On 19 June 1984 the day of the week is given as Monday. What day of the week will it be on 19 June 1985 in the same calendar system?

Introduction / Context:
Here we are asked to move from a particular date in one year to the same calendar date in the next year and determine the weekday. The day of the week on 19 June 1984 is given as Monday, and we need the weekday on 19 June 1985. This type of question highlights how the presence or absence of leap days influences the shift in weekdays from one year to the next.

Given Data / Assumptions:

• 19 June 1984 is a Monday.
• We need the weekday on 19 June 1985.
• We use the Gregorian calendar and standard leap year rules.
• We know that 1984 is a leap year, but we must see whether the extra day affects the interval between these two dates.

Concept / Approach:
Moving from a date in one year to the same date in the next year usually corresponds to a shift of 365 days or 366 days. A shift of 365 days changes the weekday by one day, while a shift of 366 days changes the weekday by two days, since 366 mod 7 equals 2. However, the effective number of days depends on whether the interval includes the extra leap day. Because both dates lie on 19 June, we need to check whether 29 February of the leap year lies between them.

Step-by-Step Solution:
Step 1: Identify that 1984 is a leap year because it is divisible by 4. Step 2: However, 19 June 1984 occurs after 29 February 1984. Step 3: The interval from 19 June 1984 to 19 June 1985 does not include 29 February 1984, since that date lies earlier in the same year. Step 4: Therefore, the number of days between 19 June 1984 and 19 June 1985 is 365 days. Step 5: Because 365 mod 7 equals 1, the weekday shifts forward by one day. Step 6: Starting from Monday on 19 June 1984, adding one day leads to Tuesday. Step 7: Hence, 19 June 1985 falls on a Tuesday.

Verification / Alternative check:
A different way to check is to recall that moving from any date after 28 February in a leap year to the same date in the next year generally causes a one day shift. The extra day of the leap year has already occurred before the starting date, so it does not influence the span between the two dates. If you construct a small table and list days for mid June around those years, you will see that the weekday moves forward by exactly one step from 1984 to 1985 on 19 June. This confirms that Tuesday is the correct weekday for the year 1985.

Why Other Options Are Wrong:
Sunday would correspond to moving backward from Monday or having a shift of 6 days in the wrong direction. Monday as an answer would require the number of days between the two dates to be a multiple of 7, which is not true here. Wednesday would require a two day shift, which would be the case only if the interval included an extra leap day, but it does not. Therefore, only Tuesday matches the correct one day forward shift resulting from the 365 days between the two dates.

Common Pitfalls:
Many learners incorrectly assume that any time a leap year is mentioned, the weekday shift between identical dates in adjacent years must be two days. This is not always correct, because you must consider where the starting date lies relative to 29 February. Another mistake is to forget whether you are moving forward or backward when adjusting weekdays. Always confirm whether the path between dates actually includes the leap day and then apply 365 or 366 accordingly.

Final Answer:
Therefore, the day of the week on 19 June 1985 is Tuesday.