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Question

Difficulty: EasyClocks and Calendars

If 1st January 2004 was a Thursday, what day of the week was 1st January 2005?

Answer: Saturday / saturday

Answer

Saturday
The correct answer is Saturday. The year 2004 is a leap year containing 366 days. Since the time period from 1st January 2004 to 1st January 2005 includes February 29th, there are 2 odd days. Advancing 2 days from Thursday results in Saturday.

Step-by-Step Solution

1
Determine if the year 2004 is a leap year.
2004 is divisible by 4, so it is a leap year containing 366 days.
Leap years include an extra day (29th February).
2
Calculate the number of odd days between 1st January 2004 and 1st January 2005.
366 days divided by 7 equals 52 weeks and 2 odd days (366(mod7)=2366 \pmod 7 = 2).
Full weeks do not change the day of the week, so only the remainder (odd days) shifts the day.
3
Advance the given day by the number of odd days.
Thursday + 2 days = Saturday.
Adding 2 odd days to Thursday moves the day forward to Saturday.

Key Concept

Calculating day of the week shifts across leap years using odd days
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Topics

Clocks and Calendars

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