Calender of 2014

Number Theory Level 3

Which year will have a common starting weekday and equal number of days to year 2014?

2020 2025 2018 2022

Parth Panchal by Parth Panchal , 26, India

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1 solution

Duc Anh
Aug 1, 2014
  • 1 year = 365 days = 1 mod 7
  • 1 leap year = 366 = 2 mod 7
  • So each normal year shift the starting weekday by 1 and each leap year by 2.
  • To have the same weekday, we need the shift to be 0 mod 7 (which is 7, 14,...).
  • The year is 2025 = 2014 + 11 (including 3 leap year : 2016, 2020, 2024)
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