Doomsday: Other Centuries

How to apply the Doomsday Algorithm to years in other centuries

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

Previously, we learned that Doomsday for 1900 was Wednesday. What is Doomsday for other centuries?

Let's start with the 21st century, i.e. the 2000's.

The 2000's

Well, it turns out the 2000's are real easy. Recall the chart we were looking at earlier. Here it is again, extended into the 2000's a few years...

   Sun  Mon  Tue  Wed  Thu  Fri  Sat
  1999 ---- 2000 2001 2002 2003 ----
  2004 2005 2006 2007 ---- 2008 2009
  2010 2011 ---- 2012 2013 2014 2015
  ---- 2016 2017 2018 2019 ...

Notice that Doomsday for 2000 is Tuesday, i.e. "2000=Tue". This is the mnemonic that helps us anchor the other years in this century.

Remember the formula we learned for the 1900's, where we got the multiples of 12, kept the remainder, and added the number of 4's in the remainder? That still works, we just apply it to this century with Tuesday as the Doomsday for the 2000's.

Let's work through a couple of examples.

Example: what day of the week is May 29, 2017? (That would have been John F. Kennedy's 100th birthday, had he lived.)
Answer: 17 / 12 = 1 ... remainder 5 ... 5 / 4 is 1 ... 1 + 5 + 1 = 7 which is 7=0 days to be added to Tuesday (for the 2000's) ... Doomsday 2017 is Tuesday (which the chart above confirms) ... May(5) 9th is Tuesday, 23rd is Tuesday ... May 29th, 2017 is Monday.

Example: what day of the week is July 20, 2069? (That will be the 100th anniversary of the Apollo 11 moon landing.)
Answer: 69 / 12 = 5 ... remainder 9 ... 9 / 4 is 2 ... 5 + 9 + 2 = 16 which is 2 days to be added to Tuesday (for the 2000's) ... Doomsday 2069 is Thursday ... July(7) 11th is Thursday ... July 18th is Thursday, so July 20th, 2069 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
  1599      1600 1601 1602 1603
  1700 1701 1702 1703      1704 1705
       1796 1797 1798 1799 1800 1801
  1897 1898 1899 1900 1901 1902 1903
  1999      2000 2001 2002 2003
  2100 2101 2102 2103      2104 2105
       2196 2197 2198 2199 2200 2201
  2297 2298 2299 2300 2301 2302 2303
  2399      2400 2401 2402 2403
  2500 2501 2502 2503      2504 2505

Examine this chart carefully, until you convince yourself that it is behaving exactly as you would expect for leap century years and non-leap century years. Remember the rule for determining a leap year:

Each normal year advances Doomsday by one day. Each leap year advances Doomsday by two days. Now look at the century years again:

   Sun  Mon  Tue  Wed  Thu  Fri  Sat
  1700      1600
  2100      2000 1900      1800
  2500      2400 2300      2200

What's the best way to memorize century Doomsdays? I'm not sure. Here's what I use. Notice that century Doomsdays fall only on "Sun-Tue-Wed-Fri". I say this as "Son to wed Friday", thinking of my own (second) son and how pleased I would be if he were indeed getting married this Friday (my first son got married on a Saturday in 2003).

Combine "Sun-Tue-Wed-Fri" with Dr. Conway's "We-in-dis-day" for 1900=Wednesday and "2000=Tuesday", and I can reconstruct the chart mentally. The tricky part is that the years go right to left in each row, but 2000=Tue and 1900=Wed help with this. The easy part is that if you can get just that one row, with 2000=Tue and 1900=Wed in it, then the other years have the same Doomsday, plus or minus 400 years.

Example: what day of the week is Canada's 300th birthday, July 1st, 2167?
Answer: 67 / 12 = 5 ... remainder 7 ... 7 / 4 = 1 ... 5 + 7 + 1 = 13 i.e. 6 ... 6 + 2100=Sunday = Saturday ... July(7) 11th is a Saturday, so July 1st, 2167, is Wednesday.

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