4/4 (April 4th), 6/6, 8/8, 10/10 and 12/12 all fall on the same day of the week in any given calendar year. This year, they are all Sundays. Next year, all Mondays. In 2023, all Tuesdays. In 2024, a leap year, they are all Thursdays (Wednesday was skipped).
One can use this fact to figure out the day of the week for any date in any year if you know what the key day for that year is. If 8/8 was a Sunday, a week later, 8/15 was as well, making today, 8/17, a Tuesday.
What if it's an odd numbered month? 5/9, 9/5, 7/11, and 11/7 will also be the key day. The pneumonic is 7-Eleven is open 9 to 5. Talk Like A Pirate Day falls on September 19th every year. This year, since 9/5 is the key day and is a Sunday, so is 9/19.
The first three months of the year are harder. Remember that March 0, the day before March 1, which is usually February 28th except in leap years, when it's 2/29, is also a key day.
One more ad hoc rule for January: the key day is January 3rd when February 28 is a key day in ordinary years, and 1/4 on leap years.
So what day of the week will January 21st be next year, 2022, when the key day is Monday? January 3 will be a key day, Monday, therefore, so will 1/17, making 1/21, four days later, a Friday.
There are actually more rules for those who want to go further forward or back on the calendar. Since the key day goes up one day each regular year and two days on leap years, what was the key day in 1932? Count the four-year periods that have passed, and add five days for each. Easier yet, since the key day goes up 15 days in 12 years (12/4 x 5), that's one day (fifteen days after a Tuesday is always a Wednesday).
What day of the week was July 4, 1936? 1936 is 85 years ago, which is 7 twelves plus 1 year. Add subtract one calendar day for each 12 years going back, which is seven days, so no change in the key day, and one more for the 85th year, so, Since this year, 2021 has a Sunday key day, 1936 had a Saturday. The key day for July is the 11th (7-Eleven), which was a Saturday, so a week later on the 4th, it was also a Saturday.
Are you a glutton for punishment? We crossed a century mark going into the 20th century. The year 2000 was a leap year, but were you aware that when the century year (1700, 1800, 1900, 2000) is not exactly divisible by 400, there is no leap year in that year? This needs to be taken into account if trying to figure out what day December 25, 3021 will be.
And for the truly committed, there is a rule for when one goes back to before the adoption of the Gregorian calendar. You need to know that the Julian calendar day Thursday, 4 October 1582 was immediately followed by the first day of the Gregorian calendar, Friday, 15 October 1582.
But for most daily purposes like figuring out days from dates last year, this year, and next year, the first few rules cover it. And people are regularly amazed if you can get it right. American Thanksgiving always falls on the fourth Thursday in November. Is that the 26th this year? November is the 11th month, so the key day, Sunday this year, is 11/7. That makes the first Thursday of the month three days earlier, 11/4, and three Thursdays later, or 21 days later, falls on the 25th (4+21). That's the date for this year.
How about the 20 year anniversary of 9/11? I happen to remember that the event fell on a Tuesday, and since we add 5 calendar days to the key day for every 4 years that have passed, and 5 fours have passed in 20 years, we add 5x5 calendar days = 25. 25 days after a Tuesday is the same as 4 days after a Tuesday, or Saturday.
Or, use the rule that 9/5 is a key day, Sunday in 2021, so 9/11, 6 days later, is a Saturday.
