Question

Show that the calendars for the year $\text{1990 and 2001}$ were identical.

Answer 1

To show calendars for the year 1990 and 2001 identical we will find the number of odd days between $\text{31 December 1989 and 31 December 2000}$. The number of odd days should be zero in order to have the same calendar.
Odd days can be calculated as follows
Years $19901991199219931994199519961997199819992000$
Odd days $11211121112$
The numbers of odd days from $\text{31 December 1989 to 31 December 2000}=1+1+2+1+1+1+2+1+1+1+2=14=2\text{weeks and 0 odd days}$.
Further, both $\text{1990 and 2001}$ are ordinary years.
Hence, the years $\text{1990 and 2001}$ had the same calendar.