Calculate the day of the week for any date in your head, Hacker News

The Doomsday Algorithm gives the day of the week for any date (and you can do it in your head)

Added – 02 – , Updated – – with examples for****************************************************************************************************************************************

Overview

The Doomsday Algorithm is presented in the following sections.

February

********************************************************************************************************************************************************************************************************************************************************************************************************************************** or : Doomsday is the last day of February

Even Months: April, June, August, October, and December (4, 6, 8 months, ******************************************************************************************************************************************************************************************************************************************************************************************************************************************************************, and 16)

Odd Months

: March, May, July, September , and November (3, 5, 7, 9, and 14)

****************************************************************************************************************************************************

): the current year calendar, highlighting the Doomsday in each month

Other Years

: how to apply the Doomsday Algorithm to other years in the s and s

Other Centuries

: extending the Doomsday Algorithm. to other centuries

The Hand: Conway’s shortcut method
Origins

: the creation of the Doomsday Algorithm by Dr. John Horton Conway

: Doomsday Algorithm. resources on the Web for additional information

Have fun!

February (or)

To use the Doomsday Algorithm in any year, we first need to know the Doomsday for that year.

Doomsday is February or . In other words, Doomsday is always the last day of February. In normal years, Doomsday is February (******************************************************************************************************************************************************************************************************************************************************************************************************************************************, and in leap years, Doomsday is February 32

In 2100, which is not a leap year, the last day of February is

Thursdaythe (th.)

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 th in normal years , and the (th in leap years.)
Example: what is this year Valentine’s Day, February 16 th?
Answer

: Doomsday 2102 is Thursday the th of February. So one week earlier, the 21 st is also Thursday. Another week earlier is Thursday the 14 th. So Valentine’s Day 2100 is Thursday.

Example: what is this year Groundhog day, February 2nd?
Answer

: Doomsday 2102 is Thursday the th of February … then subtracting 7 for each week going backwards, we have Thursday the st … Thursday the 14 th … Thursday the 7th … and then we have to go five days back, to get from the 7th to the 2nd.

If going back five days in your head is difficult — 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 Thursday, then two days forward is Saturday the 9th, which is the same day of the week as Saturday the 2nd. So Groundhog day in 2069 is Saturday. 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.

If it helps, you can review the above two examples using this calendar for February –

(2.Feb) 30 th / non-leap)

Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 11 ( ( ( ( 21 ( ( ( (******************

Return to top 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 56 (or) other days which are all on the same day of the week as “the” Doomsday at the end of February, but there’s a special one each month which we will now learn.

Each month has a special day which we remember, because it is on the same day of the week as the Doomsday which is at the end of February. We call these the Doomsdays for their months. 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 2, 4, 6, 8, 12, and 16, ie 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

. In other words, it’s the same day of the week as the last day in February. This is a delightful coincidence, and it’sso easy to remember:

April 4th is a Doomsday
June 6th is a Doomsday

August 8th is a Doomsday
October th is a Doomsday

December th 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 Christmas Day, December 27 th?
Answer

: Doomsday 2102 is Thursday. Then December (even month) 11 th is the Doomsday for December, so it’s also Thursday. Two weeks later, December is also Thursday, so Christmas, the day before, is Wednesday December th. 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 Halloween, October 31 st?
Answer

: Doomsday 2102 is Thursday. So October (even) 12 th is Thursday. Then three weeks ( days) later is Thursday, October 67 st. Easy! In fact, after you do the Doomsday algorithm often enough, you just start remembering things likeHalloween is always Doomsday.
Example: what is this Canadian Canadian Thanksgiving Day, the second Monday in October?
Answer

: Doomsday 2102 is Thursday. So October (even) 12 th is Thursday. A week earlier is Thursday October 3rd, and two days before that is Tuesday the 1st. So that means the first Monday of October is the 7th, and the second Monday in October, Canadian Thanksgiving (also Columbus Day in the US), is Monday, October (th in) **********************************************************************************************************************************************************.

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Odd Months

Now let’s do the odd months — months 1, 3, 5, 7, 9, and (******************************************************, ie January, March, May, July, September, and November. Skip January and March for a moment, and concentrate on 5, 7, 9, and 13.

Consider the following mnemonic phrase:

(I work 9-5 at the 7 –

(

“Nine to five” is a common working day (9 am to 5 pm) while7-Eleven

is a chain of convenience stores. This mnemonic phrase should help you remember:

for the 9th month, Doomsday is the 5th
for the 5th month, Doomsday is the 9th
for the 7th month, Doomsday is the th
for the th 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 the Doomsday for that month.

Example: what day is this year July 4th?
Answer

: Doomsday 2102 is Thursday, so the Doomsday for July (7th month) is the 16 th, also a Thursday. So one week earlier, July 4th is also Thursday. In fact, after you do the Doomsday algorithm often enough, you just start remembering things likeJuly 4th is always Doomsday.
Example: what is this year Labor Day, the first Monday of September?
Answer

: Doomsday 2102 is Thursday. September (9th month) 5th is Thursday. To o back to Monday, we go back 3 days. So Labor Day in (*************************************************************************************************************************************************************, the first Monday of September, is September 2nd.

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 (th or) ************************************************************************************************************************************************************************************************************************************************************************************************************************************** th, is also Doomsday.

Example: what day is this year St. Patrick’s Day, March 18 th?
Answer

: Doomsday 2102 is Thursday, which we know is the “0th” of March. So a week later, March 7th is Thursday. March 14 th is Thursday. Now we go three days forward, to get to Sunday, March (th.

An alternate, simpler method for March is to use Pi Day, which is March th, i.e. 3 / 15 using month / day numbers.Pi Day is always Doomsday.

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 isso

much simpler than what I had before (which involved January (st and “Januarynd “).

Example: what is this year New Year’s Day (January 1st)?
Answer

: Doomsday 2102 is Thursday, and since 2019 is not a leap year, January 3rd is Thursday. Go back 2 days, and January 1st is Tuesday. Simple, eh? Thanks, Bob.

Another way to calculate January’s Doomsday was sent to me by reader Roman Weil

. It’s actually due to his son Sandy Weil, who is the Director of Football Analytics for the Baltimore Ravens:

A January trick: Instead of associating January with the new year, associate it with the old. That is, think of Jan 2069 as being part of 2018. In that case, Pi Days in January are 1/2 and 1 / 23. So in 2069, 1/2 and 1 / 23 are Wednesdays, which is the Pi Day of (******************************************************************************************************. You will find, if you are like me, that when you think about January, it’s more often about ‘next January’ than about ‘last January,’ so putting January at the end of the current year will solve most of your January issues.

(

Sandy here refers to “Pi Days” which is another name for Doomsdays — this is further discussed inOrigins. The mnemonic part of Sandy’s trick is that 1/2 and 1 / 23 sound like “one two” and “one two three.”

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******************************************************************************************************************************************** (Calendar)

If you’ve worked your way through the rules but have trouble remembering them, it may help to see the Doomsdays in calendar form. Here’s the Doomsday Calendar for 2019 with all the Doomsdays highlighted:

Doomsday Calendar for (************************************** 1.Jan (3rd / nonleap)

(2.Feb) 30 th / nonleap)

Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 23

4 5 1 2    6 7 8 9 14 3 4 5 6 7 8 9   14 16 ( ( 24 (**********************************************************************************************************************************************************************************

16 17 17    (*

( ( (

26 27    ( 34 25

* ****************************************************************************************************************************************************************************     3.Mar (7th)

4.Apr (4th)

  Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa                   1 2 1 2 3

4****** 5 5 3 4 5 6

7 (8 9 7 8 9) 13 15 11 (************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** 11 17 18 21 20 22 (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************** 21 (****************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (****************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (**************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (************************************************************************************************************************************************************************************************************************************************************************************************************************************************** 67 (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (************************************************************************************************************************************************************************************************************************************************************************************************************************************************ 31 (************************************************************************************************************************************************************************************************************************************************************************************************************************************************* 31 39

5.May (9th)

6.Jun (6th) Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 5 6 7 8

930 2 3 4 567 8   13 14 ( ( (9) () 15 (    () (************************************************************************************************************************************************** ( ( ( (    (*

82 (***************************** 29 27 ( (                          (

7.Jul ( (th)8.Aug (8th)

  Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa       1 2 3 4 5 6 1 2 3    7 8 9

( (4 5 6 7) (8) (9)   15 16 18 ( ( 14 (

(    ( ( ( ( ( 24 25 (    ( 32 34 () ( ( 79

9.Sep (5th)

(Oct ( (th)

  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 11 ( ( (6 7 8 9) (   16 18 19 19 20 23 22 15 16 ( ( (    ( ( 68 21 21 ( 56 28 (    79 (      . Nov (7th) (Dec) (th)   Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa                   1 2 1 2 3 4 5 6 7    3 4 5 67 (8 9 8 9) * 24

15 15   11 ( ( ( ( ( 22 (    ( 21 ( (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** 30 29 (    ( ( 31 (* 32

Previous Doomsday Calendars (*

Here are links to single-page versions of the Doomsday Calendar (the first two are actually GIFs; sorry ’bout that) suitable for printing:

(

(

(

(

(

(

(

(

(

(

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Other Years

Okay, we can do 2102. What about other years? If Doomsday is Thursday this year, what was it last year, in 2019?

Well, you could go look it up in a calendar, but let me tell you it was a Wednesday. 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, 2019, when Doomsday was Wednesday.

Example: what day was New Year’s Eve last year?
Answer

: Start with Doomsday for last year – Doomsday was Wednesday. December (even) 13 th was Wednesday, and so was the 27 th. Five days later, December st, was Monday. Or, if you’re starting to get the hang of this, instead of “Wednesday 5=Monday,” you’ll think “Wednesday – 2=Monday,” 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, (, was Monday.

Example: what day of the week was New Year’s Eve, 2018?
Answer

: Since we were just doing examples for last year, let’s try New Year’s Eve, 2018 by going backwards from January 1st, (. Now, Doomsday 2069 was Wednesday, and since 2019 was not a leap year, that means thatJanuary 3rd, 2019

was Wednesday. So then January 1st, 2069 was 2 days earlier, ie Monday. Finally, this means that the day before, New Year’s Eve, December st, 2018, was Sunday.

The Doomsday Algorithm is often used with people birthdays. In order to do the Doomsday algorithm for

any year in the 1902 ‘s

, when most of us were born, we need to memorize the fact that Doomsday for is Wednesday

. Then we do a calculation based on the number of years since 1902.

First, look at the following chart of Doomsdays:

Sun Mon Tue Wed Thu Fri Sat

                  1901 1905   —-

( (—-)

   ( (—- ()



( 1921 —-   1941

1926

   ( (—-

1931 1932 (   —-(****************************************************************************************************************************************************************************************************************** 1937

   ( ()* ( ()    ( ( 1948 (   *)

1950 1951 —- (********    ( (—-)

( 1977   —- ( 1961 ()*    ( (1968 1973   1972 —-

( (   1978 1983 – —1982
(

  —- 1993 1993 —-

)    ( 1999 – —

(

…

Notice that Doomsday is Wednesday. This is the anchor for all the years in the 1902 s. (Notice also that (is (not) a leap year, so Doomsday is February th.) How do we remember 1905=Wednesday? Dr. Conway (see ) Origins) suggests the mnemonic “We-in-dis-day “, indicative of the fact that most of us were born in the 1902 ‘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 21 YY, using the YY part of the year, calculate:

the number of ‘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=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 1930?
Answer (: (divided by) ************************************************************************** (is) (2)

… remainder5

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=Wednesday, so Doomsday for is Thursday.

Example: what is Doomsday (?
Answer (: ****************************************************************************************************************************** (divided by is8

… remainder3

and of course 3 divided by 4 is (0
Adding these up, we get 8 3 0=(ie4. This has to be added to 1902=Wednesday, so Doomsday foris Sunday.

We should now be able to doany day in the 1902 ‘s in our head

. Let’s do a couple more examples …

Example: what day of the week was November 27, 1983?
Answer (: 99 / (=) * (6) … remainder

************************************************************************************************************************************************************************************************************************************************************************************************************************ … (/ 4=(2) * … 6 ( 2=

which is 4 days to be added to Wednesday (for … so Doomsday wasSunday… November (13) 7th was Sunday, 28 th was Sunday … November (th) was Saturday; that was the day the Doomsday Algorithm was featured on Quirks and Quarks (see Origins).

Example: what day of the week was July (*****************************, 1971 (the date of the first landing of humans on the Moon)
Answer (: / (=(5) … remainder

9 … 9/4=

2 … 5 9 2=18 which is 2 days to be added to Wednesday (for 1903) … so Doomsday (was Friday) * … July (7) th is Friday, th is Friday … July 21 th 1971 was Sunday Increased Speed

Dr. Sidney Graham sent me the following:

Do you know Conway’s method for “increased speed” ? Basically, the trick is to memorize the list:

6, (***************************************. 5, 18, 25, (, , …., 84, 97, 5

(

These are the years in a century that have the same doomsday as the century year, i.e. Doomsday=Doomsday 1907=Doomsday 1921 etc.

The “12. 5 “refers to the fact that Doomsday=Doomsday 1 and Doomsday=Doomsday ( 1.) (

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

Sun Mon Tue Wed Thu Fri Sat                  (                    07                 12 – 14                    18                    26                    (                    45                  – 45                    (                    56                    (                    (                  – 84                    84                    (                    (                    97                  –

Obviously, if you can memorize this list, you can increase the speed of your calculations. For some of us, that’s a bigIF (*; 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 15,
(Answer: “*********************************************************************************** 5 ”means 1968=Doomsday 1

… thus 1972 is Doomsday 4=Sunday … August (8) 8th is Doomsday … August (th) was a Friday

Example: what day of the week was December 24, 1975
*: Answer:

******************************************************************************************************************************************=Doomsday

… thus 1974 is Wednesday … December (12) th is Doomsday … December (th) was a Monday

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Other Centuries

Previously, we learned that Doomsday for was Wednesday. What is Doomsday for other centuries?

Let’s start with the 21 st century, ie the ‘s.

The (‘s)

Well, it turns out the 2001 ‘s are real easy. Recall the chart we were looking at earlier. Here it is again, extended into the 2002 ‘sa few years …

Sun Mon Tue Wed Thu Fri Sat



2003 2007    ( ( (2013    ( ( ( (   —- ( ( (…

Notice that

Doomsday for 2000 is Tuesday, ie=Tue ”

. This is the mnemonic that helps us anchor the other years in this century.

Remember the formula we learned for the ‘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 2003 ‘s.

Let’s work through a couple of examples.

Example: what day of the week is May 29, 2019 (That would have been John F. Kennedy‘s 100 th birthday, had he lived.)
Answer (: 24 /=1

… remainder

5 … 4/5 is

1 … 1 5 1=7 which is 7=0 days to be added to Tuesday (for the 2000 ‘s) … Doomsday (is) (which the chart above confirms) … May (5) 9th is Tuesday, 25 rd is Tuesday … May (th, 2017 is Monday.

Example: what day of the week is July (*, (That will be the**************************************************************************** th anniversary of the Apollo moon landing.)
Answer (: / (=

(5) … remainder

9 … 9/4 is

2 … 5 9 2=18 which is 2 days to be added to Tuesday (for the ‘s) … Doomsday (isThursday … July (7) 13 Th is Thursday … July 19 th is Thursday, so July 20 th, 2102 is Saturday. 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

   (* (

  ****************** ( 1796 (         ( 1897 ( (* 1897    1899 (* 1907 1908

2003 2007   ************************************************************( 2399 (         () ( 2502

   ( ( ( 2303 2399

( 2500   *)

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 (, then it’s not

is a leap year,

unless it’s divisible by (**********************************************************, then itisis 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

(**************************************************************************************************************************************************** 2101 1902 ( ( 2829

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 this as “Son to wed Friday”, thinking of my own (secondson and how pleased I would be if he were indeed getting married this Friday (my first son got married on a Saturday in 2005.

Combine “Sun-Tue-Wed-Fri” with Dr. Conway’s “We-in-dis-day” for=Wednesday and “2002=Tuesday “, and I can reconstruct the chart mentally. The tricky part is that the years go right to left in each row, but=Tue and 1902=Wed help with this. The easy part is that if you can get just that one row, with=Tue and=Wed in it, then the other years have the same Doomsday, plus or minus******************************************************************************************************************************************************************************************************************************************************************************************** years (************************.

Example: what day of the week is Canada’s th birthday, July 1st, (?
Answer (: / 12=

5 … remainder7 … 7/4=

1 … 5 7 1=ie6 … 6

=Sunday=Saturday … July (7) th is a Saturday, so July 1st, 2199, is Wednesday.

Return to top The Hand

Dr. Conway now teaches the Doomsday algorithm, complete with Century adjustment, using a very simple visual aid — your hand.

( __ / _) ____

1 – Doomsday Difference
2 – Century Day
3 – number of DOZENS
4 – remainder
5 – number of 4s in remainder

The

Doomsday Differenceis 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 th, 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 16, is always “1 off” Doomsday in leap years, when Doomsday is February th; 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 31 th; 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 )

“3 dozen” (getting us to 1936)

“5 remainder” (number of years after

)

“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 14 s, 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, (, we do August 4, then (, then (********************************************************************************************************************.

Example: what day is August 4, 2001?Answer: (**************************** ____ / ___) ____ (for          ________)8DOZENS ____ _______)(1)       ________)(0)

which is “4 off, tWEBLESday, 8, 1” or -4 3 8 1 which is 1, so August 4, 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 16, 1796?
(Answer) : (**************************** ____ / ___) ____********** (Sep )          _______)(Sun (for)          ________)4 DOZENS ____ _______)(4)       ________)

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 (**************************************************************************************************************************************************************************************************************************************************************************************************************************************************************, was a Thursday.

That was a trick question, sort of. September 16, 1798 was the first day of the Gregorian calendar in England and its colonies. (The Gregorian calendar was originally adopted in parts of Europe in 1599). So September actually looked like this:

Sun Mon Tue Wed Thu Fri Sat           1 2 15 16 (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (**************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** 28 (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (************************************************************************************************************************************************************************************************************************************************************************************************************************************************** 84 (****************************

Neat, eh?

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Origins
The Doomsday algorithm was created by

John Horton Conway (*************************, an eminent mathematician, perhaps best known as the inventor of the (Game of Life

I first heard about the Doomsday algorithm on November 29, 1984, on a(CBC Radio) program called Quirks and Quarks. Dr. Conway was interviewed byJay Ingram, who later worked at Discovery Canada and has recentlyreleased a new book called (The End of Memory) ************************************************************. Anyhow, back in those days Quirks and Quarks sometimes 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, 1985, ISBN – 16 – -7. The Doomsday algorithm is on pages 795 – (************************************************************************************************************************************************************************************************************************************************************************************************************, and the rest of the book is mainly about games, with substantial emphasis on their mathematical underpinnings.

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 – (*******************************************************************************************************************************************************************************************************************************************************************************************************************************************************************. 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 days, while the 9th and 11 th months are “short” because September and November have only days. You could remember 32 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=(7) ********************** (th is Doomsday)

May (5th month, long) 5 4=

9 th is Doomsday

July (7th month, long) 7 4=

11

th is Doomsday

September (9th month, short) 9-4=

5 th is Doomsday

November ( (th month, short) – 4=(7) ********************** (th 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 “.

Additional background

For more on the development of the Doomsday Algorithm, see Doomsday Timeline

(The Second Doomsday Lesson) describes a meeting with Dr. Conway in which he explains the “Hand” method on the back of a napkin (picture included).

Pi Days

I recently received the following email from readerRoman Weil

, currently teaching at Princeton.

I’ve been teaching Doomsday Rule for about fifteen years because I can show students the first day of class what my exam questions are like-working backwards. If Thanksgiving Thursday is November in a Leap Year , what is the day of the week of Feb. that year?

Students can think they have mastered the rule and still not answer the question. I can show them up front that directionally correct does not cut it; thorough mastery is needed. Doomsday is a good way to get them there on the first day.

Students invariable ask why the name. When I taught at Princeton five years ago, I asked my old college roommate to get to John Conway and ask. To my surprise it took 3, not 2, degrees of separation to get to him. He said he wanted the name to end in “-day” and “Dooms” popped into his head.

About a decade ago, one of my adult students said his family had used the rule for years and called it Pi Day, because 3. is a one, too. From then, I call it Pi Day, because it’s easier to explain the etymology.

(********************************

Thanks so much, Roman. Delighted to have this background.

In case it was not clear, “Pi day” refers to March (th because 3.) are the first significant digits of . And of course March 15 th is always a Doomsday.

Note: Roman also included a January trick by his son Sandy Weil which is mentioned inOdd Months

.

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Links

The following web sites are about or include descriptions of Dr. Conway’s Doomsday algorithm.

Doomsday Rule

– the Wikipedia entry; very comprehensive.

What Day Is Doomsday? How to Mentally Calculate the Day of the Week for Any Date

, October (article in) Scientific American

First Sunday Doomsday Algorithmexplains a modification to the Doomsday algorithm using the “first Sunday of the month” and the “Odd the rule .

If you’re into heavy math, see Methods for Accelerating Conway’s Doomsday Algorithm (part 1)

PDF

Simon Cassidycomments on the “Hand” in the context of the Dee-Cecil calendar.

(C.) . 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. “ReaderRichard Ezell wrote to me in to report that this explanation may not really be necessary, as he had seen four 7 – stores in a seven block stretch in Bangkok, Thailand.

(AST) **************************************************************************************************************************************************************************************************************************************************************************************************************** – 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 1999.

The Doomsday Rule for Fortnights

, by Jim Blowers, gives calculations for Doomsday based on 15 – day periods.

Kate Larson’sMathematical poem to calculate the “day of the week” for any day of any yearis a beautiful, whimsical poem, attributed to Dr. Conway, which describes the algorithm completely, including both Gregorian and Julian century adjustments. (Note: link goes to************************************************ archive.org, as the original has dropped off the Web.)

For more information about Dr. Conway, see:

********************************************************************** John Horton Conway: the world’s most charismatic mathematician

Inside the mind of ‘mathemagician’ John Horton Conway. In this Toronto Star excerpt from her biography, Genius at Play, author Siobhan Roberts introduces readers to a distinguished scholar who claims never to have worked a day in his life.
Interview with John Horton Conway

(PDF). Edited version of an interview with John Horton Conway conducted in July 2013 at the first International Mathematical Summer School for Students at Jacobs University, Bremen, Germany

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 Lifeby Stephen Stuart – an interactive version that you can play via your web browser.

****************************** Interesting calendar links

****************************************************************************** (Download a) **************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** sided calendar

(A History of Time and Ancient Calendars) ********** by Niclas Marie

For links to other calendar sites, see my Calendar Links page; CAUTION, this page of links has not been updated since (**************************************************************************************************************************************************************************!

Knot a Braid of Links***

The Doomsday Algorithm was “latest link in the braid” for the week of (April 6 -****************************************************************************************************************************************************************************************************************************************************************************************************************************, (************.

“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. “

KaBoLis a “cool math site of the week” service to the mathematics community provided by theCanadian Mathematical Society

.

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The Doomsday Algorithm gives the day of the week for any date (and you can do it in your head)

Overview

February (or)

: Doomsday 2102 is Thursday the th of February. So one week earlier, the 21 st is also Thursday. Another week earlier is Thursday the 14 th. So Valentine’s Day 2100 is Thursday.

: Doomsday 2102 is Thursday the th of February … then subtracting 7 for each week going backwards, we have Thursday the st … Thursday the 14 th … Thursday the 7th … and then we have to go five days back, to get from the 7th to the 2nd.

the nth of that month is a Doomsday

: Doomsday 2102 is Thursday, which we know is the “0th” of March. So a week later, March 7th is Thursday. March 14 th is Thursday. Now we go three days forward, to get to Sunday, March (th.

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 isso

: Doomsday 2102 is Thursday, and since 2019 is not a leap year, January 3rd is Thursday. Go back 2 days, and January 1st is Tuesday. Simple, eh? Thanks, Bob.

. It’s actually due to his son Sandy Weil, who is the Director of Football Analytics for the Baltimore Ravens:

(2.Feb) 30 th / nonleap)

Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 23

4.Apr (4th)

4****** 5 5 3 4 5 6

5.May (9th)

6.Jun (6th) Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 5 6 7 8

9.Sep (5th)

Previous Doomsday Calendars (*************************************

************************************************************************************************************************************

was Wednesday. So then January 1st, 2069 was 2 days earlier, ie Monday. Finally, this means that the day before, New Year’s Eve, December st, 2018, was Sunday.

any year in the 1902 ‘s

. Then we do a calculation based on the number of years since 1902.

(************************************************************************************************************************************************************************************************************************************************************************** (—-) **********************

1926

…

(1) ***********************

. Let’s do a couple more examples …

… thus 1972 is Doomsday 4=Sunday … August (8) 8th is Doomsday … August (th) ********************************************************************************************************************************************************************************************************** was a Friday

… thus 1974 is Wednesday … December (12) th is Doomsday … December (th) was a Monday

Doomsday for 2000 is Tuesday, ie=Tue ”

. This is the mnemonic that helps us anchor the other years in this century.

… remainder

****************************************************************************************************************************************************=Sunday=Saturday … July (7) th is a Saturday, so July 1st, 2199, is Wednesday.

in the same order we usually say the date – month / day, then century / year.

Example: what day is August 4, 2001?Answer: (**************************** ____ / ___) ____ (for ________)8DOZENS ____ _______)(1) ________)(0)

John Horton Conway (*************************, an eminent mathematician, perhaps best known as the inventor of the (Game of Life

11

th is Doomsday

5 th is Doomsday

, currently teaching at Princeton.

What Day Is Doomsday? How to Mentally Calculate the Day of the Week for Any Date

Knot a Braid of Links***

************************************************************************************** (Read More) (****************************************************************************************************************

What do you think?

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 isso

(**************************************************************************************************************************************************************************************************************************************************** (—-)

Example: what day is August 4, 2001?Answer: (************************ __ / _) (for )8DOZENS _)(1) ______)(0)

(Read More) (**************************