# Crowdsourcing lunacy

Back in October 2010, people were lauding that the month was the first in hundreds of years that featured five Fridays, five Saturdays and five Sundays. And this month, people are similarly bowled over about the rarity with which we witness a month that contains five Saturdays, Sundays and Mondays.

Immediately upon hearing the first example, I knew it was bunkum. But this time, I decided to document the idiocy.

Every single year features no fewer than seven months containing 31 days. This is a prerequisite for three separate days to appear five times. And in those months, the days that fall on the first, second and third of the month will feature five times. It’s as simple as that.

Now over the course of time, the probability of each day of the week hitting the first day of one of those months tends to 1/7, or 14.28%. So the first of January in a randomly chosen year is (roughly) equally likely to fall on a Monday, a Tuesday, Wednesday, Thursday, Friday, Saturday or Sunday.

And given that there are seven candidate months each year, you should expect to see an average of one month a year containing five Fridays, Saturdays and Sundays. Or any other combination of three consecutive days for that matter.

The likelihood of getting five Saturdays in February on the other hand is much smaller. It happened three times in the 20th century (1920, 1948 and 1976) and will next happen in 2032.  *That* would be something worth writing about, were it not for the lunacy that is the Gregorian calendar.