Calculating the day of the week for 2011

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#1 15 May, 2011 - 14:04
Joined: 6 years 7 months ago

Calculating the day of the week for 2011

One of the memory skills I use is Dominic O’Brien’s method for calculating the day of the week for a given date. It’s part mnemonics, combined with basic addition and subtraction. I’m not going to present the full method here, but I will present a partial method you can use for calculating the day of the week for 2011. It’s really easy.

To simplify things, though, the first concept you need to be aware of is called Casting Out 7s. Our calculation is based on the seven day week, so 1 though 7 are the only numbers we need. If you can count by 7s, 0, 7, 14, 21, 28, 35, then you’re halfway there. Casting out 7s means that if you have a number like 23, you cast out 7, 14, 21, leaving you with a two remainder. I like to think of it as reducing…23 is reduced to 2. 19 is reduced to 5. 33 is also reduced to 5. In fact, you can easily see this on a calendar


Second, our reduction answers, 1 though 7, represent the days of the week. 1 is Sunday, 4 Wednesday, 7 is Saturday. 13 is reduced to 6 which is Friday. 24 is reduced to 3 which is Tuesday. If any of that doesn’t make sense, then give the above calendar a good look-see. All the information you need is there.

Now, here’s the memory part. You have to remember a number for each month.

January 6
February 2
March 2
April 5
May 0
June 3
July 5
August 1
September 4
October 6
November 2
December 4

The math is really simple. You add the month number (above) to the day of the month, cast out 7s, and your answer is the day of the week for this year.

January 1st. 6+1=7 That was a Saturday.
October 25th. 6+25=31. Reduce that to 3. That will be a Tuesday.
August 22nd. 1+22=23 Reduce that to 2. That will be a Monday.
December 25th. 4+25=29. Reduce that to 1. Christmas will be on a Sunday.

Tips: 7 also equals 0. If the day of the month is 7, 14, 21, or 28, go head and call it 0. When you cast 7s out of 21, you reduce all the way to 0.

Cast out numbers at any time. In the above example August 22nd, I’d reduce the 22 to 1 just out of habit, so the math becomes 1+1=2=Monday.

The full system requires you to remember a number, 0-6, for all years from 00-99, and a number for the centuries. By a happy coincidence, the numbers for 2011 are both zero, which is why for this year we only need to add the month number and the day of the month. (I’m going to post a followup about calculating for 2012, which is a slightly bit trickier since it’s a leap year.)

If you have any questions, let me know.


15 May, 2011 - 15:38
Joined: 6 years 7 months ago

I've always used the Doomsday Algorithm.

17 May, 2011 - 01:50
Joined: 2 years 8 months ago

I haven't tried Dominic O'Brien's method yet. I learned a method from the book Mind Performance Hacks, though haven't practiced it much. It is described here:

The Doomsday Algorithm looks interesting:

17 May, 2011 - 10:14
Joined: 6 years 7 months ago

I can recommend Arthur Benjamin's "Secrets of Mental Math." Lots of good tricks and techniques, including calculating the day of the week. Here's a link to his TED Talk:


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