Would you like to raise some eyebrows as you confidently guess the day of any date your friends throw at you? “November 17, 2030″ they challenge. “Sunday” you respond correctly.

This is an easy method that I learned during my Computer Science days. It’s called the ‘Doomsday Algorithm’, and you can learn to do it in your head without much practice.

Here is a good explanation of how it works, copied from the website Rudy.ca.

February 28/29

To use the Doomsday Algorithm in any year, we first need to know the ‘Doomsday’ for that year, which is essentially the day that we will use as an anchor to be able to guess any other day in that year.

Doomsday is February 28 or 29. In other words, Doomsday is always the last day of February. In normal years, Doomsday is February 28, and in leap years, Doomsday is February 29.

In 2007, which is not a leap year, the last day of February is Wednesday the 28th.

Once we know Doomsday, it’s pretty easy to get the day of the week for any day in February. This is done by adding and subtracting, using multiples of 7, and you should be comfortable doing this in your head, otherwise the rest of the algorithm will give you trouble! Luckily, most people, through practice or whatever, are good at mentally picturing a month if they have something to anchor it on, and Doomsday is this anchor. For February, it’s always the 28th in normal years, and the 29th in leap years.

Example: what is this year’s Valentine’s Day, February 14th?
Answer: Doomsday 2007 is Wednesday the 28th of February. So one week earlier, the 21st is also Wednesday. Another week earlier is Wednesday the 14th. So Valentine’s Day 2007 is a Wednesday.

Example: what is this year’s Groundhog day, February 2nd?
Answer: Doomsday 2007 is Wednesday the 28th… Wednesday the 21st… Wednesday the 14th… Wednesday the 7th… and then we have to go five days back, to get from the 7th to the 2nd. So Groundhog Day, February 2nd, is, um, Friday this year.

If going back five days is hard (and it often is, looking back over a weekend), there’s a little trick we can use here. Going two days forward gives the same day of the week as five days back. So if February 7th is Wednesday, then two days forward is Friday the 9th, which is the same day of the week as seven days earlier, Friday the 2nd. Remember, all we’re after is the day of the week, so “-5″ is the same as “+2″ but “+2″ is usually easier to do.

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Even Months

Okay, the last day of February is Doomsday. Once we know what day of the week Doomsday is, we immediately know the day of the week of certain other days in the year. There are actually 52 (or 53) other Doomsdays each year, all on the same day of the week as “the” Doomsday at the end of February.

So each month has a special day which we remember, because it is on the same day of the week as the Doomsday at the end of February. Just keep in mind that the entire year is determined by the Doomsday at the end of February, and that all the other Doomsdays within the year are on the same day of the week.

Let’s begin with the even months. These are months 2, 4, 6, 8, 10, and 12, i.e. February, April, June, August, October, and December. Actually, we never do February this way, because it’s special, and we’ve already covered it.

For even months (not including February), the Nth of that month is a Doomsday (i.e. the same day of the week as the last day in February). This is a delightful coincidence, and it’s so easy to remember:

• April 4th is a Doomsday
• June 6th is a Doomsday
• August 8th is a Doomsday
• October 10th is a Doomsday
• December 12th is a Doomsday

Neat, eh? Now we can simply work our way around any even month based on its Doomsday.

Example: what is this year’s Christmas Day, December 25th?
Answer: Doomsday 2007 is Wednesday. So December (even month) 12th is the Doomsday for December, so it’s also Wednesday. Two weeks later, December 26th is also Wednesday, so Christmas this year is Tuesday December 25th. Easy! In fact, after you do the Doomsday algorithm often enough, you just start remembering things like Christmas is always the day before Doomsday.

Example: what is this year’s Canadian Thanksgiving Day, the second Monday in October?
Answer: Doomsday 2007 is Wednesday. So October (even) 10th is Wednesday, and so two days earlier, October 8th is Monday. This has to be the second Monday of October, since a week earlier is October 1st, but a week earlier than that is in September. So the Canadian Thanksgiving, the second Monday in October, is Monday, October 8th.

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Odd Months

Now let’s do the odd months—months 1, 3, 5, 7, 9, and 11, i.e. January, March, May, July, September, and November.

Skip January and March for a moment.

Consider the following mnemonic phrase:

I work 9-5 at the 7-11

“Nine to five” is a common working day, and 7-Eleven is a chain of convenience stores. The phrase means:

• for the 9th month, Doomsday is the 5th
• for the 5th month, Doomsday is the 9th
• for the 7th month, Doomsday is the 11th
• for the 11th month, Doomsday is the 7th

This gives us Doomsday for May, July, September, and November. Now we just work our way around again within each month, using Doomsday for that month.

Example: what day is this year’s July 4th?
Answer: Doomsday 2007 is Wednesday. The Doomsday for July (7th month) 11th is Wednesday. So one week earlier, July 4th is also Wednesday. In fact, after you do the Doomsday algorithm often enough, you just start remembering things like July 4th is always Doomsday.

Example: what is this year’s Labour Day, the first Monday of September?
Answer: Doomsday 2007 is Wednesday. September (9th month) 5th is Wednesday. So September 3rd is Monday. This has to be the first Monday in September, because seven days earlier would put us back into August. So Labour Day this year, the first Monday of September, is September 3rd.

Now March.

Doomsday, the last day of February, is often also called the “0th” of March. You might have to think about that for a moment, until you realize that the next day is the 1st of March. So if the “0th” of March is Doomsday, then the 7th of March, exactly one week after the last day of February, no matter whether it’s the 28th or 29th, is also Doomsday.

Example: what day is this year’s St. Patrick’s Day, March 17th?
Answer: Doomsday 2007 is Wednesday. March “0th” is Wednesday. March 7th is Wednesday. March 14th is Wednesday. Go three days forward, to get to Saturday, March 17th.

Finally, we have to be able to do January.

The easiest way to calculate January’s Doomsday was described at Rudy.ca by reader Bob Goddard:

It’s January 3rd three years out of four, the non-leap years. It’s January 4th only in the fourth year, the years divisible by 4.

This is so much simpler than what I had before (which involved January 31st and “January 32nd”). Why couldn’t I have seen the simple way?!

Example: what is this year’s New Year’s Day (January 1st)?
Answer: Doomsday 2007 is Wednesday, and since this year is not a leap year, January 3rd is Wednesday. Go back two days, and January 1st is Monday. Simple, eh? Thanks, Bob.

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If you learn the above, you will be ready for the next step: other years and centuries! You can learn that on Rudy.ca.