Which of the following years has exactly the same calendar as the year 2009?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2015
A later year has the same calendar as 2009 when it is also an ordinary year and the years from 2009 up to it add up to 0 odd days, so that it starts on the same day. An ordinary year gives 1 odd day, a leap year 2.
2009, 2010, 2011, 2013, 2014: 1 odd day each, 5 in all
2012 is a leap year: 2 odd days
Total from 2009 to 2014 \(=5+2=7\), so 0 odd days and 2015 starts on the same day as 2009
2015 is not a leap year, like 2009, so the two calendars match
Why the other options are incorrect
Option (1) 2012 — Incorrect. 2012 is a leap year, so it has a 29th February that 2009 does not have.
Option (2) 2013 — Incorrect. 2009 to 2012 give \(1+1+1+2=5\) odd days, so 2013 starts 5 days later in the week.
Option (3) 2014 — Incorrect. 2009 to 2013 give \(5+1=6\) odd days, so 2014 starts 6 days later in the week.