Math: I'll get 27 paychecks in 2004.

Normaly I only get 26 but in 2004 I’ll get 27. I get paid bi-weekly and in 2004 my first paycheck will be on the first friday of the new year. What I want to know is how long before that happens again? And if you’re really smart whats the formula for figuring that out.

Or could I’ve of asked how long before we see 53 fridays in one year? (or no because I still wouldn’t know on which friday my paycheck fell on)

{shrugs shoulders)

Or maybe I guess the real question would be how long before a year repeats itself with the exeact calender days as before?

Identical Calendar Years

In a 28 year cycle (see above link) there are 21 regular years and 7 leap years.

In a regular year, there is ‘one day left over’ (365 divided by 7). This means if the year start on a Friday, it ends on a Friday, giving you 53 Fridays. In those 21 of 28 years, the start days are evenly distributed, and so, within those 21 years, three of them begin on Friday and have 53 Fridays.

In a leap year, there are two days ‘left over.’ And so, a leap year beginning either on a Fridar or a Thursday has 53 Fridays. Again in those 7 years of the 28 year cycle, the start days are evenly distributed. Among those 7 years, one starts on Thursday and one starts on Friday, giving 2 of those 7 years having 53 Fridays.

And so 5 out of 28 years will have 53 Fridays. To figure out when is the next, check a calendar. If you’re using Windows, double click on the date in your status bar. Set the month to January and scroll through the years. Scan for years that start on Friday and leap years that start on Thursday or Friday (and when done cancel out so you don’t reset your system time).


Hint: 2010.