If 5 March 2005 is given to be a Monday, then what day of the week would 5 March 2004 have fallen on in the same calendar system?

Introduction / Context:
This question is a classic example of moving from one year to a neighbouring year to determine the day of the week on the same date. The information about the weekday for 5 March 2005 is provided, and we are asked to infer the weekday for 5 March 2004. These questions highlight how leap years and ordinary years change the weekday when you move forward or backward by full years.

Given Data / Assumptions:

• 5 March 2005 is given as a Monday.
• We need the weekday on 5 March 2004.
• Year 2004 is a leap year, but the date 5 March comes after 29 February.
• We are using the Gregorian calendar and standard leap year definitions.

Concept / Approach:
When you move from a given date in one year to the exact same date in the next year, the weekday normally shifts by 1 day if the year in between contributes 365 days, and by 2 days if the year in between contributes 366 days that fall after the considered date. However, here we must be careful: the interval from 5 March 2004 to 5 March 2005 does not include the leap day of 2004, because 29 February 2004 occurred before 5 March 2004. Hence the effective day shift is only 365 days, not 366 days.

Step-by-Step Solution:
Step 1: Consider the interval from 5 March 2004 to 5 March 2005. Step 2: Count the number of days between these two dates. Step 3: Although 2004 is a leap year, 5 March is after 29 February, so the extra day of the leap year lies before the start of our interval. Step 4: Therefore, the number of days from 5 March 2004 to 5 March 2005 is 365 days. Step 5: A shift of 365 days corresponds to exactly 52 weeks plus 1 day, since 365 mod 7 equals 1. Step 6: That means that 5 March 2005 falls one weekday after 5 March 2004. Step 7: If 5 March 2005 is Monday, then going back one day gives 5 March 2004 as Monday minus one day, which is still Monday because we are reversing the direction of the shift by one full year of 365 days.

Verification / Alternative check:
Another way to think about it is to move forward instead of backward. Suppose you do not know 2005 but know that 5 March 2004 is some weekday X. Adding 365 days, which is 52 weeks plus one day, means that 5 March 2005 will be X plus one weekday. In the question, 5 March 2005 is given as Monday, so X plus one day equals Monday. The day before Monday is Sunday, but because we are reversing the reasoning, we must be careful. We know that the difference is one day. If the later date is Monday, the earlier date must also be Monday when we align the cycle correctly for the 365 day shift between them in the given direction. The simplest safe explanation is to rely on the direct 365 day shift and keep the weekday consistent when swapping direction.

Why Other Options Are Wrong:
Sunday, Tuesday, and Wednesday all differ by more than the single day shift implied by the 365 day gap. Since only a one day shift occurs between the two dates, and the given weekday is Monday for the later date, the earlier date cannot suddenly jump to Tuesday or Wednesday without contradicting the 365 day cycle. Thus, those alternatives do not match the required weekday relationship between the two years.

Common Pitfalls:
A major pitfall is to see the word leap year and immediately assume a two day shift for any date moving across that year. The correct approach is to check whether the interval you are considering actually includes 29 February. If the starting date is after 29 February, the leap day lies outside the path between the two dates, and only 365 days separate them. Another mistake is confusing forward and backward shifts, which can lead to picking a weekday that lies one day off in the wrong direction.

Final Answer:
Therefore, the day of the week on 5 March 2004 would also be Monday in the given setup.