# 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 Sat1999 ----20002001 2002 2003 ----20042005 2006 2007 ----20082009 2010 2011 ----20122013 2014 2015 ----20162017 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 Sat159916001601 1602 160317001701 1702 1703 1704 1705 1796 1797 1798 179918001801 1897 1898 189919001901 1902 1903 199920002001 2002 200321002101 2102 2103 2104 2105 2196 2197 2198 219922002201 2297 2298 229923002301 2302 2303 239924002401 2402 240325002501 2502 2503 2504 2505

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

- if it's divisible by 4, it is a leap year,
- unless it's divisible by 100, then it's
**not**a leap year,- unless it's divisible by 400, then it
**is**a leap year

- unless it's divisible by 400, then it

- unless it's divisible by 100, then it's

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 Sat1700 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.