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[[File:John H Conway 2005.jpg|thumb|[[John Horton Conway|John Conway]], inventor of the Doomsday algorithm.]]
 
The '''Doomsday rule''' or '''Doomsday algorithm''' is a way of [[calculating the day of the week]] of a given date. It provides a [[perpetual calendar]] since the [[Gregorian calendar]] moves in cycles of 400 years.
 
This [[algorithm]] for [[mental calculation]] was devised by [[John Horton Conway|John Conway]]<ref>John Horton Conway, "Tomorrow is the Day After Doomsday", Eureka, volume 36, pages 28-31, October 1973.</ref><ref>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 0-12-091102-7.</ref> after drawing inspiration from [[Lewis Carroll|Lewis Carroll's]] work on a perpetual calendar algorithm.<ref>Lewis Carroll, "To Find the Day of the Week for Any Given Date", Nature, March 31, 1887.</ref><ref>Martin Gardner, "The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays", pages 24-26, Springer-Verlag, 1996</ref> It takes advantage of the fact that each year has a certain day of the week (the ''doomsday'') upon which certain easy-to-remember 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 given year. Applying the Doomsday algorithm involves three steps:
# Determine the "anchor day" for the century.
# Use the anchor day for the century to calculate the doomsday for the year.
# Choose the closest date out of the ones that always fall on the doomsday (e.g. 4/4, 6/6, 8/8), and count the number of days ([[Modular arithmetic|modulo 7]]) between that date and the date in question to arrive at the day of the week.
 
This technique applies to both the [[Gregorian calendar]] [[Anno Domini|A.D.]] and the [[Julian calendar]], although their doomsdays will usually be different days of the week.
 
Since this algorithm involves treating days of the week like numbers modulo 7, [[John Horton Conway|John Conway]] suggests thinking of the days of the week as "Noneday" or "Sansday" (for Sunday), "Oneday", "Twosday", "Treblesday", "Foursday", "Fiveday", and "Six-a-day".
 
The algorithm is simple enough for anyone with basic arithmetic ability to do the calculations 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.<ref>Alpert, Mark. "Not Just Fun and Games", [[Scientific American]], April, 1999.</ref>
 
== Doomsdays for some contemporary years ==
Doomsday for the current year in the Gregorian calendar '''({{CURRENTYEAR}})''' is '''{{#switch:{{CURRENTYEAR}}
|2010=Sunday
|2011=Monday
|2012=Wednesday
|2013=Thursday
|2014=Friday
|2015=Saturday
|2016=Monday
|2017=Tuesday
|2018=Wednesday
|2019=Thursday
}}'''.
 
For some other contemporary years :
 
{|class="wikitable" style="line-height:normal;margin:auto;table-layout:fixed;text-align:center"
|+'''Doomsdays for the Gregorian calendar'''
|-
!scope="col" style="width:2.5em"|<abbr title="Monday">Mon.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Tuesday">Tue.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Wednesday">Wed.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Thursday">Thu.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Friday">Fri.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Saturday">Sat.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Sunday">Sun.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Monday">Mon.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Tuesday">Tue.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Wednesday">Wed.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Thursday">Thu.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Friday">Fri.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Saturday">Sat.</abbr>
!scope="col" style="width:2.5em"|<abbr title="Sunday">Sun.</abbr>
|-
|  →||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
|}
'''Notes:''' Fill in the table horizontally, skipping one column for each leap year. This table cycles every 28 years, except in the Gregorian calendar on years multiple of 100 (like 1900 which is not a leap year) that are not 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 easily 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 easy-to-remember dates for each month that always land on the Doomsday.  
 
As mentioned above, the last day of February always falls on the doomsday, as do the double dates 4/4, 6/6, 8/8, 10/10, and 12/12. Four of the odd month dates (May 9, September 5, July 11, and November 7) can be remembered with the mnemonic "I work from [[Working time#9-to-5|9 to 5]] at the [[7-Eleven|7-11]]." For March, one can remember the pseudo-date "March 0", which refers to the day before March 1, i.e. the last day of February; one can alternately remember the date a week later, March 7, or March 21 which is traditionally regarded as the first day of spring in the northern hemisphere and autumn in the southern hemisphere (although after 2007 the [[March equinox|Northward equinox]] will not fall on that date in Europe again until 2102).<ref>{{cite web |url=http://www.space.com/881-date-changed-start-spring.html |title=Why Has Date Changed for Start of Spring? |publisher=www.space.com |accessdate=15 February 2013}}</ref> For January, January 11 is a Doomsday during leap years, while January 10 is a Doomsday during common years; 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 '''4'''th".
 
{| class="wikitable"
|-
! Month !! Memorable date !! Month/Day !! Mnemonic
|-
| January || January 3 (common years), January 4 (leap years)<br>January 11 (leap years) || 1/3 or 1/4<br>1/11 || the 3rd '''3''' years in 4 and the 4th in the '''4'''th<br>all ones
|-
| February ||February 14 (common years)<br>February 22 (leap years)<br>February 28 (common years), February 29 (leap years) || 2/14<br>2/22<br>2/28 or 2/29 || [[Valentine's Day]]<br>all twos<br>last day of February
|-
| March || "March 0"<br>March 14<br>March 21 || 3/0<br>3/14<br>3/21 || last day of February<br>[[Pi day]]<br>traditionally first day of spring/autumn
|-
| April || April 4 || 4/4 || even month
|-
| May || May 9<br>May 30 || 5/9<br>5/30 || '''9-to-5''' at 7-11<br>Traditional [[Memorial Day]] (United States)
|-
| June || June 6<br>June 20 || 6/6<br>6/20 || even month<br>traditionally first day of summer/winter
|-
| July || July 4<br>July 11 || 7/4<br>7/11 || [[Independence Day (United States)]]<br>9-to-5 at '''7-11'''
|-
| August || August 8 || 8/8 || even month
|-
| September || September 5 || 9/5 || '''9-to-5''' at 7-11
|-
| October || October 10<br>October 31 || 10/10<br>10/31 || even month<br>[[Halloween]]
|-
| November || November 7 || 11/7 || 9-to-5 at '''7-11'''
|-
| December || December 12<br>December 26 || 12/12<br>12/26 || even month<br>[[Boxing Day]]
|}
 
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.
 
===Examples===
Suppose you want to know which day of the week [[Christmas Day]] of 2006 was. In the year 2006, Doomsday was Tuesday. Since December 12 is a Doomsday, December 25, being thirteen days afterwards (two weeks less a day), fell on a Monday.
 
It's useful to note that Christmas Day is always the day before Doomsday ("One off Doomsday").  In addition, July 4 is always on a Doomsday, and so is [[Halloween]].
 
Suppose that you want to find the day of week that the September 11, 2001 [[September 11, 2001 attacks|attacks]] on the [[World Trade Center]] occurred. The century anchor was Tuesday, and Doomsday for 2001 is one day beyond, which is Wednesday. September 5 was a Doomsday, and September 11, six days later, fell on a Tuesday.
 
==Finding a year's Doomsday==
We 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.
 
{| class="wikitable" style="margin: 1em auto 1em auto"
! Century || Anchor day || Mnemonic || Index (day of week)
|-
|- 1700-1799 || Sunday || -|| 0 (Noneday)
|-
| 1800–1899 || Friday || - || 5 (Fiveday)
|-
| 1900–1999 || Wednesday || We-in-dis-day<br />(most living people were born in that century) || 3 (Treblesday)
|-
| '''2000–2099''' || Tuesday || Y-Tue-K or Twos-day<br />([[Y2K]] was at the head of this century) || '''2 (Twosday)'''
|-
| 2100–2199 || Sunday || Twenty-one-day is Sunday<br />(2100 is the start of the next century) || 0 (Noneday)
|}
 
Next, we 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 and ceiling functions|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.
 
:<math>\begin{matrix}\left({\left\lfloor{\frac{y}{12}}\right\rfloor+y \bmod 12+\left\lfloor{\frac{y \bmod 12}{4}}\right\rfloor}\right) \bmod 7+\rm{anchor}=\rm{Doomsday}\end{matrix}</math>
 
For the twentieth-century year 1966, for example:
:<math>\begin{matrix}\left({\left\lfloor{\frac{66}{12}}\right\rfloor+66 \bmod 12+\left\lfloor{\frac{66 \bmod 12}{4}}\right\rfloor}\right) \bmod 7+\rm{Wednesday} & = & \left(5+6+1\right) \bmod 7+\rm{Wednesday} \\
\ & = & \rm{Monday}\end{matrix}</math>
 
As described in bullet 4, above, this is equivalent to:
 
:<math>\begin{matrix}\left({66 + \left\lfloor{\frac{66}{4}}\right\rfloor}\right) \bmod 7+\rm{Wednesday} & = & \left(66+16\right) \bmod 7+\rm{Wednesday} \\
\ & = & \rm{Monday}\end{matrix}</math>
 
So Doomsday in 19'''66''' fell on Monday.
 
Similarly, Doomsday in 20'''05''' is on a Monday:
:<math>\left({\left\lfloor{\frac{5}{12}}\right\rfloor+5 \bmod 12+\left\lfloor{\frac{5 \bmod 12}{4}}\right\rfloor}\right) \bmod 7+\rm{Tuesday}=\rm{Monday}</math>
 
=== Why it works ===
[[File:Doomsday Rule.svg|thumb|Doomsday rule]]
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 plus y/4 (rounded down).  But 365 equals 52*7+1, so after taking the remainder we get just
 
:<math>(y + \lfloor \frac{y}{4} \rfloor) \bmod 7.</math>
 
This gives a simpler formula if one is comfortable dividing large values of y by both 4 and 7.  For example, we can compute <math>(66 + \lfloor \frac{66}{4} \rfloor) \bmod 7 = (66 + 16) \bmod 7 = 82 \bmod 7 = 5</math>, which gives the same answer as in the example above.
 
Where 12 comes in is that the pattern of <math>(y + \lfloor \frac{y}{4} \rfloor) \bmod 7</math> ''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 <math>\lfloor \frac{y}{12} \rfloor</math> compensates for this error, giving the final formula.
 
=== The Odd+11 method ===
[[File:Odd+11 doomsday flowchart.svg|thumb|right| A simple flowchart showing the Odd+11 method.]]
A simpler method for finding the year's doomsday was discovered in 2010 by Chamberlain Fong and Michael K. Walters,<ref name=Odd11paper>Chamberlain Fong, Michael K. Walters: [http://arxiv.org/abs/1010.0765 "Methods for Accelerating Conway's Doomsday Algorithm (part 2)"], 7th International Congress on Industrial and Applied Mathematics (2011)</ref> and described in their paper submitted to the 7th International Congress on Industrial and Applied Mathematics (2011). Called the '''Odd+11''' method, it has been proved<ref name=Odd11paper /> equivalent to computing
:<math>(y + \lfloor \frac{y}{4} \rfloor) \, \operatorname{mod} \, 7.</math>
 
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 1966, for example, the steps as outlined would be:
#''T'' = 66
#''T'' = 66 (Do nothing since ''T'' is even.)
#''T'' = 66/2 = 33
#''T'' = 33+11 = 44 (Add 11 because T is odd.)
#''T'' = 7 − (44 mod 7) = 7 − 2 = 5
#Doomsday for 1966 = 5 + Wednesday = Monday
 
<br>
 
 
The explicit formula for the odd+11 method is:
:<math> -[ \frac{y+11(y \bmod 2)}{2} + 11 (\frac{y+11(y \bmod 2)}{2}\bmod 2) ] \bmod 7 .</math>
 
Although this expression looks daunting and complicated, it is actually simple<ref name=Odd11paper /> because of a [[common subexpression]] <math> \frac{y+11(y \bmod 2)}{2}</math> that only needs to be calculated once.
 
===Dominical letter method===
A year's doomsday (DD) can be determined from a year's [[dominical letter]] (DL), too.
:<math> \mbox{DD} = (3 - \mbox{DL})\bmod 7 </math>
Note: A = 1, B = 2, ..., G = 0.
 
For the year 1966 the dominical letter is B, so the doomsday DD = 3 - 2 = 1 = Monday.
 
==Finding a century's anchor day==
 
For the Gregorian calendar:
:<math>5\times(c\bmod 4)\bmod 7 + \rm{Tuesday = anchor.}</math>
For the Julian calendar:
:<math>6\times(c\bmod 7)\bmod 7 + \rm{Sunday = anchor}.</math>
Note: <math>c = \lfloor year/100 \rfloor.</math>
 
==Overview of all Doomsdays==
 
{| class="wikitable sortable"
!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
|}
 
<nowiki>*</nowiki> In leap years the ''n''th Doomsday is in [[ISO week date|ISO week]] ''n''. In common years the day after the ''n''th 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:
 
:<math>\mbox{Doomsday} =  \mbox{Tuesday} + y + \left\lfloor\frac{y}{4}\right\rfloor - \left\lfloor\frac{y}{100}\right\rfloor + \left\lfloor\frac{y}{400}\right\rfloor = \mbox{Tuesday} + 5\times (y\mod 4) + 4\times (y\mod 100) + 6\times (y\mod 400)</math>
For example, the year 2009 has a doomsday of Saturday under the Gregorian calendar (the currently accepted calendar), since
 
:<math>\mbox{Saturday (6)} \mod 7 =  \mbox{Tuesday (2)} + 2009 + \left\lfloor\frac{2009}{4}\right\rfloor - \left\lfloor\frac{2009}{100}\right\rfloor + \left\lfloor\frac{2009}{400}\right\rfloor</math>
:<math>  = ( 2 + 2009 + 502 - 20 + 5) \mod 7 = (2 + 0 + 5 - 6 + 5) \mod 7 = 6 </math>
 
For the Julian calendar:
 
:<math>\mbox{Doomsday} =  \mbox{Sunday} + y + \left\lfloor\frac{y}{4}\right\rfloor = \mbox{Sunday}+ 5\times (y\mod 4) + 3\times (y\mod 7)</math>
 
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 [[Julian day#Calculation|the calculation of a Julian day number]].
 
==400-year cycle of Doomsdays==
{|class="wikitable" style="clear:right;float:right;margin:0.5em 1em 0.5em 0;text-align:center"
|-
!style="text-align:center"|Julian<br /> centuries<br /> <br /> ———<br /> <br /> Gregorian<br /> centuries<br /> <br /> \<br /> <br />Years
!valign="top" scope="col"|-200J<br />  500J<br /> 1200J<br /> 1900J<br /> —<br /> -400<br />  0<br /> 400<br />  800<br /> 1200<br /> 1600<br /> 2000<br /> 2400
!valign="top" scope="col"|-100J<br />  600J<br /> 1300J<br /> 2000J<br /> —<br />
!valign="top" scope="col"|  0J<br /> 700J<br /> 1400J<br /> 2100J<br /> —<br /> -300<br /> 100<br /> 500<br />  900<br /> 1300<br /> 1700<br /> 2100<br /> 2500
!valign="top" scope="col"| 100J<br />  800J<br /> 1500J<br /> 2200J<br /> —<br />
!valign="top" scope="col"| 200J<br />  900J<br /> 1600J<br /> 2300J<br /> —<br /> -200<br /> 200<br /> 600<br /> 1000<br /> 1400<br /> 1800<br /> 2200<br /> 2600
!valign="top" scope="col"| 300J<br /> 1000J<br /> 1700J<br /> 2400J<br /> —<br />
!valign="top" scope="col"| 400J<br /> 1100J<br /> 1800J<br /> 2500J<br /> —<br /> -100<br /> 300<br /> 700<br /> 1100<br /> 1500<br /> 1900<br /> 2300<br /> 2700
|-style="background:#EEF"
!scope="row" style="text-align:left"|00 28 56 84
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-
!scope="row" style="text-align:left"|01 29 57 85
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-
!scope="row" style="text-align:left"|02 30 58 86
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-
!scope="row" style="text-align:left"|03 31 59 87
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-style="background:#EEF"
!scope="row" style="text-align:left"|04 32 60 88
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|-
!scope="row" style="text-align:left"|05 33 61 89
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-
!scope="row" style="text-align:left"|06 34 62 90
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-
!scope="row" style="text-align:left"|07 35 63 91
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-style="background:#EEF"
!scope="row" style="text-align:left"|08 36 64 92
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-
!scope="row" style="text-align:left"|09 37 65 93
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-
!scope="row" style="text-align:left"|10 38 66 94
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|-
!scope="row" style="text-align:left"|11 39 67 95
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-style="background:#EEF"
!scope="row" style="text-align:left"|12 40 68 96
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-
!scope="row" style="text-align:left"|13 41 69 97
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-
!scope="row" style="text-align:left"|14 42 70 98
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-
!scope="row" style="text-align:left"|15 43 71 99
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-style="background:#EEF"
!scope="row" style="text-align:left"|16 44 72
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-
!scope="row" style="text-align:left"|17 45 73
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-
!scope="row" style="text-align:left"|18 46 74
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-
!scope="row" style="text-align:left"|19 47 75
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-style="background:#EEF"
!scope="row" style="text-align:left"|20 48 76
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-
!scope="row" style="text-align:left"|21 49 77
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|-
!scope="row" style="text-align:left"|22 50 78
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-
!scope="row" style="text-align:left"|23 51 79
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-style="background:#EEF"
!scope="row" style="text-align:left"|24 52 80
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-
!scope="row" style="text-align:left"|25 53 81
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-
!scope="row" style="text-align:left"|26 54 82
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-
!scope="row" style="text-align:left"|27 55 83
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|}
 
Since in the Gregorian calendar there are 146097 days, or exactly 20871 seven-day 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 400-year cycle of Doomsdays is given in the table to the right. 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.
 
{|class="wikitable" style="margin:1em auto;text-align:center"
|+ '''Frequency of Gregorian Doomsday in the 400-year cycle per weekday and year type'''
|-
! !!scope="col"|Sunday!!scope="col"|Monday!!scope="col"|Tuesday!!scope="col"|Wednesday!!scope="col"|Thursday!!scope="col"|Friday!!scope="col"|Saturday
!!scope="col"|Total
|-
!scope="row" style="text-align:left"|Non-leap years
| 43 || 43 || 43 || 43 || 44 || 43 || 44 || '''303'''
|-
!scope="row" style="text-align:left"|Leap years
| 13 || 15 || 13 || 15 || 13 || 14 || 14 || '''97'''
|-style="font-weight:bold"
!scope="row" style="text-align:left"|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 497-day 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.
 
===28-year cycle===
Regarding the frequency of Doomsdays in a Julian 28-year 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|date=January 2008}} 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 5-year 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|Gregorian calendar]] accurately lines 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.
{{Clr}}
 
==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, we'll add three things, called ''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 8. 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. 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+floor(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 ==
*[[Common year starting on Saturday|Mon]] - [[Common year starting on Sunday|Tue]] - [[Common year starting on Monday|Wed]] - [[Common year starting on Tuesday|Thu]] - [[Common year starting on Wednesday|Fri]] - [[Common year starting on Thursday|Sat]] - [[Common year starting on Friday|Sun]] – common years with the given Doomsday
*[[Leap year starting on Friday|Mon]] - [[Leap year starting on Saturday|Tue]] - [[Leap year starting on Sunday|Wed]] - [[Leap year starting on Monday|Thu]] - [[Leap year starting on Tuesday|Fri]] - [[Leap year starting on Wednesday|Sat]] - [[Leap year starting on Thursday|Sun]] – leap years with the given Doomsday
*[[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==
{{Reflist}}
 
==External links==
{{commons}}
*[http://translate.googleusercontent.com/translate_c?hl=en&sl=de&u=http://www.lybrary.com/kalender-kopf-gral-p-35993.html&rurl=translate.google.com&twu=1&usg=ALkJrhjGBsfFgwmsN6emA0SwOE9BeTVCGw Encyclopedia of Weekday Calculation by Hans-Christian Solka, 2010]
* [http://homer.freeshell.org/dd.cgi Doomsday calculator that also "shows all work"]
* [http://www.recordholders.org/en/records/dates.html World records for mentally calculating the day of the week in the Gregorian Calendar ]
* [http://quasar.as.utexas.edu/BillInfo/doomsday.html What is the day of the week, given any date?]
* [http://rudy.ca/doomsday.html Doomsday Algorithm]
* [http://www.theworldofstuff.com/other/day.html Finding the Day of the Week]
* {{Wayback|url=http://www.cs.wustl.edu/~ksl2/mathpoem.html|title=Poem explaining the Doomsday rule|date=20061018103244}}
 
{{DEFAULTSORT:Doomsday Rule}}
[[Category:Gregorian calendar]]
[[Category:Julian calendar]]
[[Category:Calendar algorithms]]

Revision as of 18:47, 16 November 2013

John Conway, inventor of the Doomsday algorithm.

The Doomsday rule or Doomsday algorithm is a way of calculating the day of the week of a given date. It provides a perpetual calendar since the Gregorian calendar moves in cycles of 400 years.

This algorithm for mental calculation was devised by John Conway[1][2] after drawing inspiration from Lewis Carroll's work on a perpetual calendar algorithm.[3][4] It takes advantage of the fact that each year has a certain day of the week (the doomsday) upon which certain easy-to-remember 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 given year. Applying the Doomsday algorithm involves three steps:

  1. Determine the "anchor day" for the century.
  2. Use the anchor day for the century to calculate the doomsday for the year.
  3. Choose the closest date out of the ones that always fall on the doomsday (e.g. 4/4, 6/6, 8/8), and count the number of days (modulo 7) between that date and the date in question to arrive at the day of the week.

This technique applies to both the Gregorian calendar A.D. and the Julian calendar, although their doomsdays will usually be different days of the week.

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 "Sansday" (for Sunday), "Oneday", "Twosday", "Treblesday", "Foursday", "Fiveday", and "Six-a-day".

The algorithm is simple enough for anyone with basic arithmetic ability to do the calculations 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.[5]

Doomsdays for some contemporary years

Doomsday for the current year in the Gregorian calendar (2024)' is '.

For some other contemporary years :

Doomsdays for the Gregorian calendar
Mon. Tue. Wed. Thu. Fri. Sat. Sun. Mon. Tue. Wed. Thu. Fri. Sat. Sun.
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

Notes: Fill in the table horizontally, skipping one column for each leap year. This table cycles every 28 years, except in the Gregorian calendar on years multiple of 100 (like 1900 which is not a leap year) that are not 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 easily 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 easy-to-remember dates for each month that always land on the Doomsday.

As mentioned above, the last day of February always falls on the doomsday, as do the double dates 4/4, 6/6, 8/8, 10/10, and 12/12. Four of the odd month dates (May 9, September 5, July 11, and November 7) can be remembered with the mnemonic "I work from 9 to 5 at the 7-11." For March, one can remember the pseudo-date "March 0", which refers to the day before March 1, i.e. the last day of February; one can alternately remember the date a week later, March 7, or March 21 which is traditionally regarded as the first day of spring in the northern hemisphere and autumn in the southern hemisphere (although after 2007 the Northward equinox will not fall on that date in Europe again until 2102).[6] For January, January 11 is a Doomsday during leap years, while January 10 is a Doomsday during common years; 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".

Month Memorable date Month/Day Mnemonic
January January 3 (common years), January 4 (leap years)
January 11 (leap years)
1/3 or 1/4
1/11
the 3rd 3 years in 4 and the 4th in the 4th
all ones
February February 14 (common years)
February 22 (leap years)
February 28 (common years), February 29 (leap years)
2/14
2/22
2/28 or 2/29
Valentine's Day
all twos
last day of February
March "March 0"
March 14
March 21
3/0
3/14
3/21
last day of February
Pi day
traditionally first day of spring/autumn
April April 4 4/4 even month
May May 9
May 30
5/9
5/30
9-to-5 at 7-11
Traditional Memorial Day (United States)
June June 6
June 20
6/6
6/20
even month
traditionally first day of summer/winter
July July 4
July 11
7/4
7/11
Independence Day (United States)
9-to-5 at 7-11
August August 8 8/8 even month
September September 5 9/5 9-to-5 at 7-11
October October 10
October 31
10/10
10/31
even month
Halloween
November November 7 11/7 9-to-5 at 7-11
December December 12
December 26
12/12
12/26
even month
Boxing Day

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.

Examples

Suppose you want to know which day of the week Christmas Day of 2006 was. In the year 2006, Doomsday was Tuesday. Since December 12 is a Doomsday, December 25, being thirteen days afterwards (two weeks less a day), fell on a Monday.

It's useful to note that Christmas Day is always the day before Doomsday ("One off Doomsday"). In addition, July 4 is always on a Doomsday, and so is Halloween.

Suppose that you want to find the day of week that the September 11, 2001 attacks on the World Trade Center occurred. The century anchor was Tuesday, and Doomsday for 2001 is one day beyond, which is Wednesday. September 5 was a Doomsday, and September 11, six days later, fell on a Tuesday.

Finding a year's Doomsday

We 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 We-in-dis-day
(most living people were born in that century)
3 (Treblesday)
2000–2099 Tuesday Y-Tue-K or Twos-day
(Y2K was at the head of this century)
2 (Twosday)
2100–2199 Sunday Twenty-one-day is Sunday
(2100 is the start of the next century)
0 (Noneday)

Next, we find the year's Doomsday. To accomplish that according to Conway:

  1. Divide the year's last two digits (call this y) by 12 and let a be the floor of the quotient.
  2. Let b be the remainder of the same quotient.
  3. Divide that remainder by 4 and let c be the floor of the quotient.
  4. 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.)
  5. 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 twentieth-century 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

Doomsday rule

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 plus 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 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 compensates for this error, giving the final formula.

The Odd+11 method

A simple flowchart showing the Odd+11 method.

A simpler method for finding the year's doomsday was discovered in 2010 by Chamberlain Fong and Michael K. Walters,[7] and described in their paper submitted to the 7th International Congress on Industrial and Applied Mathematics (2011). Called the Odd+11 method, it has been proved[7] equivalent 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:

  1. Let T be the year's last two digits.
  2. If T is odd, add 11.
  3. Now let T = T/2.
  4. If T is odd, add 11.
  5. Now let T = 7 − (T mod 7).
  6. Count forward T days from the century's anchor day to get the year's Doomsday.

Applying this method to the year 1966, for example, the steps as outlined would be:

  1. T = 66
  2. T = 66 (Do nothing since T is even.)
  3. T = 66/2 = 33
  4. T = 33+11 = 44 (Add 11 because T is odd.)
  5. T = 7 − (44 mod 7) = 7 − 2 = 5
  6. Doomsday for 1966 = 5 + Wednesday = Monday



The explicit formula for the odd+11 method is:

Although this expression looks daunting and complicated, it is actually simple[7] because of a common subexpression that only needs to be calculated once.

Dominical letter method

A year's doomsday (DD) can be determined from a year's dominical letter (DL), too.

Note: A = 1, B = 2, ..., G = 0.

For the year 1966 the dominical letter is B, so the doomsday DD = 3 - 2 = 1 = Monday.

Finding a century's anchor day

For the Gregorian calendar:

For the Julian calendar:

Note:

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

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.

400-year cycle of Doomsdays

Julian
centuries

———

Gregorian
centuries

\

Years
-200J
500J
1200J
1900J

-400
0
400
800
1200
1600
2000
2400
-100J
600J
1300J
2000J

0J
700J
1400J
2100J

-300
100
500
900
1300
1700
2100
2500
100J
800J
1500J
2200J

200J
900J
1600J
2300J

-200
200
600
1000
1400
1800
2200
2600
300J
1000J
1700J
2400J

400J
1100J
1800J
2500J

-100
300
700
1100
1500
1900
2300
2700
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 seven-day 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 400-year cycle of Doomsdays is given in the table to the right. 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.

Frequency of Gregorian Doomsday in the 400-year cycle per weekday and year type
Sunday Monday Tuesday Wednesday Thursday Friday Saturday Total
Non-leap 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 497-day 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.

28-year cycle

Regarding the frequency of Doomsdays in a Julian 28-year 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).Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. 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 5-year 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 accurately lines 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. Singapore was ranked 11 th out of sixty six cities in a 2012 International Cities Index rating on leaders in globalisation URA). In contrast, when adjusted for inflation, the property value index really fell by round 1.1% over the identical interval. In 2011, consumers from China had been the most important group of foreign property patrons in Singapore. (Yahoo! file photograph) Welcome to Singapore Property For Sale! That includes Singapore, JB Iskandar, London, Australia, Philipiines, Cambodia Property!

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One factor we've got on this country is a big group of "economists," and "market analysts." What's interesting about this group of real property market-watchers is that there are two very different ways through which they predict Boomers will influence housing markets over the next decade. Let's check out those two opposites and see how each can change the way in which real property buyers method their markets. Quiet Enjoyment 19. The Landlord covenants that on paying the Hire and performing the covenants contained in this Settlement, the Tenant will peacefully and quietly have, hold, and benefit from the Property for the agreed time period. Register now for VIP preview quickly this Might and be the 1st toselect your selection unit at particular Preview Worth. No overseas income tax

The place you might be shopping for property which is underneath building, the Singapore Academyof Law will hold a portion of the acquisition monies as stakeholders until the expiryof the defects legal responsibility interval offered in the Agreement/Contract. GST just isn't payable on residential property at present. However, as some residentialproperties (e.g. shophouse with a flat above) might contain a industrial componentyou should seek advice from your lawyer on this. Your Lawyer's Role in a Property Sale Singapore residents shopping for their second homes will likely be hit with an ABSD of seven% whereas people with permanent residency status will pay an additional stamp duty of 5% on their first dwelling purchase. For extra information and analysis on Singapore Price range 2013, click on here for ST's Massive Story coverage.

It is because the variety of new properties in singapore; additional resources, cluster-housing launches appears to be like set to fall after this yr, following a current change in Authorities regulations, say property specialists. Analysts noted that cluster homes are widespread among larger families, preferring the bigger constructed-up space typical of landed homes however want to have apartment amenities as well. Merely simply name me or fill up my Promoting / Leasing Enquiry type when you're able to put up your property in the marketplace.Your property will obtain its own internet page which includes full property data and pictures, hyperlinks to maps, community info. Deborah Legislation from Expat Realtor shares her property market update, plus prime rental flats and houses at the moment available to lease Student's boarding house or hostel

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, we'll add three things, called 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 8. 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. 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+floor(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

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

Most brokers paid and post their listings at these online property categorised portals but fail to realise that there is simply extra to it. They fail to leverage on one of the vital well-liked on-line advertising and marketing tool of their marketing campaign and that is through the social media.

In case you are among the many few who've passed the grueling Actual Estate Salesperson (RES) course, congratulations. So what next? Which agency should you be a part of? Earlier than taking the plunge, you will need to choose the proper mentor who can educate you the ropes in actual estate. An excellent mentor will allow you to navigate the complex world of real property by instructing you the way to get listings, advertising and marketing methods, real estate contracts and methods to closing your deal. He will even caution you on errors to keep away from that would land you in trouble. This has been reflected within the Industrial Production reading index for prescribed drugs. In June, the reading fell to one hundred thirty from 287. Effectively if you do not, you then're simply leaving your actual property enterprise to chance. Commons for rent

Thanks to hirepropertyagent.com.sg, i've discovered myself a good agent. He did a great job promoting my property and it was bought at an excellent value." JLL appointed unique agent for the sale of 2, 4 and 6 Dunlop Street by Expression of Curiosity. Uncommon Industrial Growth inside Pandan Meals Zone space up for sale conserving you updated with the property market 3. Work @ Residence IT Solutions As property costs cool in Hong Kong and Singapore, which have lengthy been magnets for Chinese language funding, extra money is flowing to actual property markets comparable to New York, London and Sydney. Chinese language have overtaken Russians house for sale in singapore the primary time as the biggest buyers of flats in Manhattan, in response to actual estate brokers. Condominium For Lease – Tribeca by the Waterfront (D09)

Property developer and residential landlord for flats and homes for lease and sale. Most property firms share the same database of property listings in Singapore. Due to this fact it is best to solely use only ONE agent at a time. In case you approach many agents at the similar time, very likely that they'll present you the same property. A lot confusion and embarrassment will arise should you engage many brokers. One of the best, and most of the time only, strategy to discover a good property agent in Singapore is phrase-of-mouth. Ask your friends and colleagues for reference. It is very simple to provide you with a couple of candidates since a lot of the expatriates dwelling in Singapore for a long time can have several good agent contacts to guide you. Toa Payoh, Singapore Singapore 319378 Estate

This is precisely what happened to me and my husband at the moment, to not point out a very unscrupulous developer operating in a really unprofessional manner. I need to share this story with everyone here, and please pass the message round particularly among expats communities, beware while you want to purchase property developed by VicLand Pte Ltd and if developer's agent is ECG property. There was only one unit left on the market by developer, 03-09, a 3 bed room flat. On the time my husband was out of town, and initially I liked what I saw so I instructed the developer's agent and my agent we should come back with my husband in two weeks to view it once more and make a decision after ward. Complaint / Suggestions about lousy property agent Darren Ng from Dennis Wee

This bought me thinking and I started to surprise – how much does a property agent really earn? We often hear or read about sure brokers making million dollar commissions, however is that the exception or the norm? That piqued my curiosity. Like any job, those who put in time and effort will do well and rise to the top. The ethics of exhausting work apply to the true property market as nicely. For individuals who are pondering of making a career change to develop into a property agent, you should be ready to invest the trouble to do properly. Otherwise you may just add to the statistic of brokers who eventually drop out of the realtor game. Properties that do not fall within the definition of residential properties stated above are non-residential properties Web site - www.riaschool.com.sg

Ought to you are on the lookout for new properties for investment or for own stay, we offer property recommendation and search services tailored to your needs. We have represented many together with worldwide and local buyers in efficiently finishing their property purchases. We work with main builders to bring you the latest and one of the best prime properties in Singapore. We are a one-cease service that may full your property cycle from purchase to sale. Property agents for Singapore Land Authority protecting among the government colonial properties for rent. Property leases for expatriates and foreigners. Also helps expats to purchase and promote their properties as well as property investment opportunities in Singapore and China. The Restaurant Affiliation of Singapore

  • Encyclopedia of Weekday Calculation by Hans-Christian Solka, 2010
  • Doomsday calculator that also "shows all work"
  • World records for mentally calculating the day of the week in the Gregorian Calendar
  • What is the day of the week, given any date?
  • Doomsday Algorithm
  • Finding the Day of the Week
  • The minimal educational requirement to take the REA or RES examination is four GCE "" level passes or equal. When you have taken the obligatory preparatory course offered by a CEA Authorised Course Supplier and want to apply for the exam, please click on right here.

    In an ordinary Singapore Tenancy Agreement, there is usually the reimbursement clause together with the diplomatic clause. This clause states that in the event you train the diplomatic clause, you will have to reimburse a part of the commission the landlord had paid to his agent. Figures additionally show that the number of property agents registered with the Council for Estate Companies (CEA) The property company watchdog mentioned property agents who did not continue with their registration were part timers Tuas South Road 5 Industrial Website on the market So the right way to be a Real Estate Agent in Singapore? Be registered with just one Licensed Estate Agent (Actual Estate Firm) Abroad Property Analysis Experiences Region Property Consultancy & Management Providers Pte Ltd UE Square (D09) – Residence For Hire

    final January. There are also fewer property companies in business, down by 5% to lower than 1,500. Other than passing a compulsory examination, registered property brokers also have to endure six hours of Some business players stated new agents face a tough time juggling this and shutting property deals. With a purpose to make the TA a sound authorized document to be honoured by all parties involved, it must be stamped by the Singapore Inland Revenue Authority (IRA). The costs for this process, a so-known as "stamp obligation", are to be borne by the tenant. Softening in residential property costs proceed, led by 2.8 per cent decline within the index for Remainder of Central Area Freehold improvement in the prestigious Ardmore Park / Claymore district with potential for en bloc sale

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    Vendor Pays the Buyer's Dealer Commission via his itemizing agent. Underneath a Purchaser's Broker arrangement, the named brokerage and agent represent the customer. The price paid to the broker mostly is paid by the vendor. Some buyer dealer agreements include clauses that will compensate the brokerage for the price it's due less the quantity paid by the vendor. When I managed to sell a property for my shopper at double fast time and at a really good worth. The worth was higher than most models being bought at the moment. It was a lot of onerous work and naturally Luck performed an enormous part. The Consumer was very very grateful. Sellers pay a 2% commission. May be decrease for more expensive properties. CONTACTING ME We Will Achieve Your Wants And Desires In Actual Estate
  1. John Horton Conway, "Tomorrow is the Day After Doomsday", Eureka, volume 36, pages 28-31, October 1973.
  2. 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 0-12-091102-7.
  3. Lewis Carroll, "To Find the Day of the Week for Any Given Date", Nature, March 31, 1887.
  4. Martin Gardner, "The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays", pages 24-26, Springer-Verlag, 1996
  5. Alpert, Mark. "Not Just Fun and Games", Scientific American, April, 1999.
  6. Template:Cite web
  7. 7.0 7.1 7.2 Chamberlain Fong, Michael K. Walters: "Methods for Accelerating Conway's Doomsday Algorithm (part 2)", 7th International Congress on Industrial and Applied Mathematics (2011)