A certain company gives each of its clients a 10 digit number as a sort of identification code. As a precaution, any pair of used codes should differ by at least two digits so no one accidentally gives someone else's code.

How many clients can they have before adding digits? Give an example of a set of codes they might use. What if each pair of codes must differ by at least 3 digits? 4? More?

(In reply to re: Spoiler by Charlie)

I like the method of using all combinations of the first 9 digits with the 10th being equivalent to 0 mod 10 of the sum of digits.  It is obvious in hindsight that matching the last digit to the first was not sufficient.

Looking for a proof.<o:p></o:p>

Posted by Leming on 2005-12-01 12:34:52