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 has 1 odd day and a leap year 2; the odd days are added until they make a full week (7).

• 1997 (ordinary): 1 odd day, total 1

• 1998 (ordinary): 1 odd day, total 2

• 1999 (ordinary): 1 odd day, total 3

• 2000 (leap year): 2 odd days, total 5

• 2001 (ordinary): 1 odd day, total 6

• 2002 (ordinary): 1 odd day, total 7, a full week

So 2003 starts on the same day as 1997, and it is an ordinary year like 1997.