The World Almanac†features a "perpetual calendar," a collection of 14 possible calendars. Does this suffice to ensure that there is a calendar for every conceivable year?
Why?
There are 7 choices for the day of January 1st and 2 choices for the year (leap or non-leap). The total number of calendars is 7 · 2 = 14.There are 365 choices for the day in a regular year and 366 choices for the day in a leap year. The total number of calendars is 731. There are 12 choices for the months, and 2 choices for the year (leap or non-leap). The total number of calendars is 12 · 2 = 24.There are 12 choices for the months, and 2 choices for the year (leap or non-leap). The total number of calendars is 12 + 2 = 14.There are 7 choices for the day of January 1st and 2 choices for the year (leap or non-leap). The total number of calendars is 7 + 2 = 9.