Chapter 3: The Recipe

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 third 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. So far, we have learned how to convert day codes into days of the week and how to simplify addition with the mod7 operation.

Below is the formula on two lines. There are other ways of writing it, but this is my favorite.

monthType = ⎡ y + c + m ⎤
DOW = ⎡ ⎡ dom ⎤+ MonthType ⎤

where:

DOW = day of the week (0, 1, 2, 3, 4, 5, 6).
y = year code (0, 1, 2, 3, 4 ,5, 6)
c = century code (6, 4, 2, 0)
m = month code (0, 1, 2, 3,4 ,5, 6)
dom = day of the month (1st - 31st)
“⎡ ⎤” denotes a mod7 operation, if needed

Here is a step-by-step recipe of this process, with an example. What day is July 4, 1776?

• Focus first on the two-digit year, 76. There is a year code associated with 76. You’ll know why soon enough. Knowing the year code is the most difficult step and that’s why it’s first. You don’t know why yet, but for 76, y is always 0, no matter the century.

• Now turn your attention to the century, the 1700’s. Centuries are fairly easy. You’ll know instantly that c for the 1700s is always 4.

• The third component is month, July. This is a medium difficulty step, but with practice, it becomes instantaneous. The month code m for July is always 3, no matter the year.

• So ⎡ y + c + m ⎤  =  ⎡ 0 + 4 + 3 ⎤ = ⎡ 7 ⎤ = 0. So July 1776 is monthType 0.

• At this point, I like to employ a bit of muscle memory with the monthType. If monthType is 1, 2, 3, 4, or 5, I touch a surface with 1, 2, 3, 4 or all 5 of my finger tips. For monthType 0, I make an ok sign👌. For Month Type 6(-1), I touch my pinky finger or the side of my hand to a surface. The surface can be my other arm, my thigh, a table, steering wheel, or anything handy. Why do this? Because storing the number in your hand gives your mind a break. It gives you an opportunity to clear your mind, maybe re-check monthType, or perhaps ask for the day of the month again. I think you will be pleased with storing the monthType in your hand, but it is optional.

• Having stored monthType 0 as an ok sign 👌in your hand, you can focus on the last component, which is the dom… the 4th day of the month.

• DOW =⎡ 4th + 👌 ⎤ = 4. So July 4th, 1776 was a Thursday.

• Optionally, if you still have monthType 0 stored in your hand, you can quickly answer other questions about July 1776. For example, the following week, on the 12th day of July 1776, George Washington wrote an urgent letter to the Continental Congress announcing that British Admiral Richard Howe’s fleet had reached New York. What day was that? That was ⎡ ⎡ 12 ⎤ + 👌 ⎤ = ⎡ 12 ⎤ = 5. Friday.

For a quick start, here are some starter codes. You can just write these down, use rote memory for these, or use these simple mnemonics:

• Year codes (y) for 2024, 2025 and 2026 are 4, 5, and 6. The last digit matches the year code. You’re welcome.

• Month codes (m) for November and March are 0. Think “No ma’am” or “No más” for November and March.

• The month code for May is 5. It’s the fifth month, so that’s easy.

Since we have memorized codes for 3 years and 3 months, we can solve the following problems:

What day is March 10, 2024?
monthType = ⎡ y+c+m ⎤ = ⎡ 4+0+0 ⎤ = 4 (press 4 fingers)
DOW = ⎡ 4 + ⎡ 10th ⎤ ⎤ = ⎡ 4 + 3 ⎤ = 0 (Sunday)

What day is May 17, 2024?
monthType = ⎡ y+c+m ⎤ = ⎡ 4+0+5 ⎤ = ⎡ 9 ⎤ = 2 (press 2 fingers)
DOW = ⎡ 2 + ⎡ 17th ⎤ ⎤ = ⎡ 2 + 3 ⎤ = 5 (Friday)

What day is November 27, 2026?
monthType = ⎡ y+c+m ⎤ = ⎡ 6+0+0 ⎤ = 6(-1) (press pinky finger)
DOW = ⎡ -1 + ⎡ 27th ⎤ ⎤ = ⎡ -1 + 6 ⎤ = 5 (Friday)

What day is May 26, 2025?
monthType = ⎡ y+c+m ⎤ = ⎡ 5+0+5 ⎤ = ⎡ 10 ⎤ = 3 (press 3 fingers)
DOW = ⎡ 3 + ⎡ 26th ⎤ ⎤ = ⎡ 3 + 5 ⎤ = 1 (Monday)

Practice, practice. What days are:
March 3, 2025, answers are in footnotes1
November 20, 2024,
May 9, 2026,
November 1, 2025, and
March 20, 2026.

You now have a solid understanding how the calendar mnemonic works. Up to this point, we have not strayed far from how other calendar mnemonics work. There is only the small matter of memorizing a list of century codes, a list of 100 years per century, and a list of twelve months per year (with and without leap years). Yikes! This challenge is where the Presidential Calendar Mnemonic innovations become apparent. In the next two chapters, we will learn all of the month codes and we will introduce an innovation for handling leap years.