How this formula works.
The day-of-week formula is based on “base 7”
arithmetic. By that I mean that all
numbers in the formula are translated to a number between 0 and 6 (or 1 and 7,
if you prefer to start at 1. So, using 0 to 6, the number 7 becomes 0, and
so forth. When you get to 27, the number becomes 6. Why 7? Because there are 7 days in a week and,
unlike the months and years, there is a predictable and smooth flow in the occurrence
of the days of the week in 7-day cycles.
Sunday follows Saturday and so on for as far out as you can go. The months,
for instance, do not flow smoothly in that some have 31 days, others have 30, one
has 28 and sometimes 29. Likewise, the years do not flow smoothly in that some
have 365 days and some have 366 days, but here are exceptions to the latter too.
The days of the week, however, run on a smooth cycle of Sunday to Saturday
without stop as far into the future as you can imagine. So, let’s assume today is Tuesday, which is
it as I write this. Let me ask, what day
of the week will one day from now be?
Right, Wednesday, because Tuesday plus one day is Wednesday. What about
7 days from now? Right again, Tuesday. What
about eight days from now? Right again,
Wednesday. How did you get Wednesday so quickly? Well, you subtracted the highest multiple of
7 contained in the number 8, which is 7, and you were left with 1. And 1 day from
Tuesday is Wednesday. One final quiz. What day of the week will it be 7,777,778
days from today. Right, Wednesday.
If you followed
this, you are smart enough to learn this technique. If you did not, exit this site now and take up a video game.
What makes the technique difficult for some people is that
you must compute values between 0 and 6 for the Month-and-Day, and the Year (including
the Century), and mash the two together, and then reduce that resulting number
to some number be went 0 and 6, which most kids can do by 4th grade.
Here’s a sample to whet your appetite to learn this
technique where Sunday is the first day of the week.
What day of the week will February 1, 2345 fall on? That would be (3 + 1) + (0 +1 - 0) = 5 = Thursday.
Note: Computing one of these numbers is a little cumbersome for some, but easy to do once you learn how.
Since that is my 400th birthday, please send me a
birthday card.
