A well-known savant skill is the ability to tell you what the day of the week any date is on in a matter of seconds. For example, if you tell them you were born on May 3, 1978, the savant could tell you that it was a Wednesday. Though when you ask them how they figured it, they usually tell you they don't know. Every explanation I've found credits complicated algorithms that doesn't seem feasible to conduct mentally so quickly. So I finally set out to find my own formula to quickly figure days of the week using leap years. I analyzed the past one hundred years and found a few sequences to base my calculations on which I'll try to explain as we go. While I haven't tried every possible date yet, and probably won't, every date tried so far has worked.

To build a formula I originally chose to work with years between this year and 1900, which is interrupted by the 400 rule in defining leap years. This particular approach I expect to work for dates between 1901 and 2008 though requires knowing only one day from the leap year you choose to reference. (An additional rule must be applied to figure the 1800s due to 1900 not being a leap year. Also, the formula changes to figure into the future which I won't outline at this time.)

The example I've chosen is that we will seek to find out what day of the week July 31, 1917 was on given that May 3, 1996 was on a Friday. I'll first give the equation then explain the steps.

1996-1917=79
79 divided by 4= 19 remainder of 3.
1917+3= 1920.
Figuring for 1920:
19+1= 20
20 divided by 7= 2 remainder of 6.
The sixth formula is +4.
+4 from Friday is Monday.
So May 3, 1920 was on a Monday, skip a day from leap year so in 1919 a Saturday, in 1918 a Friday, and

1917 it was on a Thursday.

Short May Graph:
Mon Tue Wed Thur Fri Sat Sun
30 1 2 3

If May 3, 1917 was on a Thursday, then April 30th was on a Monday.
Since it was a Non-Leap Year, if April 30th was on Monday so was July 30.
Therefore July 31, 1917 was on a Tuesday.

Here's the step by step explanation:
Step One: Find A Reference Date.
For simplicity, I chose one in the last leap year of the 1900s. May 3, 1996 was a Friday.

Step Two: Figure What Day The Reference Day Landed On In The Nearest Leap Year.
To find that, subtract the goal year from the reference year, so 1996-1917=79. Then divide that by 4 which equals 19 and a remainder of three. The three tells us the nearest leap year is three years prior (when counting

• 1
• 2
• next page >>

---

Add your voice

Know something about Math tricks?
We want to hear your view. Write now!