Dr. Conway developed a sweet method (called the Doomsday Algorithm) to determine the day of the week for any day in history. It takes some practice, but dealing with the current year is pretty simple, provided you know the Doomsday.

Doomsday 2013 is Friday*.

- This means that the following dates are all Thursdays:
**4/4, 6/6, 8/8, 10/10, 12/12**. - If you work nine to five at the local 7-11, you can remember four more Thursdays:
**9/5, 7/11, 5/9, 11/7**. - Einstein’s birthday = Pi Day =
**3/14**= Thursday. - The last day of February (
**2/29**this year) is a Thursday. - Lastly,
**1/3**is Thursday (3 out of 4 years it’s the 3rd… but on leap years it’s the 4th).

Adding days of the week is easier when you treat them as numbers: mONEday, TWOsday, 3ednesday, FOURsday, 5day, S6turday (Treat Sunday as 0 - "nunday"). What's ten days past Wednesday? 10 + 3 = 13. Take out any multiples of 7 and you have 6 (Saturday).

*In case you’re interested, the link up top does a thorough job of teaching the method, but here’s the quick version. Start with the century day. For 2000 it is Tuesday (2). Then look at the 2-digit year, 14, and ask how many 12’s are in it. (1). What is the remainder? (2) How many 4’s are in this number? (0). Add up (2)+(1)+(2)+(0) = 5 = 5th day of the week = Friday.

Craziness? How about one more example from the future: 2055. Century day is still (2). How many 12’s in 55? (4). What is the remainder? (7). How many 4’s in this number? (1). Add ‘em up: (2)+(4)+(7)+(1) = 14. Take out multiples of 7 and you get 0. The 0th day of the week is Sunday. Now you can find the day of the week for any date in 2055.

That's nifty, and useful! I looked at the first page of the link and will go back for the rest. Two quibbles, though, this year the last day of February is the 28th, and when you add up (2)+(1)+(1)+(0) = 4 = 4th day of the week = Thursday. Did you copy & paste from Rudy's examples from last year?

ReplyDeleteOK, here's my explanation (I don't know yet how much explanation Rudy has, and if you wanted this to be an example for students to figure out you'll have to moderate out the comment): In a 365 day year there is one more day than a whole number of weeks, and in a leap year there are two more days than a whole number of weeks. Basically, to get the Doomsday for a year you can start somewhere and add one day for every non-leap year and 2 days for every leap year, but only after February, because leap year/no leap year doesn't make a difference until after leap year day. Centuries are special for leap years: years divisible by 4 are leap years, except for century years which are only leap years if they're divisible by 400. Anyway, so long as you start with the century year, the 2-digit year is a leap year if it's divisible by 4. In 12 years there are 3 leap years (6 extra days) and 9 365-day years (9 extra days); that makes 15 extra days = 2 whole weeks + 1 extra day. That extra day is why you add 1 for every 12 in the 2-digit year. Then 1 more for every year in the remainder after 12's, plus another for every leap year after the 12's, that's "how many 4's in the remainder?"