The calendar for the year 2007 will be the same for the year:

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The calendar for the year 2007 will be the same for the year:

  1. A.

    2014

  2. B.

    2016

  3. C.

    2017

  4. D.

    2018

Show answer & explanation

Correct answer: D

Two years have the same calendar exactly when two conditions hold together: (1) the cumulative count of "odd days" between them is a multiple of 7, so 1 January falls on the same weekday in both, and (2) both years share the same leap-year status. A common (non-leap) year contributes 1 odd day and a leap year contributes 2 odd days.

Starting from 2007, add each following year's odd days to a running total until it first becomes a multiple of 7 -- the very next year after that point repeats 2007's calendar.

Year

Odd days

Running total

2007

1

1

2008

2

3

2009

1

4

2010

1

5

2011

1

6

2012

2

8

2013

1

9

2014

1

10

2015

1

11

2016

2

13

2017

1

14

The running total reaches 14 at the end of 2017, and 14 = 2 x 7 is a multiple of 7.

Independent check: 2007 is a common year (2007 divided by 4 leaves a remainder) and 2018 is also a common year (2018 divided by 4 leaves a remainder), so the leap-status condition is satisfied too -- confirming the full calendars align, not just 1 January.

Hence, the calendar for 2018 is identical to that of 2007.

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