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. N₁=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.

Posted by Ady TZIDON on 2015-01-05 17:55:54