Let us check the pair 1966 and 1977:
Type of year: Both 1966 and 1977 are Ordinary years (not divisible by 4).
Now, we count the odd days from 1966 to 1976:
1966 (Ordinary year) = 1 odd day
1967 (Ordinary year) = 1 odd day
1968 (Leap year) = 2 odd days
1969 (Ordinary year) = 1 odd day
1970 (Ordinary year) = 1 odd day
1971 (Ordinary year) = 1 odd day
1972 (Leap year) = 2 odd days
1973 (Ordinary year) = 1 odd day
1974 (Ordinary year) = 1 odd day
1975 (Ordinary year) = 1 odd day
1976 (Leap year) = 2 odd days
Total odd days = 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 = 14 odd days.
Since 14 ÷ 7 = 2 with a remainder of 0, the sum of odd days is a multiple of 7.
Because both conditions are satisfied, the years 1966 and 1977 have identical calendars.
Checking other options:
- 1972 and 1978: 1972 is a Leap year while 1978 is an Ordinary year. (Not identical)
- 1960 and 1967: 1960 is a Leap year while 1967 is an Ordinary year. (Not identical)
- 1965 and 1977: Sum of odd days from 1965 to 1976 = 1 (for 1965) + 14 = 15. 15 is not divisible by 7. (Not identical)
Hence, the correct answer is “Option 3”.