The complete calendar (days and dates pattern) of the year 2006 repeats an earlier year exactly. For which earlier year does the calendar of 2006 match perfectly, so that all days and dates fall on the same weekdays?

Introduction / Context:
Calendar repetition problems ask in which earlier or later years the exact same calendar (same weekdays for all dates) can be reused. To answer these, you must understand the pattern of leap years and how the first day of the year shifts from year to year. Here we are told that the calendar of 2006 was used before, and we must identify the previous year that has the same day-date layout.

Given Data / Assumptions:

• We are working with the Gregorian calendar.
• We want an earlier year in which every date falls on the same weekday as in 2006.
• So that year must:
  • Have the same leap-year status as 2006 (both leap or both non-leap).
  • Start on the same day of the week as 1st January 2006.
• 2006 is a non-leap year (not divisible by 4).

Concept / Approach:
Two years have the same calendar if:

• Both are common years (365 days) or both are leap years (366 days), and
• The day of the week on 1st January is the same for both.

In practice, the calendar repeats in cycles of 28 years in the Gregorian system under many circumstances, but due to century leap-year rules, it is safer to check nearer candidates. We look backwards from 2006 and find the first earlier year that is a common year and whose dates align.

Step-by-Step Solution:
Step 1: Note that 2006 is a common year (365 days) because it is not divisible by 4. Step 2: Candidate years must also be common years: check 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, etc. Step 3: Years like 2004 and 2000 are leap years, so they cannot share the same calendar as 2006. Step 4: We compare the sequence of days and dates, or equivalently, we use known calendar tables or logic that a non-leap year's calendar repeats every 6 or 11 years depending on leap-year placement. Step 5: Using this, we find that 1995, a non-leap year, has the same starting weekday and the same distribution of weekdays across dates as 2006. Step 6: Therefore, the full calendar of 2006 matches the calendar of 1995.

Verification / Alternative check:
You can verify by checking a few key dates. For example, 1st January 1995 and 1st January 2006 fall on the same weekday. Similarly, several spot checks such as 15th August or 25th December align on the same weekdays. If a few widely spaced dates match, and both years are common years, it confirms the calendars are identical for all dates.

Why Other Options Are Wrong:
1990 and 2002 do not have the same starting weekday and leap-year pattern as 2006, so their calendars differ. The year 2000 is a leap year, so its calendar structure is different from a non-leap year like 2006. Any other nearby year that is leap or starts on a different weekday cannot have an identical calendar.

Common Pitfalls:
A frequent mistake is to assume the calendar simply repeats every 7 years, ignoring leap years. Leap years introduce an extra day, shifting future calendars. Another error is to choose a leap year when the given year is non-leap, which automatically makes the calendars incompatible. Understanding the interplay between leap-year cycles and weekday shifts is crucial.

Final Answer:
The calendar of 2006 was previously used in the year 1995.