Calendar Repeats

Date: 05/06/2002 at 10:19:07
From: Agatha
Subject: Calender

The year next to 1991 having the same calendar as that of 1990 is 
________.

Date: 05/06/2002 at 12:07:48
From: Doctor Ian
Subject: Re: Calender

Hi Agatha,

That's an interesting question! In a normal year - that is, a year 
with no leap day - there are 365 days, which comes to 52 weeks of 
7 days, plus one more day. 

So if a normal year starts on a Monday, then the following year has to 
start on a Tuesday. Does that make sense?  

However, if a leap year starts on a Monday, then the following year 
has to start on a Wednesday, because of the extra day in February.  

And if two years start on the same day, and if they're both normal 
years or both leap years, then they have to have the same calendar. Do 
you see why this is true? 

1990 is a normal year, and in fact, it _does_ start on a Monday. So 
1991 must start on a Tuesday, and 1992 must start on a Wednesday. But 
1992 is a leap year, so 1993 must start on a Friday (instead of a 
Thursday). 

I've started a table below:

  Year    Starts on   Leap?    Add
  ----    ---------   -----    ---
  1990    Monday      N        1
  1991    Tuesday     N        1
  1992    Wednesday   Y        2
  1993    Friday      N        1
  1994    Saturday    N        1

If you continue the table, you'll eventually find a year that starts 
on Monday and isn't a leap year. That's the year you're looking for. 

But be careful! Make sure you understand the rules for determining 
which years are leap years, and which aren't. It's a little more 
complicated than just dividing by 4. See the Dr. Math FAQ:

   The Calendar and the Days of the Week
   http://mathforum.org/dr.math/faq/faq.calendar.html 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/