I can see where math would be required if the question were something like, “What day of the week must the 1st occur on if the month has a Tuesday the 23rd?” But Friday the 13th is more notable and thus the image of the corresponding (and simple) calendar layout sticks in the mind (at least for me).
I rarely look at actual calendars anymore and certainly don’t have them memorized or generally have an image of them complete with days and dates. It’s just not the sort of thing my mind retains. I would have had to either do math or count on my fingers to get to the answer.
Yikes. I just put a calendar in my head (as though I’m picturing it) and look at the first of the month. I know a week is 7 days, so my numbers “fill out” easier…
Me, three. This is something I’ve known for years, as Friday the 13th is such a noteworthy date when it occurs in a month. You don’t have to remember every possible combination for days in a month. It’s just one of those things you learn by observing, like New Year’s Day coming exactly a week after Christmas.
I don’t know if it’s very mathematical, but what I did was “13friday minus 14 leaves me in the previous month, 14saturday minus 14 still no go, 15sunday minus 14 leaves 1sunday”.
FTR, nothing particular about friday the 13th where I come from, other than “it’s a day that’s considered ill-luck by some foreigners, thus the name of the gore movie series”.
I’d go the Fri13-Sat14-Sun15-Sun1 route. While I’ve never used negative dates like septimus and constanze did, I have used dates like “July 73rd”.
And not that this will ever be of use to anyone, but remember the phrase “I work 9 to 5 at the 7-11.” 9/5, 5/9, 7/11, and 11/7 in the same year are all the same day of the week. These days are the same as the last day in February (28th or 29th, aka “3/0”) and 4/4, 6/6, 8/8, 10/10, and 12/12. The only one that’s hard to remember is “1/3 three years, but 1/4 in the fourth year”, because then you need to know where leap years are.
That’s basically how I (and anyone) can quickly figure out what day of the week, say, this coming January 20th will fall on, i.e. today is Thursday December 22nd, so the 29th, 36th, 43rd, and 50th of December are also Thursdays. But the 50th of December is really the (50 - 31) = 19th of January. So, the 20th must be a Friday.
(all this sounds slower and more complicated than it actually is).
I noticed the relationship a couple of decades ago without math at all. I just looked at the months with Friday the 13th, and checked the day it started.
I suppose it is a bit cultural. In my case during my formative years I did encounter a lot of people who thought Friday the 13th really was bad luck. From there it wasn’t much of a leap to notice that those “bad” days happen when the first is a Sunday. I can’t visualize any other calendar.