[net.math] End of the World

fenwick (06/02/82)

A normal (non-leap) year is 365 days = 52 weeks + 1 day.  Thus if
January 1, some non-leap year, occurs on a Monday, then January 1, the
next year, occurs on a Tuesday.  If January 1, some leap year occurs on
a Monday, then January 1, the next year occurs on a Wednesday.  Between
January 1, 2001, and January 1, 2101, there are 100 years, of which 24
are leap years.  Thus if 1/1/2001 is on the n-th day of the week,
1/1/2101 is on the ( (n+124) mod 7 )-th day of the week.  Since 124 mod
7 = 5, the first day of each century occurs 5 weekdays (modulo Sunday)
later, EXCEPT when we pass over a year that is divisible by 400.  In
this case, there are 100 normal years and *25* leap years.  125 mod 7
is 6, so from 1/1/2301 to 1/1/2401 we must add 6 weekdays (modulo
Sunday).  But looking at the series, notice that we add 5 + 5 + 5 + 6 =
21 days every 400 years, so we will cycle through only 4 unique
days-of-the-week.  We know January 1, 2001 is a Monday (try cal 2001);
then 1/1/2101 is a Saturday, 1/1/2201 is a Thursday, 1/1/2301 is a
Tuesday, and 1/1/2401 is again a Monday (fortunately).  Thus the world
will never end.

John Eldridge & Robert Snyder
harpo!floyd!jce