Difficulty: Medium
Correct Answer: 2016
Explanation:
Introduction:
Calendar repetition for leap years is slightly different from that for non-leap years. Here, we are given that 1988 is our base year and we must find a future year whose calendar is exactly the same. That means the days of the week must match each date, starting with 1 January, and both years must be leap years.
Given Data / Assumptions:
Base year = 1988. 1988 is a leap year (divisible by 4 and not a century year). We want the first future year where: (a) The year is also a leap year. (b) 1 January falls on the same day of the week as in 1988.
Concept / Approach:
In calendar problems, each non-leap year advances the starting weekday of the next year by 1 day, while each leap year advances it by 2 days. For the calendar to repeat for a leap year, the total shift from the base year to the candidate year must be a multiple of 7, and the candidate year must itself be a leap year. Typically, leap year calendars tend to repeat after 28 years, but due to the pattern of leap years, there can be earlier matches like 28 or 12 or other intervals depending on where leap years fall.
Step-by-Step Solution:
Step 1: Check that 1988 is a leap year. 1988 ÷ 4 = 497 exactly, so 1988 is a leap year. Step 2: Consider future leap years and total weekday shifts. Leap years after 1988: 1992, 1996, 2000, 2004, 2008, 2012, 2016, etc. We track the net shift in weekdays from 1988 to these years. When we reach 2016, the cumulative shift happens to be a multiple of 7 days and 2016 is a leap year. Therefore, 2016 has the same starting weekday and the same leap-year structure as 1988.
Verification / Alternative check:
An alternative is to remember that many leap year calendars repeat after 28 years. Adding 28 years to 1988 gives 2016. Since 2016 is divisible by 4, and the intervening century rules do not disturb this interval, the calendars for 1988 and 2016 are identical in their day-date arrangement.
Why Other Options Are Wrong:
2012: A leap year, but the weekday of 1 January does not align exactly with that of 1988. 2014, 2010: These are non-leap years, so their February and year patterns differ significantly from a leap year like 1988. 2020: Although 2020 is a leap year, its position in the 28-year cycle is different; the earliest correct match is 2016.
Common Pitfalls:
Learners often misapply the idea that calendars repeat every 28 years without checking if a smaller interval exists or without confirming leap-year status. Others ignore the difference between leap and non-leap years, which always invalidates an exact calendar match.
Final Answer:
The year whose calendar is the same as 1988 is 2016.
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