Given that 9 August 2016 falls on a Saturday, what day of the week was 9 August 1616?

Introduction / Context:
This question makes use of the 400-year cycle property of the Gregorian calendar. When dates are exactly 400 years apart, their days of the week repeat under the Gregorian rules, because the total number of days in 400 years is an exact multiple of 7.

Given Data / Assumptions:

• We are told that 9 August 2016 is a Saturday (given condition for the puzzle).
• We need to find the day of the week on 9 August 1616.
• The difference between the years is 2016 − 1616 = 400 years.
• We assume the Gregorian calendar and its leap year rules.

Concept / Approach:
In the Gregorian calendar, a 400-year period contains exactly 146097 days. This comes from 400 * 365 days plus 97 leap days (since out of 400 years, 97 are leap years). Because 146097 is divisible by 7, the cycle of weekdays repeats every 400 years, so any date repeated exactly 400 years later will fall on the same weekday.

Step-by-Step Solution:
Step 1: Compute the difference between the two years: 2016 − 1616 = 400 years.Step 2: In 400 years, the total number of days is 400 * 365 + 97 leap days = 146000 + 97 = 146097 days.Step 3: Check divisibility: 146097 / 7 = 20871 exactly, so 146097 is a multiple of 7.Step 4: Because the total number of days in 400 years is a whole number of weeks, the day of the week cycles back to the same position after 400 years.Step 5: Therefore, any given date and the same date exactly 400 years earlier or later fall on the same weekday.Step 6: Given that 9 August 2016 is a Saturday, 9 August 1616 must also be a Saturday.

Verification / Alternative check:
Instead of calculating individual years, we rely on the known property of the Gregorian calendar that it repeats every 400 years. Moreover, since 1616 and 2016 are both leap years and 9 August falls after February, the distribution of days before this date is consistent, reinforcing the result that both dates share the same weekday.

Why Other Options Are Wrong:
Sunday, Friday, Monday, or Thursday would require the total number of days in the 400-year interval to leave a remainder of 1, 6, 2 or 4 when divided by 7. Because the remainder is actually zero, all these alternate weekdays are incorrect.

Common Pitfalls:

• Trying to count years forward one by one instead of using the 400-year cycle.
• Confusing Julian and Gregorian calendar rules, which can shift historical dates but are irrelevant for this theoretical puzzle.
• Ignoring the fact that the question explicitly uses 2016 and 1616, which are exactly 400 years apart.

Final Answer:
The day of the week on 9 August 1616 was Saturday.