The previous post explained why the Gregorian calendar is the way it is, and that it consists of a whole number of weeks. It follows that the Gregorian calendar repeats itself every 400 years. For example, the calendar for 2025 will be exactly the same as the calendar for 1625 and 2425.
There are only 14 possible printed calendars, if you don’t print the year on the calendar. There are seven possibilities for the day of the week for New Year’s Day, and there are two possibilities for whether the year is a leap year.
A perpetual calendar is a set of the 14 possible calendars, along with some index that tells which possible calendar is appropriate in a given year.
Are each of the 14 calendars equally frequent? Almost, aside from the fact that leap years are less frequent. Each ordinary year calendar occurs 43 or 44 times, and each leap year calendar occurs 13, 14, or 15 times.
the analysis above can be extended to prove the “Friday the 13th Problem”, which explains why everyone has been having more bad luck than expected. I came across this in a statistics book around 1970.
1. On a Friday, the day in month is more likely to be 13 than any other.
2. On the 13th day of the month, it is more likely to be Friday than any other day of the week
(continued)
so Friday the 13 occurs more than any other combination. (by about a couple percent, as I recall from working it out about 55 years ago)