Question

The calendar for the year 1982 is the same as which year?

Answer 1

Hint: In this question, we first need to find the number of odd days in the given year. Then we need to find the odd days in the following years until the sum of all odd days will be a 0 odd day or 7 days. Then, check whether that year is leap or non-leap year. Now, as the given is a non-leap year we need to find the one with 0 odd days of non-leap year to get the result.

Complete step-by-step solution -
Now, from the given question we have the year as 1982
A calendar is a chart or series of pages showing the days, weeks and months of a particular year.
NON-LEAP YEAR: Any year which has 365 days is called an ordinary year or non-leap year.
As we already know that a week has 7 days. Now, 365 can be written as $$52\times 7+1$$ which means that there are 52 weeks and an extra day in a year called a non-leap year.
This 1 extra day in a non-leap year is called an odd day of the year.
Thus, a non-leap year has 1 odd day
LEAP YEAR: Any year which has 366 days is called a leap year
Now, 366 can be further written as $$52\times 7+2$$ which means that there are 52 weeks and 2 extra days in a year called leap year.
As we already know that a leap year comes for every 4 years
These 2 extra days in a leap year are called odd days of the year.
Thus, a leap year has 2 odd days.
Now, the given year 1983 is a non-leap year which has 1 odd
Now, to find the year with the same calendar we need to find the odd days of the following years until which their sum would be a 0 odd day

Year	1982	1983	1984	1985	1986	1987
Odd days	1	1	2	1	1	1

Now, the sum of odd days will be
$$\begin{array}{rl}& \Rightarrow 1+1+2+1+1+1\\ & \Rightarrow 7\end{array}$$
Now, after 1987 we have 0 odd days i.e., 1988 has 0 odd days but as 1988 is a leap year and 1982 is a non-leap year they cannot have the same calendar.
Now, from 1988 we again need to find the odd days in the following years until the sum will be a 0 odd day

Year	1988	1989	1990	1991	1992
Odd days	2	1	1	1	2

Now, the sum of odd days will be
$$\begin{array}{rl}& \Rightarrow 2+1+1+1+2\\ & \Rightarrow 7\end{array}$$
Thus, the year after 1992 will have 0 odd days which will be 1993 a non-leap year.
Hence, the year 1993 will have the same calendar as 1982.

Note: It is important to note the year till which we add the odd days will be included in the odd days calculation till where we have 0 odd days. The year next to it will be having a similar calendar depending on the type of year.
It is also to be noted that if the year we considered is a non- leap year then the year after 0 odd days should be also of the same type if not then we need to check for the next 0 odd day year. Because a non-leap year and leap year cannot have the same calendar.