How do people memorize what day of the week "x day, x month" will be?

Maybe they have photographic memories or something similar to this.

They may remember a few dates from their calendar but the formula is complex:

Uspensky and Heaslet gave the following formula, in Elementary Number Theory, 1939, for the Gregorian calendar:

W=D+floor(2.6m-0.2)+y+floor(y/4)+floor(c/4)-2c (mod 7)

Floor() means to drop the fraction; floor(6.8) is 6. m is the month starting with March as 1 and ending with February as 12. January and February of any year are considered to be in the previous year.

I usually just know each year which day my birthday falls on and I know the current date and day of the week. You know how many days past 28 there are in a given month and if it’s a leap year. Just add the end month days between your reference date and the date you’re interested in to get you to the day of the week you need. If a leap day occurs between your reference and the desired date add one more.

If your reference date is later than the desired date you go backward that many days instead of forward. I usually find myself going forward though. It’s pretty quick when you get used to it.

I agree with @cyndyh: If someone mentions a date anytime in November or December I pretty much know exactly which date is which, even if it’s 6 or 7 months in advance. I also know which days correspond to dates of most of my vacations for the coming year.

I don’t know that stuff as a memorization trick for knowing every date, it just kind of happens.

Also if you’ve ever had a job that required any long-term planning, you get used to figuring it out quickly.

There are only fourteen different possible calendars: one each for January 1st falling on each of the seven days of the week in a regular year and the same for a leap year. That’s why “perpetual calendars” are so simple. While working on a piece of historical fiction, I have looked up days of the week for dates in the fourteenth century. It makes them ever so much more real when you know that August 15th, 1308, was a Thursday. A person could easily enough learn key marker dates for each of the 14 calendars and go about astonishing people. But I don’t think many actually do that.

I can figure many dates easily because I know when family birthdays, Christmas, special events, etc., fall. Probably it’s one of those selective-perception phenomena: you would be amazed if I know immediately that next February 8th is a Monday, but you wouldn’t think a thing if I didn’t. But I know that I have tickets for the opera on the 7th, and it’s a Sunday.

There is a fairly easy way to do it, which I learned years ago. This works for dates in the 20th century, but is easy to convert to dates in the 21st century (where we are now).

First, you need to know the key number for each month. It turns out that for the 1900’s, zero is the key number for January. Then, since January has 31 days (equivalent to four weeks and three days), you add the remainder to January’s key number to get three, which is February’s key number. Or you can just memorize the key numbers for each month, and here’s the list:

Jan – 0
Feb – 3
Mar – 3
Apr – 6
May – 1
Jun – 4
Jul – 6
Aug – 2
Sep – 5
Oct – 0
Nov – 3
Dec – 5

Let’s start with an example. I’ll use July 4, 1976, since that was our Bicentennial.

Take the last two digits of the year and divide by four, then drop any remainder. 76/4 =
19, remainder zero. Then add this to the two-digit number you started with. 76+19=95. Then add the key number for the month of July, which is 6 from the above list. 95+6 = 101. Then add the month’s date to the total, which is four in this case. 101+4=105. Divide this total by 7 and see what the remainder is. 105/7=15 r.0. A remainder of zero means the date fell on a Sunday. A remainder of one is Monday, etc.

Remainders and their day equivalents: Sun = zero, Mon = one, Tue = two, Wed = three, Thur = four, Fri = five, and Sat = six.

Now what about dates in the 21st century, like today for instance? That’s easy: just do the calculations like you would for the 20th century, but subtract one from the final total. For example, today is October 9, 2009. I’ll calculate it the same way as before:

The final two digits of 2009 are 09, or simply 9. I divide this by four then drop the remainder which leaves me with 2. Then I add this to the original two digits to get 11. The key number for the month of October is zero. 11 + 0 = 11. Now I add the day. 11 + 9 = 20. I divide by seven and get 2, remainder six. Remember though, I have to subtract one to adjust for 21st century dates, which leaves me with 19 or 2, remainder five. Look at the above list and you will see that today is Friday.

Now there is an occasional exception to the above rules, and it happens on leap years between Jan. 1 and Feb. 29. There’s an extra day squished in there during those years, and you have to compensate for it by subtracting one from the total in those cases. Let’s pick a date that falls in that time period during a leap year: Feb. 15, 2008.

I take the last two digits of the year (08) and divide by four. Then I add the original last two digits. 2 + 8 = 10. The key number for February, from the above list, is three. 10 + 3 = 13. Then I add the date. 13 + 15 = 28.

Of course I have to subtract one to adjust for 21st century dates, leaving me with 27. But I also have to subtract ANOTHER one since this date falls between Jan. 1 and Feb. 29 during a leap year. That leaves me with 26. Then I divide by seven and calculate the remainder.

26 / 7 = 3 remainder 5

R = 5 means Feb 15, 2008 fell on a Friday.

Try this with different dates, like your birth day and year and those of your friends, and check your work using the perpetual calendar at Infoplease. If you do the calculations correctly you will ALWAYS get the right answer.