secrets-of-mental-math-malestrom

220
Secrets of Mental Math
For dates in the 2100s, we add 5 to the year code (or, equivalently,
subtract 2 from the year code). For example, since
2009 has a year code of 4, then 2109 has a year code of 4 5
9, which, after subtracting 7 is the same as a year code of 2.
Dates in the 1700s are treated just like in the 2100s (by
adding 5 or subtracting 2) but we need to be careful. The days
that we are calculating are based on the Gregorian calendar,
established in 1582. But this calendar was not adopted by
England (and the American colonies) until 1752, when Wednesday,
September 2, was followed by Thursday, September
14. Let’s verify that September 14, 1752, was indeed a Thursday.
Since 2052 has a year code of 2 (from page 218, or by
52 13 63 2), then 1752 has a year code of 0. Thus September
14, 1752, has
Month Code Date Year Code 4 14 0 18
and 18 14 4, so it was indeed a Thursday. However, our formula
will not work for earlier dates (which were governed by
the Julian calendar).
Finally, we remark that under the Gregorian calendar, a leap
year occurs every four years, with the exception of years that
are divisible by 100, although there is an exception to the
exception: years divisible by 400 are leap years. Thus 1600,
2000, 2400, and 2800 are leap years, but 1700, 1800, 1900,
2100, 2200, 2300, and 2500 are not leap years. In fact, the
Gregorian calendar repeats every 400 years, so you can convert
any future date into a date near 2000. For example,
March 19, 2361, and March 19, 2761, will have the same day
of the week as March 19, 1961, which, as we already determined,
is a Sunday.