The calendar for the year 1989 is exactly the same (same weekdays on the same dates) as the calendar for which of the following previous years?

Introduction / Context:
Calendar repetition questions ask you to find another year whose calendar matches exactly with a given year. For two years to have the same calendar, the years must both be leap or both be common (non-leap) years, and the total shift in weekdays between them must be a multiple of 7 days so that all dates fall on the same weekdays.

Given Data / Assumptions:

Reference year: 1989 (a non-leap year).
Candidate years: 1978, 1970, 1980, 1985.
We use the Gregorian leap-year rules:
- Years divisible by 4 are leap years, except century years not divisible by 400.
We need to compare weekday shifts from the candidate years up to 1989.

Concept / Approach:
We calculate the total day shift from each candidate year to 1989. Each common year between them adds a shift of +1 day to the next New Year’s Day, and each leap year adds +2 days. If the total shift from a candidate year to 1989 is a multiple of 7 and both years are common years, then their calendars match.

Step-by-Step Solution:
Step 1: Note that 1989 is not divisible by 4, so it is a common year. Step 2: Check 1978. Years between 1978 and 1989: 1978 to 1988 inclusive (11 years). Leap years in this range: 1980, 1984, 1988 (3 leap years). Common years = 11 - 3 = 8. Total shift = 8 * 1 + 3 * 2 = 8 + 6 = 14 days. 14 mod 7 = 0, so 1 January 1978 and 1 January 1989 fall on the same weekday. Also, 1978 is not divisible by 4, so it is a common year like 1989. Therefore, 1978 has the same calendar as 1989.

Verification / Alternative check:
Check another option to see why it fails. For 1970, count the years from 1970 to 1989. There are more leap years and a different total shift, which is not a multiple of 7. Similarly, 1980 is a leap year, so even if the shift happened to be a multiple of 7, the leap-year status would differ and the calendars would not match. 1985 is also common but does not yield a total shift that is a multiple of 7.

Why Other Options Are Wrong:
1970 and 1985 are common years but the cumulative weekday shifts from them to 1989 are not multiples of 7 days, so their calendars do not align with 1989.
1980 is a leap year, while 1989 is a common year; they cannot share the same calendar because February has a different number of days.

Common Pitfalls:
Students often attempt to apply a fixed cycle (like 11 or 28 years) without carefully counting the intervening leap years, or they ignore whether the year is leap or common. Another error is to count years inclusively or exclusively in the wrong way. Always count the number of years between the candidate and the reference year and classify each as leap or common to compute the total shift correctly.

Final Answer:
The calendar of 1989 is the same as that of 1978.