# Thread: Finding the Day of a year

1. ## Finding the Day of a year

"One year in the 1990s January 1st fell on a Monday. 11 years later, January 1st was also on a Monday. How many times did February 29th occur during those years"?

Sorry but I don't have any working out because I'm completely befuddled by this.

I don't know how to work out if a year started with a Monday or otherwise, does anyone know how?

And I also don't know what's so special about February the 29th? Is it just a normal date and Im being cynical?

2. The 11 years in question must comprise a whole number of weeks. Suppose n of those 11 years were leap years. Then 365 * 11 + n is divisible by 7. Since leap years occur every four years, n is certainly less than 7. From here, n = 3.

Indeed, January 1st fell on a Monday on 1990, 1996, 2001 and 2007. Between 1990 and 2001, the following were leap years: 1992, 1996 and 2000. Between 1996 and 2007, the following were leap years: 1996, 2000 and 2004.

3. What is so special about Feb. 29? It is "leap year day"! Three out of every four years, Febuary has only 28 days. The fourth year, the year that is divisible by 4, specifically 1992, 1996, and 2000, February has 29 days.

4. To be precise, I believe a year will be a leap year if it is divisible by 4 but not by 100 (unless it is also divisible by 400).
Consequently 2000 is a leap year while 1700, 1800, 1900 I believe are not.

5. Pranas, that is correct.