Consider all possible dates (formatted DD/MM/YY) within a span of a century , from 01/01/01 to 31/12/00 (20th century!).

In this period there are N

_{ k} dates that can be expressed by k distinct digits, e.g. N

_{1}=1 (11/11/11).

a. Derive the values of N_{ k} for all other values of k (2 to 6).

b. What is the average k for the 20st century?

c. How about the 21st century?

(In reply to

computer-aided solution by Charlie)

Charlie,

Each of us committed an error, and it **slightly** affects your otherwise

perfect solution:

a. I wrongly defined the 20 th century, shifting it forward a year.

b. You wrongly assumed that 2100 is a leap year, and it is not.

I would appreciate it if you modify your entry.

Thanks.