Introduction / Context:
This is a classic and straightforward calendar question about the shift of weekdays from one year to the next. Knowing whether the year in between is a leap year or a normal year is the only crucial step. Such problems are designed to test basic calendar logic and understanding of how many odd days a full year contributes.
Given Data / Assumptions:
- 1 January 2007 was a Monday.
- We are asked to find the weekday on 1 January 2008.
- Year 2007 is a non leap year with 365 days.
- We use the Gregorian calendar rules.
Concept / Approach:
In calendar problems, a non leap year of 365 days contributes 1 odd day because 365 = 52 full weeks + 1 extra day. A leap year of 366 days contributes 2 odd days. When moving from 1 January of one year to 1 January of the next, we simply add the corresponding number of odd days to the weekday. As 2007 is not divisible by 4, it is a normal year, so we shift the weekday by exactly one day forward.
Step-by-Step Solution:
Year 2007 has 365 days.
365 days = 52 weeks + 1 day.
Therefore, the calendar shifts by 1 weekday when we move from 1 January 2007 to 1 January 2008.
Given that 1 January 2007 was Monday, adding 1 day gives Tuesday.
Thus, 1 January 2008 must fall on a Tuesday.
Verification / Alternative check:
We could also think in terms of odd days: the number of odd days contributed by 2007 is 1.
Starting weekday: Monday.
Add 1 odd day: Monday → Tuesday.
This confirms that 1 January 2008 is Tuesday.
Why Other Options Are Wrong:
Option A (Monday): Would require 0 odd days, which is not possible for a full normal year.
Option C (Wednesday): Would require a leap year shift of 2 odd days, which does not apply to 2007.
Option D (Sunday): Would imply a shift of 6 days backwards, which is not supported by the day count.
Option B (Tuesday): Correct, because a 365 day year shifts the weekday by exactly one day.
Common Pitfalls:
Some students mistakenly treat 2007 as a leap year and add 2 days instead of 1.
Others forget the rule 365 = 52 weeks + 1 day and assume that the weekday repeats every new year.
Confusing the direction of the shift, especially when working with backward problems, can also lead to errors.
Final Answer:
1 January 2008 fell on a Tuesday.
Discussion & Comments