When can the calendar of year 1997 be used again?

The correct answer is Option (3) → 2003

A calendar can be reused 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) and a leap year by 2, so the odd days are added until the total is a multiple of 7.

• 1997 (ordinary): 1 odd day, total 1

• 1998 (ordinary): 1, total 2

• 1999 (ordinary): 1, total 3

• 2000 (leap): 2, total 5

• 2001 (ordinary): 1, total 6

• 2002 (ordinary): 1, total 7, so 2003 starts on the same day as 1997, and 2003 is an ordinary year like 1997

Tip: An ordinary year that comes just after a leap year (like 1997) repeats its calendar after 6 years; the ordinary years in the other positions repeat after 11 years.