Which of the following years has exactly the same calendar as the year 2010?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2021
A later year has the same calendar as 2010 when it is also an ordinary year and the years from 2010 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.
2010, 2011, 2013, 2014, 2015, 2017, 2018, 2019: 1 odd day each, 8 in all
2012, 2016, 2020 are leap years: 2 odd days each, 6 in all
Total from 2010 to 2020 \(=8+6=14=2\times7\), so 0 odd days and 2021 starts on the same day as 2010
2021 is not a leap year, like 2010, so the two calendars match
Why the other options are incorrect
Option (1) 2016 — Incorrect. 2016 is a leap year, so it has a 29th February that 2010 does not have.
Option (2) 2017 — Incorrect. 2010 to 2016 give 9 odd days, which leaves 2, so 2017 starts 2 days later in the week.
Option (3) 2019 — Incorrect. 2010 to 2018 give 11 odd days, which leaves 4, so 2019 starts 4 days later in the week.