# Math Chat

Hours, Days, and Years

Old junior challenge

If you live for 6,000 years, how many days will that be?

Answer

A good start is (6,000 years) x (365 days per year) = 2,190,000 days. An extra day in a leap year every four years adds another 1,500 days to make 2,191,500. But every hundred years we skip a leap year (1900 was not a leap year), so we subtract 60 days to get 2,191,440. But every 400 years we put the leap year back in (2000 will be a leap year), so we add 15 days to get 2,191,455.

Old New Year's challenge

According to our current calendar, on what day of the week will Jan. 1 fall in the year 3000? in the year 1,000,000? in the year 101,000,000?

Answer

As above, in the 1,000 years from the year 2000 to the year 3000, there are 365,243 days, or 52,177 weeks and 4 days. Since January 1 falls on a Saturday in the year 2000, it will fall 4 days later on a Wednesday in the year 3000. The calendar has a 400-year cycle of 146,097 days, or an even 20,871 weeks. Since 2000, 1,000,000, and 101,000,000 are all multiples of 400, Jan. 1 falls on the same day in all those years, namely Saturday.

Because of an accumulating error in our current calendar, long before the year 1,000,000, New Year's Day would advance into summer. So we shall have to change the calendar, perhaps skipping some leap years.

Winning answers by Bill Bond, Eric Brahinsky, Bob Cohen, and Chuck Gahr.

New time challenge

John lives in an Atlantic coast state of the United States, and Mary lives in a Pacific coast state. When talking on the telephone from home recently, they realized it was the same time in both locations. How could this have been possible?

*Send answers, comments, and new questions to:

Math Chat

Bronfman Science Center

Williams College

Williamstown, MA 01267

or by e-mail to:

Frank.Morgan@williams.edu.

The best submissions will receive a copy of the book Flatland, which helps explain higher dimensions. The challenge question answer and winner will be announced in the next column in two weeks.