Doomsday rule

To improve his speed, he practiced his calendrical calculations on his computer, which was programmed to quiz him with random dates every time he logged on.

[6] Doomsday's anchor day for the current year in the Gregorian calendar (2025) is Friday.

One can find the day of the week of a given calendar date by using a nearby doomsday as a reference point.

To help with this, the following is a list of easy-to-remember dates for each month that always land on the doomsday.

The odd numbered months can be remembered with the mnemonic "I work from 9 to 5 at the 7-11", i.e., 9/5, 7/11, and also 5/9 and 11/7, are all doomsdays (this is true for both the Day/Month and Month/Day conventions).

The chart below includes only the mnemonics covered in the sources listed.

Since this algorithm involves treating days of the week like numbers modulo 7, John Conway suggested thinking of the days of the week as "Noneday" or "Sansday" (for Sunday), "Oneday", "Twosday", "Treblesday", "Foursday", "Fiveday", and "Six-a-day" in order to recall the number-weekday relation without needing to count them out in one's head.

[10] There are some languages, such as Slavic languages, Chinese, Estonian, Greek, Portuguese, Galician and Hebrew, that base some of the names of the week days in their positional order.

The Slavic, Chinese, and Estonian agree with the table above; the other languages mentioned count from Sunday as day one.

For the purposes of the doomsday rule, a century starts with '00 and ends with '99.

To accomplish that according to Conway:[11] 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: The doomsday's anchor day 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.

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.

If we replace y by y mod 12, we are throwing this extra day away; but adding back in

A simpler method for finding the year's anchor day was discovered in 2010 by Chamberlain Fong and Michael K. Walters,[12] and described in their paper submitted to the 7th International Congress on Industrial and Applied Mathematics (2011).

Called the "odd + 11" method, it is equivalent[12] 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 anchor day, the procedure is often described as accumulating a running total T in six steps, as follows: Applying this method to the year 2005, for example, the steps as outlined would be: The explicit formula for the odd+11 method is: Although this expression looks daunting and complicated, it is actually simple[12] because of a common subexpression ⁠y + 11(y mod 2)/2⁠ that only needs to be calculated once.

Anytime adding 11 is needed, subtracting 17 yields equivalent results.

For computer use, the following formulas for the anchor day of a year are convenient.

A leap year with Monday as doomsday means that Sunday is one of 97 days skipped in the 400-year sequence.

For example, February 28 is one day after doomsday of the previous year, so it is 58 times each on Tuesday, Thursday and Sunday, etc.

February 29 is doomsday of a leap year, so it is 15 times each on Monday and Wednesday, etc.

[citation needed] The same cycle applies for any given date from March 1 falling on a particular weekday.

Thus, for any date except February 29, the intervals between common years falling on a particular weekday are 6, 11, 11.

The Gregorian calendar is currently accurately lining up with astronomical events such as solstices.

Thus, we take one away from the doomsday, Thursday, to find that September 18, 1985, was a Wednesday.)

Suppose that we want to find the day of week that the American Civil War broke out at Fort Sumter, which was April 12, 1861.