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Easily distinguished codes (Posted on 2005-11-29) Difficulty: 4 of 5
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?

See The Solution Submitted by Tristan    
Rating: 4.5000 (4 votes)

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partial answer Comment 11 of 11 |

They can have 10^9 clients. This works if, for example, the sum of all the digits mod 10 is zero for each code.

For 10 digit identification code, with any pair differing by at least two digits, the number of clients is 1000,000,000.

  Posted by K Sengupta on 2007-09-24 10:30:11
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