with substantial emphasis on their mathematical underpinnings. It is now available only in paperback.
In the original version of the Doomsday algorithm, the odd months were a bit harder to remember than "I work from 9-5 at the 7-11." You had to remember if the odd month was a long month or a short month. The 3rd, 5th, and 7th months are "long" because March, May, and July have 31 days, while the 9th and 11th months are "short" because September and November have only 30 days. You could remember "30 days hath September... and November" (but be careful because this old rhyme includes April and June which are even months). Anyway, for long odd months, Doomsday is the (N+4)th, while for short odd months, Doomsday is the (N-4)th. The mnemonic was long=add, short=subtract. Thus:
- March (3rd month, long) 3+4=7th is Doomsday
- May (5th month, long) 5+4=9th is Doomsday
- July (7th month, long) 7+4=11th is Doomsday
- September (9th month, short) 9-4=5th is Doomsday
- November (11th month, short) 11-4=7th is Doomsday
I'd agree that it's easier to remember "I work from 9-5 at the 7-11" together with "March 0th=7th".
Links
The following web sites are about or include descriptions of Dr. Conway's Doomsday algorithm.
Doomsday Rule, by S. W. Graham, includes substantial explanations, plenty o' exercises, and examples; also available in PDF format.
Simon Cassidy comments on the "Hand" in the context of the Dee-Cecil calendar.
C.07.2 Can I calculate the date of Easter? explains Conway's algorithm for Easter, and gives another explanation of his Doomsday algorithm; includes the remark "Note to non-US readers: 'Seven-Eleven' is the name of a ubiquitous chain of convenience stores." Reader Richard Ezell wrote to me in 2004 to report that this explanation may not really be necessary, as he had seen four 7-11 stores in a seven block stretch in Bangkok, Thailand.
AST 309-TIME; What is the day of the week, given any date? contains notes by William H. Jefferys for a school course on time, with another explanation of the Doomsday algorithm (examples are from 1997).
The Doomsday Rule for Fortnights, by Jim Blowers, gives calculations for Doomsday based on 14-day periods.
Kate Larson's Mathematical poem to calculate the "day of the week" for any day of any year is a beautiful, whimsical poem, attributed to Dr. Conway, which describes the algorithm completely, including both Gregorian and Julian century adjustments.
The Doomsday Algorithm, by Mike Husband, is a Powerpoint presentation. (Note: link goes to archive.org, as the original has dropped off the Web.)
Any Day of the Week Using the Doomsday Rule, by Paul J. Weiss, is a C++ implementation with downloadable code.
For more information about Dr. Conway, see:
Not Just Fun and Games April 1999 Scientific American profile of John H. Conway. (Note: this article is now available online only if you purchase the digital edition.)
Charles Seife's Mathemagician -- an amusing article about John Horton Conway.
John Conway's Game of Life by Stephen Stuart -- an interactive version that you can play via your web browser.
For links to other calendar sites, see my Calendar Links page.
Knot a Braid of Links
The Doomsday Algorithm was "latest link in the braid" for the week of
April 6-12, 1999.
"This page will teach you a simple algorithm to calculate mentally the day of the week corresponding to any given date. Give it a try, it's quite rewarding! The page features clear instructions, examples, and mnemonic tricks."
KaBoL is a "cool math site of the week" service to the mathematics community provided within Camel by the Canadian Mathematical Society.