2005

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Let's look at March and April, in 1900, and notice two interesting properties. First, the month of April has the same property as the "infinite grid," so that if you divide any particular day in April, 1900, by 7, the remainder truly indicates the day of the week, 1=Sun, 2=Mon, 3=Tue, 4=Wed, 5=Thu, 6=Fri, 0=Sat, absolutely true for April in the year 1900.

Second, if March 25th were indeed New Year's Day, then any Leap Day, in February, following the normal rules of leap years, would automatically be "tacked on" to the end of the previous year, having no effect whatsoever on "grid properties" of other months of the year.

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4:13

Let's see if we can make certain changes to the following months, to get them to "conform to the grid," such that dividing by 7 produces the day of the week.

They're all beginning to look just like April, aren't they? Instead of May having days in the range, 1-31, by adding 2 to each and every day, the days begin to fall into the range 3-33, and now, dividing by 7, we find the day of the week!

Similarly, if we add a "month code" to all the days of the year 1900, we realign each and every month such that dividing by 7, keeping only the remainder, always indicates the day of the week.

So here's the Overview: We want to determine the day of the week for any month, day and year, in the Gregorian calendar, as established by law in the British Colonies, beginning September 14, 1752.

If we can get any particular day to conform to the identical modulo-7 grid as April in the year 1900, we can always calculate the weekday by dividing by 7 and keeping the remainder, with 1=sun, 2=mon, 3=tue, 4=wed, 5=thu, 6=fri and 0=sat.

And here's the Floor Manager's point of view: In the year 1900, we can always accomplish this by adding the month code to the day of the month, then dividing by 7.

4:45