## When are there 5 Sundays in February? (Intermediate)

How many years according to the calendar we use today have had 5 Sundays in the month of February? How often does this occur?

In order for there to be 5 Sundays in February, February 1st must fall on a Sunday, and it must be a leap year, so that February 29th is the fifth Sunday. Statistically speaking, a given date is associated with a day of the week one out of every seven years. Leap years occur every four years (with a few exceptions that I'll ignore here). So, the probability of February 1st falling on a Sunday and it being a leap year is 1/7 times 1/4, or 1/28 years. So, there should be 5 Sundays in February roughly every 28 years.

The American colonies were one of the last to adopt the currently used Gregorian calendar, in 1752. If we take that year as the start of the adoption of the Gregorian calendar, then there are have been approximately 9 years with 5 Sundays in February.

Ironically, the next time there will be 5 Sundays in February is this year! Indeed, February 1st falls on a Sunday in 2004, and it's a leap year.

The last time there were 5 Sundays in February was in 1976, exactly 28 years ago; similarly, after this year, there will be 5 Sundays in February in 2032, 2060 and 2088. So at least for the next few decades, the 28-year period I estimated above is exact.