You are requested to perform 2 independent tasks:

a) Using ten distinct digits (0 to 9) plus an additional digit of your choice create the smallest 11-digit number, divisible by 495.
b) Using ten distinct digits (0 to 9) plus an additional digit of your choice create the biggest 11-digit number, divisible by 495.

simple Mathematica search gives:
10026374985/495=20255303,  extra digit is 0
99876534120/495=201770776, extra digit is 9

One can logically deduce what the extra digit needs to be from the fact that 495 is divisible by 9, thus the sum of the digits of the number must be divisible by 9.  We already know it has all the digits from 0-9, whose sum is 45.  45 is divisible by 9, thus the extra digit must also be divisible by 9.  Thus the extra digit can only be 0 or 9.  Thats as far as my logic is able to take me in solving this problem, I would be interested to see somebody is able to find a non-exhaustive solution to this problem.

Posted by Daniel on 2012-07-07 11:57:03