2015 Countdown Problem #2: 1 Jan 2115
You are given the following information:
- Christmas Day in 2014 (25 December 2014) falls on a Thursday.
- There are 7 days in a week, and 365 days in a year except for leap years (where there are 366 days).
- A year is a leap year if:
- it is divisible by 4 and not divisible by 100, or;
- it is divisible by 400.
What day is New Year’s Day in 2115 (1 January 2115)?
Please answer:
- 1 for Monday
- 2 for Tuesday
- 3 for Wednesday
- 4 for Thursday
- 5 for Friday
- 6 for Saturday
- 7 for Sunday
This problem is part of the set 2015 Countdown Problems .
The answer is 2.
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1 solution
Note that 365 = 1 (mod 7), hence a particular date in a calendar year would be shifted one day ahead in the next year (e.g. Christmas 2015 would fall on a Friday). For leap years, it would be shifted two days ahead since 366 = 2 (mod 7).
Christmas 2015: Friday
Christmas 2016: Sunday ← Leap Year
Christmas 2115: Friday + (number of leap years) × (2 days) + (number of non-leap years) × (1 day) = Friday + 24 × 2 + 75 × 1 = Friday + 5 days (mod 7) = Tuesday