I have a calendar of year 1597. When can I use it again?

The correct answer is Option (2) → 1603

A calendar can be used again in a year that starts on the same day of the week and is of the same kind (ordinary or leap). Each ordinary year moves the starting day on by 1 odd day (365 days = 52 weeks + 1 day) and each leap year by 2 odd days; the calendar repeats when the odd days add up to a multiple of 7.

• 1597 is an ordinary year (not divisible by 4)

• Odd days carried forward by each year from 1597:

  • 1597: 1, total 1

  • 1598: 1, total 2

  • 1599: 1, total 3

  • 1600: 2 (a leap year, since 1600 is divisible by 400), total 5

  • 1601: 1, total 6

  • 1602: 1, total 7, a whole week

• So 1603 starts on the same day as 1597, and 1603 is also an ordinary year: the calendar of 1597 can be used again in 1603

Tip: A year that comes just after a leap year (like 1597, after 1596) gets its calendar back after 6 years, as long as no century year that is not a leap year falls in between.