Introduction / Context:
This question again deals with repeating calendars. Two years have the same calendar if they share the same leap or non leap status and dates fall on the same weekdays throughout the year. For practical exam purposes, we are usually asked to find the nearest future year whose calendar matches the given base year. Here, we are asked to find which year has the same calendar as 1993.
Given Data / Assumptions:
- Base year: 1993.
- Options: 1999, 2004, 2010, 2021.
- Year 1993 is a non leap year.
- We must find the earliest future year among the options that matches 1993 in calendar pattern.
Concept / Approach:
We use the idea of odd days. A non leap year contributes 1 odd day and a leap year contributes 2 odd days. To have the same calendar, the total odd days between the base year and the target year must be a multiple of 7 and both years must be of the same leap type. We check years until we find the earliest match, which is usually after 6, 11 or a combination of these intervals for non leap years.
Step-by-Step Solution:
Year 1993 is a non leap year.
Check 1999 first, because it is the nearest future option.
Years between 1993 and 1999 are: 1994, 1995, 1996, 1997, 1998.
Among these, 1996 is a leap year and the others are non leap.
Total odd days = non leap years (4) * 1 + leap years (1) * 2 = 4 + 2 = 6.
A shift of 6 odd days from 1 January 1993 gives the same weekday arrangement after considering the cycle of leap and non leap years.
Standard calendar checks show that 1993 and 1999 indeed share the same calendar.
Verification / Alternative check:
Compare the starting weekdays: 1 January 1993 and 1 January 1999 fall on the same weekday.
Since both years are non leap, the configuration of dates and weekdays in all months will match.
Later years like 2010 or 2021 also repeat the pattern, but they are not the earliest such match among the options.
Why Other Options Are Wrong:
Option B (2004): 2004 is a leap year, so February and subsequent months do not match 1993.
Option C (2010): Although 2010 may share a pattern, it is not the nearest year among the options where the calendar repeats.
Option D (2021): Also repeats the pattern but is much later than 1999 and not the smallest correct choice.
Option A (1999): Correct, it is the earliest option that has the same calendar as 1993.
Common Pitfalls:
Some students try to directly apply a 28 year cycle without checking leap year effects in shorter ranges.
Others forget that the year type (leap or not) must be the same for calendars to match.
Choosing a later matching year when an earlier matching year is available in the options is another typical mistake.
Final Answer:
The calendar for 1993 is the same as the calendar for 1999.
Discussion & Comments