I’m not a savant and can’t do this in my head. How do I calculate the last time Feb 20th fell on a Tuesday?
- Sorry I don’t have the calculation method, I just looked up a perpetual calendar and went backward.
A give date advances by one day each year (since 365/7 leaves a remainder of 1), except that each leap day advances future dates by an extra day.
So:
Feb 20, 2010 = Saturday
Feb 20, 2009 = Friday
Feb 20, 2008 = Wednesday (crossed a leap day)
Feb 20, 2007 = Tuesday
Feb 20, 2006 = Monday
Feb 20, 2005 = Sunday
Feb 20, 2004 = Friday (crossed a leap day)
…
It was in 2007. The way I would do it, and have done, would be to write a computer program that starts with a given date that you know fell or will fall on a certain day of the week and then calculate forwards or backwards in time.
What you need to keep in mind are:
[ul]
[li]What number is the year[/li][li]What number is the month of the year (in the range 1…12)[/li][li]What number is the day of the month (in the range 1…28, 1…29, 1…30 or 1…31, depending on the number of the month and whether it’s a leap year or not)[/li][li]What number is the day of the week (in the range 1…7)[/li][/ul]
Say you count backwards. That means that for every day of the month you subtract one to get the previous day and at the same time subtract one from the day of the week.
If the day of the week is zero change it to seven.
If the day of the month is zero, subtract 1 from the number of the month.
If the month of the year is zero, subtract 1 from the number of the year and change the number of the month to 12.
I you have changed month look up how many days it has and give that number to day of the month.
This way you can keep track of which day of the a certain date was/will be.
Which is why calendars have only 14 basic patterns to work with (7 different days for Jan 1st, then leap/non-leap year). That’s why you sometimes see businesses giving out calendars for some year long ago – the days work out fine for the current year.
Unless, of course, the calendar also shows phases of the Moon, or any holiday that depends on phases of the Moon (such as Easter/Mardi Gras/Pentecost).
You don’t have to be a savant to work this out in your head, assuming you have access to this year’s calendar and therefore know that Feb 20th was on a Saturday this year.
Tuesday is four days before Saturday and every year any particular date falls a day later*, so go four years back, which is 2006.
Now leap years actually go forward two days, so are there any leap years between '06 and '10? Yes, '08 (years which divide by four are leap years). Therefore we only have to go back three years rather than four, so it’s 2007. Easy, yes?
(because there are 365 days in a year which is (527)+1. That is, 52 weeks and one day)