They would have a rotating 7 year schedule, but it’s messed up by leap years. You have the seven calendars you’re thinking of and 1-2 leap year calendars mixed into those 7 years. It would have to be somewhere between 1 in 8 and 1 in 9, wouldn’t it?
There are 97 leap days every 400 years, then the calendar repeats. So you have 303/400 chance of not having a leap year, and in those years, you get a 1/7 chance of having this calendar. Thus 303/2800.
This is counterintuitive to me, because 303/2800 is .108, which is between 1/9 and 1/10. But 97 out of 400 is less than 1 out of 4, so it shouldn’t be able to interfere more than twice in a 7 year cycle, on average. But your math looks correct. I must be missing something.
1 in 7 chance [if you sample from infinite years]
That can’t be correct, can it?
They would have a rotating 7 year schedule, but it’s messed up by leap years. You have the seven calendars you’re thinking of and 1-2 leap year calendars mixed into those 7 years. It would have to be somewhere between 1 in 8 and 1 in 9, wouldn’t it?
I think it’s more like 303/2800 chance.
There are 97 leap days every 400 years, then the calendar repeats. So you have 303/400 chance of not having a leap year, and in those years, you get a 1/7 chance of having this calendar. Thus 303/2800.
This is counterintuitive to me, because 303/2800 is .108, which is between 1/9 and 1/10. But 97 out of 400 is less than 1 out of 4, so it shouldn’t be able to interfere more than twice in a 7 year cycle, on average. But your math looks correct. I must be missing something.
No, since there’s only 7 different possibilities, then over a sufficiently large sample, the probabilities would all still balance out to 1 in 7.
There’s 14 different possibilities because of leap years.
Oh yeah, you’re right. I was focusing on just where the first day of the week lands, not the full month calendar.
the first day of the month moves forward one weekday each year except mar-dec on a leap year which moves forward two weekdays