I have a calendar of the year 1997. When can I use it again?

The correct answer is Option (3) → 2003

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). An ordinary year moves the starting day on by 1 day (1 odd day), a leap year by 2. 1997 is an ordinary year; add the odd days year by year until they make a full week:

• 1997: 1 odd day (total 1)

• 1998: 1 (total 2)

• 1999: 1 (total 3)

• 2000, a leap year: 2 (total 5)

• 2001: 1 (total 6)

• 2002: 1 (total 7, one full week)

So 2003 starts on the same day as 1997, and 2003 is also an ordinary year: the 1997 calendar fits 2003.