Problem

Source:

Tags: combinatorics unsolved, combinatorics



We want to choose telephone numbers for a city. The numbers have 10 digits and 0 isn’t used in the numbers. Our aim is: We don’t choose some numbers such that every 2 telephone numbers are different in more than one digit OR every 2 telephone numbers are different in a digit which is more than 1. What is the maximum number of telephone numbers which can be chosen? In how many ways, can we choose the numbers in this maximum situation?