Discussion
The calendar for the year 2007 will be the same for the year
Answer: D
A calendar repeats once the accumulated odd days come back to zero. 2007 is an ordinary year, so count forward, giving each ordinary year 1 odd day and each leap year 2:
| Year | Odd days | Running total (mod 7) |
|---|---|---|
| 2007 | 1 | 1 |
| 2008 (leap) | 2 | 3 |
| 2009 | 1 | 4 |
| 2010 | 1 | 5 |
| 2011 | 1 | 6 |
| 2012 (leap) | 2 | 1 |
| 2013 | 1 | 2 |
| 2014 | 1 | 3 |
| 2015 | 1 | 4 |
| 2016 (leap) | 2 | 6 |
| 2017 | 1 | 0 |
The total returns to 0 after 2017, so the first year whose calendar matches 2007 is 2018. Both must also be non-leap for the match to hold, and 2018 is.
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