Frank Morgan's Math Chat
April 15, 1999
OLD CHALLENGE. Ruth Leitschuck asks for years in the 1900s with the same calendar as the year 2000. She explains, "Just thought this year might be programmed into the old VCR on January 1st for correct day and date." (Also, what about years before 1900?)
ANSWER (Eric Brahinsky, Michael Marcotty, Al Zimmermann, Jean-Pierre Carmichael). An identical calendar must, like 2000, be a leap year starting on a Saturday. Leap years occur every four years, and every seventh leap year starts on a Saturday, so calendars like 2000 occur in 2000 - 28 = 1972, 1972 - 28 = 1944, and 1944 - 28 = 1916. I'd suggest setting the VCR to 1916 if possible, so that you won't have to reset it for another 82 years!
Zimmermann adds, "You may be amused to know that I've been collecting, and re-using, calendars since the late 1960s. People often do a double-take when they see a ten- or twenty-year-old calendar hanging on my wall. It sometimes turns into a triple-take when they realize the calendar is correct for the current year."
The first identical year before 1900 is not 1916 - 28 = 1888 as you might expect, because 1900 breaks the pattern by not being a leap year. According to our current calendar, century years are leap years only if divisible by 400, like the year 2000. This compensates for the fact that the seasonal "tropical" year is actually 11 minutes shorter than 365.25 days. (See Math Chat of October 14, 1998.)
It turns out that the first identical year before 1900 is 1876 rather than 1888. Joe Shipman sends in a great "heirloom" problem to give your friends based on this 12-year hitch:
"Mary has an embroidered calendar that was made by her great-great-grandmother for her great-grandmother. Family tradition is to pass it down from mother to daughter as a Christmas gift when it is about to become useful again. This year she plans to give it to her daughter. How old is the calendar?
"Answer: it was previously passed down on Christmas 1971, 1943, 1915, and ...,1875! It is 124 years old."
Brahinsky notes that in the United States the earliest year identical to 2000 was 1780, and not just because independence was declared in 1776, but because the calendar finally changed in 1752 in England and its colonies to our current "Gregorian calendar" (decreed by Pope Gregory in 1582) from the old "Julian calendar" (which had leap years every four years and years starting on March 1 instead of January 1). In Russia the earliest identical year was 1944, since Russia did not adopt the new calendar until after the revolution in 1918.
See Math Chat of January 3, 1997 and the Home Page for Calendar Reform.
NEW CHALLENGE (inspired by Robert Grafton). A physicist and a mathematician can clean a house in 6 hours; an engineer and the mathematician in 3 hours; and the physicist and the engineer in 1 hour and 12 minutes. How long would it take the physicist alone?
Send answers, comments, and new questions by email to Frank.Morgan@williams.edu, to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.
Copyright 1999, Frank Morgan.