I have a calendar of year 2001. In which year can I use it again?

The correct answer is Option (3) → 2007

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). The weekday moves on by the odd days of each year: 1 for an ordinary year of 365 days (52 weeks + 1 day) and 2 for a leap year of 366 days. 2001 is an ordinary year, so we count odd days until they make a whole week (7):

• 2001: 1 odd day, total 1

• 2002: 1 odd day, total 2

• 2003: 1 odd day, total 3

• 2004 (leap year): 2 odd days, total 5

• 2005: 1 odd day, total 6

• 2006: 1 odd day, total 7, a whole week

So 1 January 2007 falls on the same weekday as 1 January 2001, and 2007, like 2001, is not a leap year: the 2001 calendar fits 2007.