The Doomsday rule is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years. The algorithm for mental calculation was devised by John Conway in 1973,^{[1]}^{[2]} drawing inspiration from Lewis Carroll's perpetual calendar algorithm.^{[3]}^{[4]}^{[5]} It takes advantage of each year having a certain day of the week, called the doomsday, upon which certain easytoremember dates fall; for example, 4/4, 6/6, 8/8, 10/10, 12/12, and the last day of February all occur on the same day of the week in any year. Applying the Doomsday algorithm involves three steps: Determination of the anchor day for the century, calculation of the doomsday for the year from the anchor day, and selection of the closest date out of those that always fall on the doomsday, e.g., 4/4 and 6/6, and count of the number of days (modulo 7) between that date and the date in question to arrive at the day of the week. The technique applies to both the Gregorian calendar and the Julian calendar, although their doomsdays are usually different days of the week.
The algorithm is simple enough that it can be computed mentally. Conway can usually give the correct answer in under two seconds. To improve his speed, he practices his calendrical calculations on his computer, which is programmed to quiz him with random dates every time he logs on.^{[6]}
YouTube Encyclopedic

1/5Views:4 2593799 7156 3569 025

✪ Calendars 1 (Doomsday Algorithm)

✪ The Doomsday Algorithm [haphazard]

✪ JavaScript Tutorial 12 Doomsday Algorithm

✪ How to figure out the day for any date in less than 3 secAdvanced methodStep by StepRISHAV KUNAL

✪ 秒速心算任何一日是星期幾的方法！ ︳意識橋 Ezekiel
Transcription
Contents
 1 Doomsdays for some contemporary years
 2 Memorable dates that always land on Doomsday
 3 Mnemonic weekday names
 4 Finding a year's Doomsday
 5 Correspondence with dominical letter
 6 Finding a century's anchor day
 7 Overview of all Doomsdays
 8 Computer formula for the Doomsday of a year
 9 400year cycle of Doomsdays
 10 Full examples
 11 See also
 12 References
 13 External links
Doomsdays for some contemporary years
Doomsday for the current year in the Gregorian calendar (2020) is Saturday. For some other contemporary years:
Mon.  Tue.  Wed.  Thu.  Fri.  Sat.  Sun.  Mon.  Tue.  Wed.  Thu.  Fri.  Sat.  Sun. 

1898  1899  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  2001  2002  2003  →  2004  2005  2006  2007  →  2008  2009  2010 
2011  →  2012  2013  2014  2015  →  2016  2017  2018  2019  →  2020  2021 
2022  2023  →  2024  2025  2026  2027  →  2028  2029  2030  2031  →  2032 
2033  2034  2035  →  2036  2037  2038  2039  →  2040  2041  2042  2043  → 
2044  2045  2046  2047  →  2048  2049  2050  2051  →  2052  2053  2054  2055 
→  2056  2057  2058  2059  →  2060  2061  2062  2063  →  2064  2065  2066 
2067  →  2068  2069  2070  2071  →  2072  2073  2074  2075  →  2076  2077 
2078  2079  →  2080  2081  2082  2083  →  2084  2085  2086  2087  →  2088 
2089  2090  2091  →  2092  2093  2094  2095  →  2096  2097  2098  2099  2100 
The table is filled in horizontally, skipping one column for each leap year. This table cycles every 28 years, except in the Gregorian calendar on years that are a multiple of 100 (like 1900 which is not a leap year) that are not also a multiple of 400 (like 2000 which is still a leap year). The full cycle is 28 years (1,461 weeks) in the Julian calendar, 400 years (20,871 weeks) in the Gregorian calendar.
Memorable dates that always land on Doomsday
One can find the day of the week of a given calendar date by using a nearby doomsday as a reference point. To help with this, the following is a list of easytoremember dates for each month that always land on the doomsday.
As mentioned above, the last day of February defines the doomsday. For January, January 3 is a doomsday during common years and January 4 a doomsday during leap years, which can be remembered as "the 3rd during 3 years in 4, and the 4th in the 4th year". For March, one can remember the pseudodate "March 0", which refers to the day before March 1, i.e. the last day of February.^{[citation needed]}
For the months April through December, the even numbered months are covered by the double dates 4/4, 6/6, 8/8, 10/10, and 12/12, all of which fall on the doomsday. The odd numbered months can be remembered with the mnemonic "I work from 9 to 5 at the 711", i.e., 9/5, 7/11, and also 5/9 and 11/7, are all doomsdays.^{[citation needed]}
Several common holidays are also on doomsday. The chart below includes only dates covered by the mnemonics in the sources listed.
Month  Memorable date  Month/Day  Mnemonic^{[7]}  Complete list of days 

January  January 3 (common years), January 4 (leap years) 
1/3 OR 1/4  the 3rd 3 years in 4 and the 4th in the 4th  3, 10, 17, 24, 31 OR 4, 11, 18, 25 
February  February 28 (common years), February 29 (leap years)  2/28 OR 2/29  last day of February  0, 7, 14, 21, 28 OR 1, 8, 15, 22, 29 
March  "March 0"  3/0  last day of February  0, 7, 14, 21, 28 
April  April 4  4/4  4/4, 6/6, 8/8, 10/10, 12/12  4, 11, 18, 25 
May  May 9  5/9  9to5 at 711  2, 9, 16, 23, 30 
June  June 6  6/6  4/4, 6/6, 8/8, 10/10, 12/12  6, 13, 20, 27 
July  July 11  7/11  9to5 at 711  4, 11, 18, 25 
August  August 8  8/8  4/4, 6/6, 8/8, 10/10, 12/12  1, 8, 15, 22, 29 
September  September 5  9/5  9to5 at 711  5, 12, 19, 26 
October  October 10  10/10  4/4, 6/6, 8/8, 10/10, 12/12  3, 10, 17, 24, 31 
November  November 7  11/7  9to5 at 711  0, 7, 14, 21, 28 
December  December 12  12/12  4/4, 6/6, 8/8, 10/10, 12/12  5, 12, 19, 26 
Since the doomsday for a particular year is directly related to weekdays of dates in the period from March through February of the next year, common years and leap years have to be distinguished for January and February of the same year.
Example
To find which day of the week Christmas Day of 2018 was, proceed as follows: in the year 2018, doomsday was Wednesday. Since December 12 is a doomsday, December 25, being thirteen days afterwards (two weeks less a day), fell on a Tuesday. Christmas Day is always the day before doomsday. In addition, July 4 (U.S. Independence Day) is always on a doomsday, as are Halloween (October 31), Pi Day (March 14), and Boxing Day (December 26).
Mnemonic weekday names
Since this algorithm involves treating days of the week like numbers modulo 7, John Conway suggests thinking of the days of the week as "Noneday"; or as "Sansday" (for Sunday), "Oneday", "Twosday", "Treblesday", "Foursday", "Fiveday", and "Sixaday" in order to recall the numberweekday relation without needing to count them out in one's head.
day of week  Index number 
Mnemonic 

Sunday  0  Noneday or Sansday 
Monday  1  Oneday 
Tuesday  2  Twosday 
Wednesday  3  Treblesday 
Thursday  4  Foursday 
Friday  5  Fiveday 
Saturday  6  Sixaday 
There are some languages, such as Greek, Portuguese and Galician, that base some of the names of the week days in their positional order.
Finding a year's Doomsday
First take the anchor day for the century. For the purposes of the doomsday rule, a century starts with '00 and ends with '99. The following table shows the anchor day of centuries 1800–1899, 1900–1999, 2000–2099 and 2100–2199.
Century  Anchor day  Mnemonic  Index (day of week) 

1800–1899  Friday  —  5 (Fiveday) 
1900–1999  Wednesday  Weindisday (most living people were born in that century) 
3 (Treblesday) 
2000–2099  Tuesday  YTueK or Twosday (Y2K was at the head of this century) 
2 (Twosday) 
2100–2199  Sunday  Twentyoneday is Sunday (2100 is the start of the next century) 
0 (Noneday) 
Next, find the year's doomsday. To accomplish that according to Conway:
 Divide the year's last two digits (call this y) by 12 and let a be the floor of the quotient.
 Let b be the remainder of the same quotient.
 Divide that remainder by 4 and let c be the floor of the quotient.
 Let d be the sum of the three numbers (d = a + b + c). (It is again possible here to divide by seven and take the remainder. This number is equivalent, as it must be, to the sum of the last two digits of the year taken collectively plus the floor of those collective digits divided by four.)
 Count forward the specified number of days (d or the remainder of d/7) from the anchor day to get the year's doomsday.
For the twentiethcentury year 1966, for example:
As described in bullet 4, above, this is equivalent to:
So doomsday in 1966 fell on Monday.
Similarly, doomsday in 2005 is on a Monday:
Why it works
The doomsday calculation is effectively calculating the number of days between any given date in the base year and the same date in the current year, then taking the remainder modulo 7. When both dates come after the leap day (if any), the difference is just 365y + y/4 (rounded down). But 365 equals 52 × 7 + 1, so after taking the remainder we get just
This gives a simpler formula if one is comfortable dividing large values of y by both 4 and 7. For example, we can compute
which gives the same answer as in the example above.
Where 12 comes in is that the pattern of (y + ⌊y/4⌋) mod 7 almost repeats every 12 years. After 12 years, we get (12 + 12/4) mod 7 = 15 mod 7 = 1. If we replace y by y mod 12, we are throwing this extra day away; but adding back in ⌊y/12⌋ compensates for this error, giving the final formula.
The "odd + 11" method
A simpler method for finding the year's doomsday was discovered in 2010 by Chamberlain Fong and Michael K. Walters,^{[8]} and described in their paper submitted to the 7th International Congress on Industrial and Applied Mathematics (2011). Called the "odd + 11" method, it is equivalent^{[8]} to computing
 .
It is well suited to mental calculation, because it requires no division by 4 (or 12), and the procedure is easy to remember because of its repeated use of the "odd + 11" rule.
Extending this to get the doomsday, the procedure is often described as accumulating a running total T in six steps, as follows:
 Let T be the year's last two digits.
 If T is odd, add 11.
 Now let T = T/2.
 If T is odd, add 11.
 Now let T = 7 − (T mod 7).
 Count forward T days from the century's anchor day to get the year's doomsday.
Applying this method to the year 2005, for example, the steps as outlined would be:
 T = 5
 T = 5 + 11 = 16 (adding 11 because T is odd)
 T = 16/2 = 8
 T = 8 (do nothing since T is even)
 T = 7 − (8 mod 7) = 7 − 1 = 6
 Doomsday for 2005 = 6 + Tuesday = Monday
The explicit formula for the odd+11 method is:
 .
Although this expression looks daunting and complicated, it is actually simple^{[8]} because of a common subexpression y + 11(y mod 2)/2 that only needs to be calculated once.
Correspondence with dominical letter
Doomsday is related to the dominical letter of the year as follows.
Doomsday  Dominical letter  

Common year  Leap year  
Sunday  C  DC 
Monday  B  CB 
Tuesday  A  BA 
Wednesday  G  AG 
Thursday  F  GF 
Friday  E  FE 
Saturday  D  ED 
Look up the table below for the dominical letter (DL).
100s of Years  D L 
Remaining Year Digits  #  

Julian (r ÷ 7) 
Gregorian (r ÷ 4)  
r5 19  16 20 r0  A  00 06 17 23  28 34 45 51  56 62 73 79  84 90  0 
r4 18  15 19 r3  G  01 07 12 18  29 35 40 46  57 63 68 74  85 91 96  1 
r3 17  F  02 13 19 24  30 41 47 52  58 69 75 80  86 97  2  
r2 16  18 22 r2  E  03 08 14 25  31 36 42 53  59 64 70 81  87 92 98  3 
r1 15  D  09 15 20 26  37 43 48 54  65 71 76 82  93 99  4  
r0 14  17 21 r1  C  04 10 21 27  32 38 49 55  60 66 77 83  88 94  5 
r6 13  B  05 11 16 22  33 39 44 50  61 67 72 78  89 95  6 
For the year 2017, the dominical letter is A  0 = A.
Finding a century's anchor day
For the Gregorian calendar:
 Mathematical formula
 5 × (c mod 4) mod 7 + Tuesday = anchor.
 Algorithmic
 Let r = c mod 4
 if r = 0 then anchor = Tuesday
 if r = 1 then anchor = Sunday
 if r = 2 then anchor = Friday
 if r = 3 then anchor = Wednesday
For the Julian calendar:
 6 × (c mod 7) mod 7 + Sunday = anchor.
Note: c = ⌊year/100⌋.
Overview of all Doomsdays
Month  Dates  Week numbers * 

January (common years)  3, 10, 17, 24, 31  1–5 
January (leap years)  4, 11, 18, 25  1–4 
February (common years)  7, 14, 21, 28  6–9 
February (leap years)  1, 8, 15, 22, 29  5–9 
March  7, 14, 21, 28  10–13 
April  4, 11, 18, 25  14–17 
May  2, 9, 16, 23, 30  18–22 
June  6, 13, 20, 27  23–26 
July  4, 11, 18, 25  27–30 
August  1, 8, 15, 22, 29  31–35 
September  5, 12, 19, 26  36–39 
October  3, 10, 17, 24, 31  40–44 
November  7, 14, 21, 28  45–48 
December  5, 12, 19, 26  49–52 
* In leap years the nth doomsday is in ISO week n. In common years the day after the nth doomsday is in week n. Thus in a common year the week number on the doomsday itself is one less if it is a Sunday, i.e. in a common year starting on Friday.
Computer formula for the Doomsday of a year
For computer use, the following formulas for the doomsday of a year are convenient.
For the Gregorian calendar:
For example, the year 2009 has a doomsday of Saturday under the Gregorian calendar (the currently accepted calendar), since
As another example, the year 1946 has a doomsday of Thursday, since
For the Julian calendar:
The formulas apply also for the proleptic Gregorian calendar and the proleptic Julian calendar. They use the floor function and astronomical year numbering for years BC.
For comparison, see the calculation of a Julian day number.
400year cycle of Doomsdays
Julian centuries  1600J 900J 200J 500J 1200J 1900J 2600J 3300J 
1500J 800J 100J 600J 1300J 2000J 2700J 3400J 
1400J 700J 0J 700J 1400J 2100J 2800J 3500J 
1300J 600J 100J 800J 1500J 2200J 2900J 3600J 
1200J 500J 200J 900J 1600J 2300J 3000J 3700J 
1100J 400J 300J 1000J 1700J 2400J 3100J 3800J 
1000J 300J 400J 1100J 1800J 2500J 3200J 3900J  

Gregorian centuries Years 
1600 1200 800 400 0 400 800 1200 1600 2000 2400 2800 3200 3600 
1500 1100 700 300 100 500 900 1300 1700 2100 2500 2900 3300 3700 
1400 1000 600 200 200 600 1000 1400 1800 2200 2600 3000 3400 3800 
1300 900 500 100 300 700 1100 1500 1900 2300 2700 3100 3500 3900  
00  28  56  84  Tue.  Mon.  Sun.  Sat.  Fri.  Thu.  Wed. 
01  29  57  85  Wed.  Tue.  Mon.  Sun.  Sat.  Fri.  Thu. 
02  30  58  86  Thu.  Wed.  Tue.  Mon.  Sun.  Sat.  Fri. 
03  31  59  87  Fri.  Thu.  Wed.  Tue.  Mon.  Sun.  Sat. 
04  32  60  88  Sun.  Sat.  Fri.  Thu.  Wed.  Tue.  Mon. 
05  33  61  89  Mon.  Sun.  Sat.  Fri.  Thu.  Wed.  Tue. 
06  34  62  90  Tue.  Mon.  Sun.  Sat.  Fri.  Thu.  Wed. 
07  35  63  91  Wed.  Tue.  Mon.  Sun.  Sat.  Fri.  Thu. 
08  36  64  92  Fri.  Thu.  Wed.  Tue.  Mon.  Sun.  Sat. 
09  37  65  93  Sat.  Fri.  Thu.  Wed.  Tue.  Mon.  Sun. 
10  38  66  94  Sun.  Sat.  Fri.  Thu.  Wed.  Tue.  Mon. 
11  39  67  95  Mon.  Sun.  Sat.  Fri.  Thu.  Wed.  Tue. 
12  40  68  96  Wed.  Tue.  Mon.  Sun.  Sat.  Fri.  Thu. 
13  41  69  97  Thu.  Wed.  Tue.  Mon.  Sun.  Sat.  Fri. 
14  42  70  98  Fri.  Thu.  Wed.  Tue.  Mon.  Sun.  Sat. 
15  43  71  99  Sat.  Fri.  Thu.  Wed.  Tue.  Mon.  Sun. 
16  44  72  Mon.  Sun.  Sat.  Fri.  Thu.  Wed.  Tue.  
17  45  73  Tue.  Mon.  Sun.  Sat.  Fri.  Thu.  Wed.  
18  46  74  Wed.  Tue.  Mon.  Sun.  Sat.  Fri.  Thu.  
19  47  75  Thu.  Wed.  Tue.  Mon.  Sun.  Sat.  Fri.  
20  48  76  Sat.  Fri.  Thu.  Wed.  Tue.  Mon.  Sun.  
21  49  77  Sun.  Sat.  Fri.  Thu.  Wed.  Tue.  Mon.  
22  50  78  Mon.  Sun.  Sat.  Fri.  Thu.  Wed.  Tue.  
23  51  79  Tue.  Mon.  Sun.  Sat.  Fri.  Thu.  Wed.  
24  52  80  Thu.  Wed.  Tue.  Mon.  Sun.  Sat.  Fri.  
25  53  81  Fri.  Thu.  Wed.  Tue.  Mon.  Sun.  Sat.  
26  54  82  Sat.  Fri.  Thu.  Wed.  Tue.  Mon.  Sun.  
27  55  83  Sun.  Sat.  Fri.  Thu.  Wed.  Tue.  Mon. 
Since in the Gregorian calendar there are 146097 days, or exactly 20871 sevenday weeks, in 400 years, the anchor day repeats every four centuries. For example, the anchor day of 1700–1799 is the same as the anchor day of 2100–2199, i.e. Sunday.
The full 400year cycle of doomsdays is given in the adjacent table. The centuries are for the Gregorian and proleptic Gregorian calendar, unless marked with a J for Julian. The Gregorian leap years are highlighted.
Negative years use astronomical year numbering. Year 25BC is −24, shown in the column of −100J (proleptic Julian) or −100 (proleptic Gregorian), at the row 76.
Sunday  Monday  Tuesday  Wednesday  Thursday  Friday  Saturday  Total  

Nonleap years  43  43  43  43  44  43  44  303 
Leap years  13  15  13  15  13  14  14  97 
Total  56  58  56  58  57  57  58  400 
A leap year with Monday as doomsday means that Sunday is one of 97 days skipped in the 400year sequence. Thus the total number of years with Sunday as doomsday is 71 minus the number of leap years with Monday as doomsday, etc. Since Monday as doomsday is skipped across 29 February 2000 and the pattern of leap days is symmetric about that leap day, the frequencies of doomsdays per weekday (adding common and leap years) are symmetric about Monday. The frequencies of doomsdays of leap years per weekday are symmetric about the doomsday of 2000, Tuesday.
The frequency of a particular date being on a particular weekday can easily be derived from the above (for a date from 1 January – 28 February, relate it to the doomsday of the previous year).
For example, 28 February is one day after doomsday of the previous year, so it is 58 times each on Tuesday, Thursday and Sunday, etc. 29 February is doomsday of a leap year, so it is 15 times each on Monday and Wednesday, etc.
28year cycle
Regarding the frequency of doomsdays in a Julian 28year cycle, there are 1 leap year and 3 common years for every weekday, the latter 6, 17 and 23 years after the former (so with intervals of 6, 11, 6, and 5 years; not evenly distributed because after 12 years the day is skipped in the sequence of doomsdays).^{[citation needed]} The same cycle applies for any given date from 1 March falling on a particular weekday.
For any given date up to 28 February falling on a particular weekday, the 3 common years are 5, 11, and 22 years after the leap year, so with intervals of 5, 6, 11, and 6 years. Thus the cycle is the same, but with the 5year interval after instead of before the leap year.
Thus, for any date except 29 February, the intervals between common years falling on a particular weekday are 6, 11, 11. See e.g. at the bottom of the page Common year starting on Monday the years in the range 1906–2091.
For 29 February falling on a particular weekday, there is just one in every 28 years, and it is of course a leap year.
Julian calendar
The Gregorian calendar is currently accurately lining up with astronomical events such as solstices. In 1582 this modification of the Julian calendar was first instituted. In order to correct for calendar drift, 10 days were skipped, so doomsday moved back 10 days (i.e. 3 days): Thursday 4 October (Julian, doomsday is Wednesday) was followed by Friday 15 October (Gregorian, doomsday is Sunday). The table includes Julian calendar years, but the algorithm is for the Gregorian and proleptic Gregorian calendar only.
Note that the Gregorian calendar was not adopted simultaneously in all countries, so for many centuries, different regions used different dates for the same day.
Full examples
Example 1 (1985)
Suppose you want to know the day of the week of September 18, 1985. You begin with the century's anchor day, Wednesday. To this, add a, b, and c above:
 a is the floor of 85/12, which is 7.
 b is 85 mod 12, which is 1.
 c is the floor of b/4, which is 0.
This yields a + b + c = 8. Counting 8 days from Wednesday, we reach Thursday, which is the doomsday in 1985. (Using numbers: In modulo 7 arithmetic, 8 is congruent to 1. Because the century's anchor day is Wednesday (index 3), and 3 + 1 = 4, doomsday in 1985 was Thursday (index 4).) We now compare September 18 to a nearby doomsday, September 5. We see that the 18th is 13 past a doomsday, i.e. one day less than two weeks. Hence, the 18th was a Wednesday (the day preceding Thursday). (Using numbers: In modulo 7 arithmetic, 13 is congruent to 6 or, more succinctly, −1. Thus, we take one away from the doomsday, Thursday, to find that September 18, 1985 was a Wednesday.)
Example 2 (other centuries)
Suppose that you want to find the day of week that the American Civil War broke out at Fort Sumter, which was April 12, 1861. The anchor day for the century was 99 days after Thursday, or, in other words, Friday (calculated as (18 + 1) × 5 + ⌊18/4⌋; or just look at the chart, above, which lists the century's anchor days). The digits 61 gave a displacement of six days so doomsday was Thursday. Therefore, April 4 was Thursday so April 12, eight days later, was a Friday.
See also
Year starts  Common years  Leap years  

1 Jan  Count  Ratio  31 Dec  DL  DD  Count  Ratio  31 Dec  DL  DD  Count  Ratio  
Sun  58  14.50 %  Sun  A  Tue  43  10.75 %  Mon  AG  Wed  15  3.75 %  
Sat  56  14.00 %  Sat  B  Mon  43  10.75 %  Sun  BA  Tue  13  3.25 %  
Fri  58  14.50 %  Fri  C  Sun  43  10.75 %  Sat  CB  Mon  15  3.75 %  
Thu  57  14.25 %  Thu  D  Sat  44  11.00 %  Fri  DC  Sun  13  3.25 %  
Wed  57  14.25 %  Wed  E  Fri  43  10.75 %  Thu  ED  Sat  14  3.50 %  
Tue  58  14.50 %  Tue  F  Thu  44  11.00 %  Wed  FE  Fri  14  3.50 %  
Mon  56  14.00 %  Mon  G  Wed  43  10.75 %  Tue  GF  Thu  13  3.25 %  
∑  400  100.0 %  303  75.75 %  97  24.25 % 
 Ordinal date
 Computus – Gauss algorithm for Easter date calculation
 Zeller's congruence – An algorithm (1882) to calculate the day of the week for any Julian or Gregorian calendar date.
 Mental calculation
References
 ^ John Horton Conway, "Tomorrow is the Day After Doomsday", Eureka, volume 36, pages 28–31, October 1973.
 ^ Richard Guy, John Horton Conway, Elwyn Berlekamp : "Winning Ways: For Your Mathematical Plays, Volume. 2: Games in Particular", pages 795–797, Academic Press, London, 1982, ISBN 0120911027.
 ^ Lewis Carroll, "To Find the Day of the Week for Any Given Date", Nature, March 31, 1887. doi:10.1038/035517a0
 ^ Martin Gardner, The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays, pages 24–26, SpringerVerlag, 1996.
 ^ "What Day is Doomsday". Mathematics Awareness Month. April 2014.
 ^ Alpert, Mark. "Not Just Fun and Games", Scientific American, April, 1999. doi:10.1038/scientificamerican049940
 ^ Limeback, Rudy (3 January 2017). "Doomsday Algorithm". Retrieved 27 May 2017.
 ^ ^{a} ^{b} ^{c} Chamberlain Fong, Michael K. Walters: "Methods for Accelerating Conway's Doomsday Algorithm (part 2)", 7th International Congress on Industrial and Applied Mathematics (2011).
 ^ Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
External links
Wikimedia Commons has media related to Doomsday rule. 
 Encyclopedia of Weekday Calculation by HansChristian Solka, 2010
 Doomsday calculator that also "shows all work"
 World records for mentally calculating the day of the week in the Gregorian Calendar
 National records for finding Calendar Dates
 World Ranking of Memoriad Mental Calendar Dates (all competitions combined)
 What is the day of the week, given any date?
 Doomsday Algorithm
 Finding the Day of the Week
 Poem explaining the Doomsday rule at the Wayback Machine (archived October 18, 2006)