Introduction / Context:
This calendar question tests understanding of how leap years are distributed in the Gregorian calendar. Many learners know that leap years usually occur every 4 years, but the presence of century rules (years like 1900, 2000, 2100) means that the gaps between leap years are not always exactly 4 years. The key idea here is to identify the maximum possible gap between two consecutive leap years under the actual leap year rules.
Given Data / Assumptions:
- Leap year rule in the Gregorian calendar:
- A year is a leap year if it is divisible by 4.
- However, if a year is divisible by 100, it is not a leap year.
- Exception: if a year is divisible by 400, it is a leap year.
- We must find the maximum possible number of years between two leap years that follow one another in time.
Concept / Approach:
Normally leap years come every 4 years, for example 2012, 2016, 2020 and so on. But the century exception can remove a leap year such as 1900, which is divisible by 100 but not by 400. When this happens, the regular pattern of every 4 years is broken. The largest gap will therefore occur around such a century year that is skipped as a leap year, and we need to examine what happens before and after such a year.
Step-by-Step Solution:
Consider the sequence of years around 1900: 1896, 1900, 1904.
Year 1896 is a leap year because 1896 is divisible by 4 and not by 100.
Year 1900 is divisible by 100 but not by 400, so it is not a leap year.
The next leap year after 1896 is therefore 1904, which is divisible by 4 and not by 100.
The gap between 1896 and 1904 is 8 years.
In all other ordinary segments, leap years appear every 4 years only, giving gaps of 4 years.
No larger gap than 8 years can occur, because the only way to skip a leap year is at a century not divisible by 400, which removes exactly one leap year from the chain.
Verification / Alternative check:
Check another skipped century such as 2100. The pattern around 2100 is 2096, 2100, 2104.
Year 2100 is not a leap year, so again the leap years are 2096 and 2104.
This is again an 8 year gap, confirming that 8 is achievable and typical at such a boundary.
Between normal non century years, for example 2012 and 2016, the gap is only 4 years.
Why Other Options Are Wrong:
Option A (4): This is the normal gap but not the maximum possible.
Option C (2): A 2 year gap never occurs between consecutive leap years in the Gregorian system.
Option D (1): Also impossible, since leap years always have at least three non leap years between them.
Option B (8): Correct, as demonstrated by the pairs 1896 and 1904, 2096 and 2104 and similar examples.
Common Pitfalls:
Many learners forget the special century rule and assume that leap years are always 4 years apart.
Some confuse Julian and Gregorian rules, which leads to incorrect conclusions about the spacing of leap years.
Ignoring the 400 year exception can also create confusion about which century years are actually leap years.
Final Answer:
The maximum possible gap between two successive leap years in the Gregorian calendar is 8 years.
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