May 10, 2010 falls on a Monday

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By John Pawlak

Sept. 2, 1752 was a Wednesday. Adding fourteen days (two weeks), can you figure out what day of the week Sept. 16, 1752 was?

Halloween falls on a Saturday this year. July 4 next year will be on a Sunday.

If you own a perpetual calendar, you can look these dates up.

But without having a calendar handy, could you determine on what day of the week Valentines Day falls next year? Or Christmas? Your birthday? Uh, okay ... how about Easter Sunday?

It’s actually pretty easy to figure out these dates in your head and I thought it might be fun to write up the technique for anyone who might want to learn it.

The algorithm for calculating days of the week for a given date is called the Doomsday Algorithm. Why they didn’t call it the “Calculate Day of the Week Algorithm,” I can’t say. I prefer to just call it the D-day algorithm.

Let’s see how this works for the years 2009 and 2010. You rarely need to know the day of the week for any date more than two years out.

First, we define “D-day.” For any given year, the day of the week on which the last day of February falls is the D-day for that year.

This year, the last day of February was the 28th and was a Saturday. So D-day for 2009 is Saturday. Just remember that D-day for 2009 is Saturday. Knowing this makes it easy to determine the day of week for any day in February.

Feb. 10 was 18 days prior to the 28th, which is 14 days (two weeks) plus four days. Just go four days prior to Saturday and you see that Feb. 10 was a Tuesday.

Next, look at the even months after February. We have the fourth, sixth, eighth, tenth and twelfth months (April, June, August, October, December). It turns out that 4/4, 6/6, 8/8, 10/10 and 12/12 all fall on D-day. To determine April 19, just note that 19 is 15 days (two weeks and one day) past the 4th, and so 4/19 fell on a Sunday. Oct.  28 is 18 days after 10/10 and so 10/28 falls on a Wednesday. Christmas is 13 days (one day less than two weeks) after 12/12, and so Christmas falls on a Friday. With a little practice, you will find the even months a snap!

Now let’s look at the fifth, seventh, ninth and eleventh months (May, July, September, November).

For these months, you use the mnemonic phrase - “I work 9 to 5 at the 7-11.” This helps you with the following dates - 5/9, 9/5, 7/11 and 11/7 - all four of which also fall on D-day! Note that since July 11 falls on D-day, so does July 4th.

Using the same method as before, you can calculate days of the week for Sept. 19 (exactly two weeks after 9/5, so it falls on a Saturday), Nov. 10 (three days after 11/7, so it’s a Tuesday) and May 7 (two days before 5/9, so it’s a Thursday).

The last day of February next year (2010) happens to fall on a Sunday. Using this fact and the patterns above, you can now determine that Halloween (10/31), which is exactly three weeks after 10/10, will fall on a Sunday next year! June 10, 2010 (four days after 6/6) will fall on a Thursday.

Okay, let’s do a few dates for practice. Try them first and then you can check your answers below. April 23, 2010 ... Nov 3, 2010 ... August 16, 2010.

The algorithm doesn’t include January or March. The month of March is fairly straightforward since its days following immediately after the D-day. Each day in March that is a multiple of seven falls on the D-day.

So March 16, 2010 (two weeks and two days after the last day in February) will fall on a Tuesday. For January, just work backwards from the end of February.

Since February 2010 has 28 days, the last day of January is also D-day. So Jan. 31, 24, 17, 10 and 3 would all fall on D-day (Sunday).

Answers to above: Friday, Wednesday, Monday

Now, as I stated earlier, Sept.2, 1752 was a Wednesday. In 1752, Europe changed from the Julian calendar to the Gregorian calendar. At that time, the two calendars were out of sync by 11 days and so

11 days were “discarded”. As a result, the day immediately after Sept. 2 was

Sept. 14 (a Thursday). Therefore, Sept. 16 was a Saturday! I guess kids born on days between Sept. 3 and Sept. 13 didn’t get a birthday party that year, eh?