5 weekends in the same month happens more often than every 823 years

5 weekends in the same month happens more often than every 823 years

5 Fridays, 5 Saturdays and 5 Sundays in one month – happens only every 823 years? This popular urban myth has been circulating on the internet for a while. However, it is precisely that: a myth.


The "5 Fridays, 5 Saturdays & 5 Sundays" myths.
Before you get too excited about this once-in-a-lifetime event and start telling your family and friends, know this: any such claims are false. Special combinations of days like 5 Fridays, 5 Saturdays and 5 Sundays occur much more often than every 823 years!

 

The 823 years myth
If you own an email, Twitter, Facebook or any other social media account, chances are that you have come across an email or a post that claims that an upcoming month has a very rare specific combination of days. A recent version goes something like this:

January 2016 will have 5 Fridays, 5 Saturdays and 5 Sundays. This happens only once every 823 years. The Chinese call it silver pockets full.

The email is right in that January 2016 has 5 Fridays, 5 Saturdays, and 5 Sundays. But this is nothing special or unusual. You will not have to wait another 823 years for the next time this happens in the month of January. Only 6 years later, in 2021, January will also have 5 Fridays, 5 Saturdays, and 5 Sundays.

In fact, a calendar month that contains 5 Fridays, 5 Saturdays and 5 Sundays occurs nearly every year – in 2016 both January and July will have 5 Fridays, 5 Saturdays and 5 Sundays.

In fact, the calendar 823 years in the future is not even the same as the calendar of the month in the many versions of the hoax! For instance, August 2014 had 5 Fridays, 5 Saturdays and 5 Sundays. 823 years later, August 2837 has 5 Saturdays, 5 Sundays and 5 Mondays.

Not a special combination
The combinations of days that these messages or emails refer to are also not very special. This is because the first three weekdays of any 31-day month are repeated 5 times within that month. So, any month that has 31 days and begins on a Friday will have 5 Fridays, 5 Saturdays, and 5 Sundays. Similarly, any 31-day month that begins on a Tuesday, will have 5 Tuesdays, 5 Wednesdays and 5 Thursdays.

 

 

Recurring monthly calendars
Here's a more mathematical reasoning as to why the 823 year claim is a myth:

Every year has 7 months with 31 days. Each of these months have at least 3 weekdays that happen 5 times during the month. For example, August 2014 has 5 Fridays, 5 Saturdays and 5 Sundays. October 2014 has 5 Wednesdays, 5 Thursdays and 5 Fridays.

There are 7 different days a month can start on. So on average, the combination of any 3 days occuring 5 times in a calendar month will happen once a year.

In any given year, there are only 6 such combinations of days. This is because 2 months with 31 days start on the same weekday. In a common or regular year, January and October have the same calendar, while in a leap year, January and July look the same.

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