Help on the doomsday equation/birthday equation

[lilxchristina]

here's the equation


d = date of the month
m = number of the month in the year
y = year


W = d + 2m + [3(m+1)/5] + y + [y/4] - [y/100] + [y/400] + 2

afterwards, divide w by 7, and the remainder is the day of the week, according to:

1 - sunday
2 - monday
3 - tuesday
4 - wednesday
5 - thursday
6 - friday
0 - saturday


now, i totally understand the equation, and it works. but i just don't understand what the significance of the [y/4] [y/100] and [y/400] is.
why is it needed in the equation?

 

[arildno]

Take them out. Does the formula work then?

 

[lilxchristina]

no, the formula is off. when i tried it with today's date without them, it turned out 1 day behind.

 

[HallsofIvy]

Think about leap years.

 

[ohlhauc1]

I tried this equation for Monday, January 29 and it did not work. It also did not work for Tuesday, January 30 or Monday, January 01. It always comes up one day behind. Does it stop working at some year?

 

[HallsofIvy]

Think about leap years!