Chapter 8: Mastery

Presidential Calendar Mnemonic (PDF coming soon)
Chapter 1: A Simpler Method
Chapter 2: Mod7 Magic
Chapter 3: The Recipe
Chapter 4: Ten Months
Chapter 5: Zanuary and Zebruary
Chapter 6: US Presidential Elections
Chapter 7: Silly Stories
Chapter 8: Mastery

This is the eighth post in a series describing the Presidential Calendar Mnemonic. Our goal is to calculate the day of the week, given any date in any century. In this chapter we master the Gregorian calendar by learning century codes.

The 1900s is our “home base century” because we know all of the US presidential elections in that century and the century code is 0 (by design). Every other century is an offset from the 1900s, and that offset is the century code c. The offset for the 2000s is -1. So the remainder of the 2000s is achieved by solving for the 1900s and subtracting 1.

So the year codes in every year of the 21st Century (2000s) is one less than its counterpart year in the 20th Century (1900s). We can see this with the corresponding year codes below:

1900 (3) and 2000 (2)
1904 (1) and 2004 (0)
1908 (6(-1)) and 2008 (5)
1912 (4) and 2012 (3)
1916 (2) and 2016 (1)
1920 (0) and 2020 (6(-1)
1924 (5) and 2024 (4)

So there are actually two ways to get year codes from 2000-2027. The direct method is to use elections from Bush#2 (2000) to Trump’s re-election(2004). The indirect method is to calculate the 1900s and subtract 1. The direct method is faster and easier, but that’s available only when presidential elections are available. Starting in 2028, we don’t know who will be elected, so the indirect method is the only method available. The indirect method is available for every other century too. We just need to know what the offset is, and that’s why we have century codes.

I have found the best way to remember century codes is simply to be aware of the pattern “6 4 2 0” in groups of four centuries.

1500s 0

1600s 6(-1)
1700s 4
1800s 2
1900s 0

2000s 6(-1)
2100s 4
2200s 2
2300s 0

Recognizing this pattern, we can use this recipe for any century:

• If the first two digits of a given century is a multiple of 4 (like the 4400s) then the century code c = 6(-1).

• If it is not, (like 4500s), find the closest multiple of 4 that is closest and lower than the given century (4400 in this case). That’s the start of a group of four centuries with a “6(-1) 4 2 0” pattern. It’s reminiscent of groups of 4 years that we learned in Chapter 6.

What is the century code for the 2700s? 24 is divisible by 4, so the relevant group of four is:
2400s 6(-1)
2500s 4
2600s 2
2700s 0
So for 2700s, c = 0. Day calculations are identical to the 1900s.

What are the century codes for the 3500s, 1700s, 4800s, 6600s, and 9900?1

A reasonable upper limit to this enterprise is the the Hundredth Century (the 9900s), ending on December 31, 9999. If someone asks what day is January 1, 10,000 (or higher) ask them how they are going to check the answer, because I haven’t found a perpetual calendar calculator that will go that high. Or tell them we have a “Y10K crisis.”

That’s it! We have mastered the entire Gregorian calendar. You can mentally calculate the day of the week from October 15, 1582 to December 31, 9999. That’s over 3 million days!

I think the Presidential Calendar Mnemonic is doable. Do you?