Sunday, April 4, 2010

How Many Different Calendars Are There?

While talking with my friend Cody about the possibility of reusing calendars every few years due to them repeating, we wondered if every possible calendar could occur, and how many years one would have to wait to have all the possible calendars. When I got home, I made a spreadsheet that identified the pattern.

It turns out that if we started saving calendars this year, we would have all possible calendars by 2036, and that some of the calendars from common years would begin repeating in 2019, so from 2019-2036 we would only need to save the calendars from leap years.

This pattern would continue until 2099. The rules for leap years would make 2100 NOT a leap year and the pattern would start over again in 2101. The rule for leap years is that every year that is divisible by four, except for multiples of 100 that are not divisible by 400 ARE leap years.