Five For Three Fifths

NORTHWEST ARKANSAS — Maybe you’ve had it pointed out to you that this October features the oddity of having five Fridays, five Saturdays and five Sundays.

And maybe you’ve also heard - or read in a mass e-mail, or seen posted on someone’s Facebook status - that this occurrence only happens every 823 years.

“Nonsense, of course,” says professor Chaim Goodman-Strauss, chairman of the Department of Mathematical Sciences at the University of Arkansas. “The calendar cycles every 28 years,” repeating the whole sequence of dates and days of the week. (There is the obligatory rule exception, however, because the 28-year cycle gets interrupted on century years; but this is righted every four-hundred years, when EVERYTHING totally re-coincides. Thanks, leap year guidelines, for always managing to keep us on our toes.)

So, the greatest length of time possible between calendrical cycles is usually o 28 years - and 400 at the very most.

But five Fridays, Saturdays and Sundays in October happens far more frequently that - every 5 to 11 years, actually, in a pattern. The most recent one was in 2004, and the next will be in 2021.

However, would you believe it gets even less spectacular?

Any month with 31 days in it will have a series of three consecutive days that occurs five times. So any 31-day-long month that starts on a Friday will boast five weekends. January of this year would be the most recent.

“In fact, almost every year has a month with five full weekends in it - only about one in seven on average doesn’t!” Goodman-Strauss says. “And on average, one in seven has two, just like this year does.”

So, what does this mean?

“You can’t believe everything you read on the Internet.”

Regardless - and it’s a big regardless, we know - “it’s kind of cool,” Goodman-Strauss admits of this month’s five weekends. And since “numbers have a mystique for us all,” he says, there’s no reason we can’t enjoy our much-less-extraordinary-than-we-thought rarity.