The Universe of Discourse

Watch out for the Calendar Geeks
Yesterday on the private IRC server run by my employer, one of my co-workers said:

<MHO> [My wife] just informed me that this year, July has five Fridays, five Saturdays and five Sundays. This only happens every 800 or so years.

<MHO> Calendar geeks, rejoice!

First, I note that any weird calendar event that occurs, will recur in no more than 400 years, because the Gregorian calendar repeats in a 400-year cycle and 400 Gregorian years is also an exact multiple of 7 days. (It is 400·365 days + (100 - 4 + 1) leap days = 146,097 days, which is exactly 20,871 weeks.) So it is impossible that the event could be as rare as once every 800 or so years. If it happens in 2011, then it happened in 1611 (in Catholic countries) and it will happen in 2411 also.

Now in the particular case cited by MHO, it's clear that since the length of July doesn't vary, the number of Fridays, Saturdays or Sundays depends only on the day of the week on which July 1 falls. You get five Fridays, Saturdays, and Sundays whenever July 1 falls on a Friday. Common sense suggests that this should happen about 1/7 of the time, and so around every 7 years, not every 800, or even every 400 years. And in fact it last occurred in 2005, and will occur next in 2016.

[ Addendum 20110527: It turns out this is actually a Thing; there is even a Snopes page about it. People will tweet almost anything, it seems. ]

[ Addendum 20110701: Matt Parker posted an extensive article about why he found this particular non-fact so dismaying. ]

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