IMC 2010 Q10
10. One year in the 1990s, January 1st fell on a Monday. Eleven years later, January 1st was also a Monday. How many times did February 29th occur during those eleven years?
- A 1
- B 2
- C 3
- D 4
- E 5
Intermediate Mathematical Challenge 2010, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 3
Every year, the day of the week on which a particular date falls is one day later than it fell the previous year unless February 29th has occurred in the meantime, in which case it falls two days later. As January 1st returned to a Monday after 11 years, it must have ‘moved on’ 14 days during that time, so February 29th occurred three times in those 11 years.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.