Happy New Year!

With a new calendar year, you deserve a couple of new calendar feats to go with it. In this post, you'll learn how to quickly give the day of the week AND the moon phase for any date in 2015.

Even better, both of these feats are much easier than they sound!

DAY OF THE WEEK FOR ANY DATE IN 2015: The method to do this is quite simple, and is known as the Doomsday method, originally developed by John Horton Conway.

Start by going to last week's post, Calendar Calculation Made Simple, and learning the simple calendar calculation techniques taught there.

To work out dates in only 2015, all you have to remember is that 2015's "Doomsday" is Saturday. If you think about it, you can already work out any date in February using just this knowledge.

For example, Valentine's Day, Feb. 14th, must also be a Saturday, because it's exactly 2 weeks before Feb. 28th. How about Feb. 2nd (Groundhog Day)? Well, Feb. 7th is a Saturday, and Feb. 2nd is 5 days before that. What's 5 days before a Saturday? The answer is Monday! Therefore, Groundhog Day will be on Monday in 2015.

On which day will Christmas fall in 2015? We know from the technique taught in last week's videos that December 12th is a Saturday, so 2 weeks later, December 26th, is also a Saturday. Since Christmas is one day before that, it must be on a Friday!

When is July 4th this year? It's exactly 1 week before July 11th, so it must be a Saturday, as well.

St. Patrick's Day, March 17th, is 3 days after March 14th (Pi Day, mentioned in the videos from last week), so it's 3 days after a Saturday, making it a Tuesday in 2015.

January 15th is Martin Luther King, Jr.'s birthday, but what day does it fall on in 2015? January 3rd is a Saturday this year, and so is January 17th (2 weeks later). Take back 2 days, and we get January 15th being a Thursday this year!

With the knowledge from last week's videos, and a little practice, you can quickly and easily determine the day of the week for any 2015 date. You could get practice at the Day For Any Date (Mentalist Challenge) page, changing the year to 2015, and then trying to determine the date before you click the Show button.

When you're demonstrating this ability for someone, it's nice to be able to prove that you're right about the date. I use Wolfram|Alpha and/or timeanddate.com's calendars.

MOON PHASE FOR ANY DATE IN 2015: 2 years ago, I posted a new tutorial about determining the moon phase for any date. Similar to the year calculations, focusing on a particular year, such as 2015, greatly simplifies the required calculations. Like the doomsday algorithm above, this formula was also developed by John Conway.

In fact, working out the moon phase for any date in 2015 is even simpler than working out the date! How simple is it?

(Month key number + date + 8) mod 30

It's probably best if I explain each part:

Month key number: January's key number is 3, February's key number is 4, and all other months' keys are their traditional numbers; March is 3, April is 4, May is 5, and so on up to December, which is 12.

Date: This is simply the number represented by the particular date in the month. For the 1st, add 1. For the 2nd, add 2. For the 3rd, add 3, and so on.

+ 8: The addition of 8 takes the starting point of 2015 into account, which is why this particular formula works ONLY for 2015.

mod 30: If you get a total of 30 or more, simply subtract 30. Otherwise, just leave the number as is. Betterexplained.com has an intuitive explanation of modular arithmetic.

The resulting number will be the approximate age of the moon in days, from 0 to 29. This formula only gives an approximation, so there's a margin of error of ±1 day.

As an example, let's figure the phase of the moon on July 4, 2015. July is the 7th month, and the 4th is the date, so we work out (7 + 4 + 8) mod 30 = (11 + 8) mod 30 = 19 mod 30, which is just 19.

In that example, we estimate the age of the moon to be 19 days old.

What exactly does the age of the moon in days mean in practical terms? Here's a quick guide:

• 0 days = New moon (the moon is as dark as it's going to get)
• 0 to 7.5 days = Waxing crescent (Less than half th moon is lit, and it's getting brighter each night)
• 7.5 days = 1st quarter moon (Half the moon is lit, and gets brighter each night)
• 7.5 to 15 days = Waxing gibbous (More than half the moon is lit, and getting brighter each night)
• 15 days = Full moon (The moon is as bright as it's going to get, and will start getting darker each night)
• 15 to 22.5 days = Waning gibbous (More than half the moon is lit, and it's getting darker each night)
• 22.5 days = 3rd quarter moon (Half the moon is lit, and gets darker each night)
• 22.5 to 29 days = Waning crescent (Less than half the moon is lit, and it's getting darker each night)