Is there a Friday XIII every year, or are there years without? 1) Are there years with lots and lots?2) How many is the most in one year? 3) The following simple table answers all these questions for you: I've already done the work. Just find the row that corresponds to the day of the week the first of January falls; the months with a Friday XIII are listed according to whether it is a leap year or not.
Months with a Friday XIII | ||
---|---|---|
1 Jan | Leap Year | Non-Leap Year |
Sun | January, April, July | January, October |
Mon | September, December | April, July |
Tue | June | September, December |
Wed | March, November | June |
Thu | February, August | February, March, November |
Fri | May | August |
Sat | October | May |
These days, with the availability of computing power, it is quite possible to “brute force” the problem; that is, write a little program, or even a simple spreadsheet, to calculate the fourteen possible calendars 4). However, I'm old enough to prefer finding the solution on the back of an envelope, and that is exactly what I did; I just recopied the result to this wiki.
With these rules, one can construct a table of the off-set to the weekday on which the 13th falls in each month relative to the weekday of January 1.
13th of… | Non-Leap | Leap |
---|---|---|
January | +5 | +5 |
February | +1 | +1 |
March | +1 | +2 |
April | +4 | +5 |
May | +6 | 0 |
June | +2 | +3 |
July | +4 | +5 |
August | 0 | +1 |
September | +3 | +4 |
October | +5 | +6 |
November | +1 | +2 |
December | +3 | +4 |
Reading this table, one sees, for instance that in leap years, May 13th falls on the same weekday as January 1, and in non-leap years August 13th does (instead). So if January 1st falls on a Friday, there will be a Friday XIII in May (leap years) or August (non-leap years). The other offsets are converted in the same way :
An earlier treatment of this topic is Friday XIII on one of my blogs; I hope this one is an improvement. I've also written Delocalization and Globalization of Holidays about “when does a year start.” Then there is a treatment much like to one above applied to Public Holidays in France.
Another question came up: what year might that have been? Given an invitation for an event on “Saturday, April 26th,” for instance, might it (if correct, of course) have been from last year?