Given that 9 August 2016 falls on a Saturday (assumed for this problem), what was the day of the week on 9 August 1616, using standard Gregorian calendar reasoning?

Introduction:
This problem links two dates that are exactly 400 years apart: 9 August 1616 and 9 August 2016. We are told that 9 August 2016 is a Saturday, and we must determine the weekday on 9 August 1616. Questions involving 400-year gaps are well suited to applying the special properties of the Gregorian calendar.

Given Data / Assumptions:
9 August 2016 is assumed to be Saturday. We are to find the day on 9 August 1616. We assume the proleptic Gregorian calendar for both dates (as is common in aptitude exams).

Concept / Approach:
In the Gregorian calendar, a span of 400 years corresponds to exactly a whole number of weeks. Specifically, there are 97 leap years and 303 non-leap years in 400 years. The total number of days in 400 years is 146,097, and 146,097 is divisible by 7. Therefore, the day of the week for a given date repeats every 400 years. So any date and the same date exactly 400 years apart fall on the same weekday.

Step-by-Step Solution:
Step 1: Compute the length of a 400-year cycle. Leap years in 400 years = 97. Non-leap years = 400 − 97 = 303. Total days = 97 * 366 + 303 * 365. 97 * 366 = 97 * (365 + 1) = 97 * 365 + 97. So total days = (97 * 365 + 97) + 303 * 365 = (97 + 303) * 365 + 97 = 400 * 365 + 97 = 146,000 + 97 = 146,097 days. Step 2: Check divisibility by 7. 146,097 ÷ 7 = 20,871 exactly, so it is an integer. Therefore, 400 years correspond to an integral number of weeks with no leftover days. Step 3: Apply to the given dates. The time from 9 August 1616 to 9 August 2016 is exactly 400 years. Since 400 years shift the calendar by a whole number of weeks, the weekday repeats exactly. Thus, the day for 9 August 1616 is the same as for 9 August 2016, namely Saturday.

Verification / Alternative check:
Any algorithm for days of the week that accounts correctly for the Gregorian 400-year pattern (for example, Zeller's congruence adapted to the proleptic Gregorian calendar) will also yield Saturday for both dates, confirming the theory-based reasoning above.

Why Other Options Are Wrong:
Sunday, Friday, Monday, Wednesday: These alternatives would require that 400 years correspond to an offset of 1, 2, 3, or 4 days, but we have shown that 400 years equal an exact number of weeks, so there is zero offset in weekday.

Common Pitfalls:
Some candidates forget the special property of the 400-year Gregorian cycle and try to count leap years and non-leap years manually, often leading to mistakes. Others may mistakenly think that 100-year or 200-year intervals reset the weekday exactly, which is not true unless you consider the full 400-year cycle.

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